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CHAMBERS’ EDUCATIONAL COURSE. 
 
 ELEMENTS 
 
 OF 
 
 NATURAL PHILOSOPHY. 
 
 3n &l)rcc parte. 
 
 L 
 
 LAWS OF MATTER AND MOTION. 
 
 MECHANICS. 
 
 hi. 
 
 HYDROSTATICS, HYDRAULICS, AND PNEUMATICS. 
 
 WILLIAM 8c ROBERT CHAMBERS. 
 
 EDITED BY D. M. REESE, M. D., LL. D. 
 
 NEW-YORK: 
 
 PUBLISHED BY A. S. BARNES k CO. 
 
 PHILADELPHIA: JOHN BALL. 
 
 H. W. DERBY & CO. 
 
 CINCINNATI. 
 
 1849. 
 
CHAMBERS’ EDUCATIONAL COURSE. 
 
 The object of the following works is to furnish the friends of an improved 
 system of education with the books required for carrying out their views, in 
 the actual business of the school-room, and the family circle. 
 
 The Messrs. Chambers (whose works are so favorably known in the different 
 departments of literature, throughout this country as well as Europe) have 
 employed the first professors in Scotland in the preparation of these works. 
 They are now offered to the schools of the United States, under the American 
 revision of D. M. Reese, M. D., LL. D., late superintendent of public schools 
 of the city and county of New-York. 
 
 I.— CHAMBERS’ TREASURY OF KNOWLEDGE. (3 parts in one.) 
 
 BY W. & R. CHAMBERS. 
 
 Part 1 Embraces Elementary Lessons in Common Things - or things which lie most imme- 
 diately around us, and first attract the attention of the young mind. Part 2 Embraces 
 Practical Lessons on Common Objects — such as articles or objects from the Mineral. Vege- 
 table, and Animal Kingdoms, manufactured articles, miscellaneous substances and objects. &c. 
 Part 3 Embraces Introduction to the Sciences. This presents a systematic view of nature, 
 under the various sciences. Care is taken that the information given should not be a 
 superficial view of a few unconnected phenomena, but a chain of principles calculated, in 
 combination, tf^npress a distinct and comprehensive idea to the mind of the very young child. 
 This volume is designed for an early reading book, that the scholar may be exercised in reading, 
 and at the same time acquire knowledge of such subjects as bis capacity will enable him to 
 understand. It contains much useful information upon common objects of life. 
 
 ||. —CHAMBERS’ ELEMENTS OF DRAWING. (2 parts in one.) 
 
 BY JOHN CLARK. 
 
 Part 1 Embraces Exercises , for the Slate. Part 2 Embraces the Principles of Drawing 
 and Perspective. 
 
 With but very few exceptions, children are fond of makiug efforts in Drawing. Furnished with 
 a black-lead pencil and sheet of paper, or slate and pencil, they are delighted to scribble 
 whatever their fancy suggests. Followed up methodically by the teacher, their infant 
 aspirations may lead to the development of much valuable talent. Illustrated by Engravings. 
 
 III.— CHAMBERS’ ELEMENTS OF NATURAL PHILOSOPHY. 
 
 THREE PARTS IN ONE. 
 
 Part 1 Embraces Laws of Matter and Motion. Part 2 Embraces Mechanics. Part 3 
 Embraces Hydrostatics , Hydraulics , and Pneumatics. 
 
 In tha treatment of the several subjects great care has been taken to render the language simple 
 and intelligible. Illustrated by Wood Engravings- 
 
 IV.— CHAMBERS’ CHEMISTRY AND ELECTRICITY. 
 
 (TWO PARTS IN ONE.) BY D. B. REID AND ALEXANDER BAIN. 
 
 Part 1 Embraces Illustrations, and experiments of the Chemical Phenomena of Daily Life. 
 By D. B. Reid, M. D., F. R. S. E. Part 2 Embraces Electricity , (statical and current.) 
 By Alexander Bain, the original inventor of Electric and Telegraphic clocks. 
 
 This work is designed to facilitate the introduction of Chemistry as an elementary branch of 
 education in schools. Illustrated by Engravings. 
 
 V.— CHAMBERS’ VEGETABLE AND ANIMAL PHYSIOLOGY. 
 
 BY G. HAMILTON, M. D. 
 
 Part 1 Embraces the General Structure and Functions of Plants. Part 2 Embraces the 
 Organization of Animals. 
 
 The object of this work is to unite Vegetable and Animal Physiology, and bring both systems 
 under one head, as properly connected and adapted to the mind of tne student. 
 
 VI. — CHAMBERS’ ELEMENTS OF ZOOLOGY. (Illustrated.) 
 
 Presenting a complete view of the Animal Kingdom as a portion of external nature. As the 
 
 composition of one of the most eminent physiologists of our age, it possesses an authority not 
 attributable to such treatises in general. 
 
 VII. — CHAMBERS’ ELEMENTS OF GEOLOGY. (Illustrated.) 
 
 BY DAVID PAGE. 
 
 The subject is here presented in its two aspects of interesting and important. Interesting, 
 inasmuch as it exhibits the progressive conditions of the earth from the remotest periods, and 
 reveals the character of the plants and animals which have successively adorned and peop ed 
 its surface ; and important, as it determines the position of those metals and minerals upon 
 which the arts and manufactures so intimately depend. 
 
 Entered according to Act of Congress, in the year 1S49, by 
 A. S. B ARNES' & CO.. 
 
 in the Clerk’s Office of the District Court of the Southern District of New-York. 
 
INTRODUCTORY OBSERVATIONS 
 
 BY THE 
 
 AMERICAN EDITOR. 
 
 The present volume is appropriately styled the “First 
 Book of Natural Philosophy,” because its subject should be 
 understood by the learner before entering upon the study of 
 either of the other departments of Physics. Moreover, it lies 
 at the foundation of all natural science, and explains a multi- 
 tude of the phenomena of nature and art, which earliest 
 awaken the curiosity of children in their observation of natural 
 objects, and in their various forms of amusement. The lessons 
 here taught will enable parents or teachers to satisfy the in- 
 quisitiveness of children, who often manifest an ardent thirst 
 for knowledge in the nature and causes of things. And a 
 thousand opportunities occur, in simple and familiar occur- 
 rences transpiring in connection with the exercises of the 
 school-room and the pastimes of the play-ground, of which 
 teachers and scholars may avail themselves for creating a fond- 
 ness for this beautiful science. 
 
 No subject so forcibly impresses the young with the evi- 
 dence of a Supreme Being, or so strikingly shows the proofs 
 of the Divine wisdom and goodness, as do the topics of this 
 little volume — presenting thus to the admiration of children 
 the grandest truths of moral science, and leading them to sub- 
 mit to tbe sublime teachings of revelation. 
 
 The catechetical questions in this, as in the other volumes, 
 are so framed purposely as to admit of other and kindred 
 questions on almost every topic which will readily occur to the 
 teacher; while to the illustrations furnished by the author, 
 oilier familiar examples may be superadded. 
 
 That this work may inspire teachers and pupils with a taste 
 for kindred pursuits, and promote their intellectual and moral 
 improvement, is the confident expectation of the editor. 
 
 D. M. R. 
 
PREFACE. 
 
 The Laws of Matter and Motion, usually treated under the 
 titles of Statics, Pyronomics (or Heat) and Dynamics, form 
 not only the proper introduction to Natural Science, but that 
 particular department of it with which it is of the most im- 
 portance that all should be made familiar. For these reasons, 
 they are here presented in a small distinct treatise, the price if 
 which, as well as the simplicity of the language employed in 
 its composition, may be expected to facilitate its general intro- 
 duction into schools and families. 
 
 The remaining departments of Physics — Mechanics or 
 Mechanical Powers and Machinery, Hydrostatics and Hy- 
 draulics, Pneumatics, Acoustics, and Optics, Electricity 
 and Magnetism, Meteorology, and Astronomy, constitute 
 distinct portions of this Educational Course, already, or 
 about to be, published. 
 
 In exercising a class in this and other departments of Natural 
 Science, it will be. found to be of considerable importance to 
 cause each paragraph to be mastered or thoroughly understood 
 before proceeding to what follows ; for the whole constitutes 
 a structure in which each part rests on what has gone before 
 it. The pupil should, also, not only read, but be induced to 
 think on the nature of the principles which are unfolded, and 
 led to find examples of their action in the every-day concerns 
 of life, and the common phenomena of the universe. 
 
 To facilitate exercises, and afford a ready means of reference, 
 each paragraph is numbered. [And to add still greater facili- 
 ties both to teachers and learners, each page is furnished with 
 analytical questions.] 
 
CONTENTS. 
 
 Page 
 
 Of Matter and its Properties 7 
 
 Impenetrability . 8 
 
 Extension or Magnitude 9 
 
 Figure 10 
 
 Divisibility.. 10 
 
 Inertia 13 
 
 Attraction 17 
 
 Capillary Attraction 19 
 
 Chemical Attraction 20 
 
 Magnetic Attraction 22 
 
 Electrical Attraction 23 
 
 Attraction of Gravitation 24 
 
 The Repulsive Quality in Matter — Heat 29 
 
 Repulsive Quality of Heat 31 
 
 Modifying Quality of Heat 31 
 
 Conduction of Heat 31 
 
 Radiation of Heat. .. . 32 
 
 Production of Heat, 32 
 
 General Distribution of Heat 33 
 
 Temperature — The Thermometer 33 
 
 Repulsive Energy — Boiling Water 35 
 
 Vaporific Point — Steam 36 
 
 Spontaneous Evaporation 37 
 
 Frost — Freezing Point 38 
 
 Equilibrium of Heat and Cold 39 
 
 Artificial Freezing Apparatus 40 
 
 Gradual Alteration of Temperature 40 5 
 
 Expansion in Cooling — Crystallization 41 
 
 Point of greatest Density in Water 41 
 
 Effects of Frost 42 
 
 Shrinking of Bodies by Heat 44 
 
 Ignition of Bodies — Fire 44 
 
 5 
 
 7 
 
6 CONTENTS. 
 
 Page 
 
 Accidental Properties of Matter 45 
 
 Density of Bodies 45 
 
 Porosity 49 
 
 Compressibility 49 
 
 Elasticity..... 50 
 
 Dilatability 51 
 
 Hardness 51 
 
 Brittleness 51 
 
 Malleability 51 
 
 Ductility 52 
 
 Tenacity 52 
 
 Motion and Forces — General Explanations 53 
 
 The Phenomena of Falling Bodies — Weight 57 
 
 The Centre of Gravity 61 
 
 The Pendulum 69 
 
 The Laws of Motion 75 
 
 Uniform Motion in a Straight Line 75 
 
 Centrifugal Force and Circular Motion 77 
 
 Laws of Projectiles 82 
 
 Action and Reaction 85 
 
 Motion in Elastic Bodies 87 
 
 Reflected Motion 88 
 
 Composition of Motion and Forces 90 
 
 Common Motion 94 
 
 «■ 
 
NATURAL PHILOSOPHY. 
 
 MATTER AND MOTION. 
 
 OF MATTER AND ITS PROPERTIES. 
 
 1. Matter is a term applied to all things which are 
 supposed to possess substance. We acquire a knowledge 
 that things possess substance, through our senses, some- 
 times aided by the test of philosophical experiment. 
 
 2. Matter is organic, when it possesses organs or organ- 
 ized parts for sustaining living action. Matter is inorganic, 
 when it has no organs or organized parts to sustain living 
 action. Animals and plants are organic matter ; a stone 
 is inorganic matter. 
 
 3. Portions of matter are called bodies. The air, water, 
 the earth — a stone, a ball, an animal, a tree — any substan- 
 tial thing, which we can distinguish from other things — 
 are bodies. 
 
 4. When any portion of matter excites any of our 
 senses, the feeling of which we are sensible is called a 
 sensation ; and our knowledge of the existence of the ex- 
 citing cause, resulting from this sensation, is called a 
 perception. 
 
 5. The qualities which bodies possess of exciting par- 
 ticular sensations, are called their properties. 
 
 6. The phenomena or appearances that take place in 
 the material world, are considered to be the result of cer- 
 
 1. What is matter, and how is it recognised ? 
 
 2. Define organic and inorganic matter. 
 
 3. Explain bodies, — sensation, perception, properties, &.c. 
 
 7 
 
8 
 
 IMPENETRABILITY. 
 
 tain natural laws. A natural law is a rule, or principle, 
 according to which the same event uniformly occurs under 
 the same circumstances. 
 
 7. The natural laws which regulate the phenomena of 
 inorganic matter and its properties, are sometimes called 
 physical laws, from a Greek word signifying Nature ; 
 and the treatment of these laws is ordinarily expressed by 
 the terms Natural Philosophy or Physical Science. 
 
 8. The constitution of a body is its state of being, or 
 peculiar composition of properties and qualities. We 
 cannot alter any of the properties or qualities of a body, 
 without altering the constitution of the body. Bodies have 
 certain properties, which are called essential, because they 
 are invariably found in bodies. The essential properties 
 of bodies are Impenetrability, Extension, Figure, Divi- 
 sibility, Inertia, and Attraction. 
 
 IMPENETRABILITY. 
 
 9. By impenetrability, it is meant that two bodies can- 
 not occupy the same space at the same time. Each par- 
 ticle of matter occupies a certain space, and the same 
 space cannot at the same time be occupied by another 
 particle. What common language calls penetrability, is, 
 in the philosophical sense, only a liability to have certain 
 particles displaced. Thus a piece of dough is, in common 
 language, penetrable by the finger ; but in philosophical 
 language, the act of thrusting the finger into a piece of 
 dough would be called the displacing of as much of the 
 dough as the space occupied by the finger. Perhaps the 
 word occupancy would be a less ambiguous term for the 
 philosophical idea of impenetrability. 
 
 10. There are cases in which a condensation takes 
 place, when two fluids are mixed together, so that a con- 
 siderable deal less space is occupied by the two together, 
 than was occupied by them in a separate state. But this 
 arises from a chemical combination having taken place ; 
 the particles of the substances, by the mysterious agency 
 
 4. What of the constitution of a body ? 
 
 5 Enumerate the essential properties of bodies. 
 
 6. Define impenetrabilby, and illustrate. 
 
EXTENSION OR MAGNITUDE. 
 
 9 
 
 of chemical attraction, have been drawn closer together; 
 thus, the whole fluid occupies less space than it did 
 formerly. In the same way, a sponge, by being com- 
 pressed, has its particles brought nearer to each other, and 
 of course it has less bulk than it had before it was 
 squeezed. Indeed, the hand and the sponge together 
 may occupy the same space as the sponge did singly. 
 
 11. A nail, driven into a piece of wood or other soft 
 material, under certain circumstances does not enlarge the 
 general size of the body ; but in penetrating it, it displaces 
 its particles, and occupies the space which they occu- 
 pied ; and, accordingly, they are rendered more dense, or 
 become more solidified, than they were before, just in the 
 same way as the particles of the sponge when compressed. 
 In the one case, the particles are condensed from without, 
 and in the other from within. But these particles still 
 occupy a certain quantity of space which cannot be occu- 
 pied by other particles at the same time, for in every case 
 in which the attempt is made, although this apparently 
 seems to be effected, it will be found that the one has been 
 removed to make way for the other. 
 
 EXTENSION OR MAGNITUDE. 
 
 12. All bodies which are observable by the senses, are 
 lound to occupy a certain portion of space — that is, they 
 possess extension or magnitude ; and those which are so 
 small as to elude investigation in this manner, are con- 
 sidered by the understanding to possess it. Indeed, the 
 impenetrability of matter presupposes its extension or 
 magnitude. It is impossible to form a conception of matter, 
 however minute may be the particle, without connectmg 
 with it the idea of its having a certain bulk, and filling a 
 certain quantity of space. 
 
 13. In common phraseology, we express this property 
 of bodies by the word size ; but the most appropriate term 
 is volume. Thus, we say the volume of a terrestrial or 
 celestial globe is so many cubic inches. When the lines 
 
 1 Examples of condensation, from wi hout and within, 
 
 b. What of nv cast n > 
 
10 
 
 FIGURE DIVISI BIL1TY. 
 
 and surfaces of a body are spoken of, the external limits 
 of its magnitude are implied. Lines are the limits which 
 separate the several surfaces of the same body. They are 
 also called edges. Thus, the line which separates the top 
 from one of the sides of a box, is denominated an edge. 
 The quantity of a surface. is called its area, and the quan- 
 tity of a line is termed its length. Thus, we say the area 
 of a floor is so many yards ; and the length of a rope is 
 so many yards. Volume, area, and length, however, are 
 sometimes expressed by the word magnitude. 
 
 14. The dimensions of magnitude or extension are 
 usually entitled length, breadth, and depth ; and they vary 
 of course very considerably in different bodies, according 
 to their shape. Height and depth are the same dimen- 
 sion, considered in different points of view. When a body 
 is measured downwards, it is said to be so many feet deep ; 
 when measured upwards, it is said to be so many feet 
 high. Breadth and width express the same dimension. 
 
 FIGURE. 
 
 15. The figure of a body is its shape or form. Figure 
 or form is the result of extension, for we cannot have the 
 idea of a body possessing length and breadth, without its 
 having some kind of figure, however irregular. The 
 volume of a body has no relation to its figure. Bodies 
 which have the same figure may possess very different 
 volumes ; and bodies may have the same volume, but pos- 
 sess very different figures. Thus, two masses of matter 
 may have the same volume, although the one be round 
 and the other be square. 
 
 DIVISIBILITY. 
 
 16. Matter is divisible into parts, and these parts may 
 again be subdivided into other parts. By this is meant 
 divisibility or separability. 
 
 17. To the practical subdivision of matter there seems 
 to be no assignable limit ; and many of the instances of it 
 
 9. Define volume, area, and length, &c. 
 
 10. What of figure ? 
 
 11. Define divisibility. 
 
DIVISIBILITY. 
 
 11 
 
 which may be found in philosophical investigations, almost 
 exceed credibility. The thinnest part of a soap bubble, 
 which is a thin shell of water and the matter of soap, does 
 not exceed, in thickness, the 2,500,000th part of an inch. 
 The useful arts, also, furnish many striking examples ; 
 but it is in the organized world that the most astonishing 
 proofs of the extreme divisibility of globules, or particles 
 of matter, are to be found. 
 
 18. Animalcules — that is, animals which are so small 
 as to be invisible to the naked eye, and which, by means 
 of microscopes, are seen floating in water — are in some 
 cases so minute, that it would require a million of them to 
 form the bulk of a grain of sand. As these animalcules 
 possess, in every case, a perfect organization to enable 
 them to perform all the functions of life, the smallness of 
 their different parts, and the extreme minuteness of the 
 particles of matter which compose them, are too exquisite 
 to be made the subject of calculation : the imagination is 
 lost in the contemplation of their wonderful economy. 
 
 19. The effluvium or odour which excites the sensation 
 of sm?//, consists of an incalculable number of particles of 
 matter floating in the atmosphere, and so minute as to be 
 altogether invisible to the eye. These particles are not 
 more remarkable for their inconceivably small size than 
 for the length of time which they will remain in suspen- 
 sion in the atmosphere, or in connection with some par- 
 ticular place. The effluvium given forth by a single grain 
 of musk has been known to perfume a large apartment for 
 twenty years, and yet at the expiry of that period there 
 was no sensible diminution of the little mass of matter from 
 which the smell had proceeded. 
 
 20. The diffusion of particles of matter invisible to the 
 naked eye, is also obvious in the case of the melting of a 
 piece of sugar in our tea : the solid mass of the sugar dis- 
 appears, and the particles of which it was composed are 
 diffused in the liquid. There is a similar diffusion of par- 
 ticles of salt in the ocean. When we look through a glass 
 
 12. What example of divisibility is named? 
 
 13. What of animalcules, and of odours ? 
 
12 
 
 DIVISIBILITY. 
 
 full of sea water, we perceive that it is pure and limpid ; 
 but if we pour the water into a vessel on the fire, and boil 
 it, we shall at length discover that, while the liquid has 
 escaped in the form of vapour, the particles of salt it held 
 in solution remain encrusted on the vessel. 
 
 21. Particles of matter are never destroyed or lost, 
 although they may disappear from our immediate obser- 
 vation. Under certain circumstances, the particles may 
 again be collected into a body without change or form. 
 Mercury, water, and many other substances, may be con- 
 verted into vapour, or distilled in close vessels, without 
 any of their particles being lost. In such cases, there is 
 no decomposition of the substances, but only a change of 
 form by the heat ; and hence the mercury and water 
 assume their original state again on cooling. 
 
 22. When bodies suffer decomposition or decay, their 
 elementary particles, in like manner, are neither destroyed 
 nor lost, but only enter into new arrangements, or combi- 
 nations with other bodies. When a piece of wood is 
 heated in a close vessel, such as a retort, we obtain water, 
 an acid, several kinds of gas, and there remains a black, 
 porous substance, called charcoal. The wood is thus de- 
 composed, or destroyed, and its particles take a new arrange- 
 ment, and assume new forms ; but that nothing is lost, is 
 proved by the fact, that if the water, acid, gases, and char- 
 coal, be collected and weighed, they will be found exactly 
 as heavy as the wood was, before distillation. In the same 
 manner, the substance of the coal burnt in our fires is not 
 annihilated ; it is only dispersed in the form of smoke, or 
 particles of culm, gas, and ashes or dust. Bones, flesh, or 
 any animal substance, may in the same manner be made 
 to assume new forms, without losing a particle of the 
 matter which they originally contained. The decay of 
 animal or vegetable bodies in the open air, or in the 
 ground, is only a process by which the particles of which 
 
 14. The example of solution. 
 
 15. How do you prove that nothing is lost by vaporization ? 
 
 16. What becomes of the elements after decomposition 1 
 
 17. In the case of wood, how is this shown ? 
 
INERTIA OF MATTER. 
 
 13 
 
 they were composed change their places, and assume new 
 forms. 
 
 23. The decay and decomposition of animals and vege- 
 tables beneath the surface of the earth, fertilize the soil, 
 which nourishes the growth of plants and other vegetables ; 
 and these, in their turn, form the nutriment of animals. 
 Thus is there a perpetual change from death to life, and 
 from life to death, and as constant a succession in the forms 
 and places which the particles of matter assume. Nothing 
 is lost, and not a particle of matter is struck out of exist- 
 ence. The same matter of which every living animal and 
 every vegetable was formed in the earliest ages, is still in 
 existence. As nothing is lost or annihilated, so it is pro- 
 bable that nothing has been added, and that we ourselves 
 are composed of particles of matter as old as the creation. 
 In time, we must in our turn suffer decomposition, as all 
 forms have done before us, and thus resign the matter of 
 which we are composed, to form new existences. 
 
 24. Such are some of the remarkable phenomena con- 
 nected with the divisibility of matter ; and we are naturally 
 led to inquire, Is matter infinitely divisible, or are there 
 certain constituent atoms which are incapable of furthei 
 division ? The latter supposition is the one most generally 
 admitted, yet there is no denying that it seems scarcely a 
 legitimate inference. For however small a particle may 
 be, we can easily conceive of one still smaller — for instance, 
 by simply supposing that same particle halved. To the 
 understanding, without reference to direct observation, it 
 seems as absurd to assign limits to the divisibility of matter, 
 as boundaries to space, which is considered infinite. 
 
 INERTIA. 
 
 25. Inertia means passiveness or inactivity. Thus, 
 matter is perfectly passive in submitting to any condition 
 in which it is placed, whether of rest or motion. When 
 at rest, it shows an inability or reluctancy to move ; and 
 
 18. What of the reciprocal interchange between life and death ? 
 18. What reflections are suggested ? 
 
 20. Define inertia, both in rest and motion. 
 
n 
 
 INERTIA OF MATTER. 
 
 when in motion, it show's an equal inability or reJuctancy 
 to come to a state of rest. 
 
 2(5. It is obvious that a rock on the surface of the earth 
 never changes its position in respect to other things on the 
 earth. It has of itself no power to move, and w'ould there- 
 fore for ever lie still, unless moved by some external force. 
 Now, it is just as true that inert matter has no pow'er to 
 bring itself to rest, when once put in motion, as that it 
 cannot put itself in motion, when at rest ; for, having no 
 life, it is perfectly passive, both to motion and rest, and 
 therefore either state depends entirely upon external cir- 
 cumstances. 
 
 27. Many instances might be given of the tendency 
 which matter has to remain in the condition in w'hich it 
 happens to have been already placed. The following are 
 among the most instructive : — When the sails of a ship 
 are loosened to the breeze, slowly and heavily at first the 
 vessel gets into motion, but gradually its speed increases 
 as the force by which it is impelled overcomes the inertia 
 of its mass. A great force is necessary at first to set a 
 vehicle in motion ; but when once this is effected, it goes 
 omvard with comparative ease, so that, in fact, a strong 
 effort is necessary before it can be stopped, if a person 
 be standing in it when it is suddenly set a-going, his feet 
 are pulled forward, whilst his body, obeying the law' of 
 inertia, remains where it w r as, and he accordingly falls 
 backwards. On the other hand, if the vehicle be suddenly 
 stopped, and the individual be standing in the same posi- 
 tion as formerly, the tendency w'hich his body has to move 
 forwmrd — for it acquired the same motion as the carriage 
 by which it was borne along — will cause him to fall in the 
 opposite direction. Casualties of this description fre- 
 quently occur to persons on horseback, who are thrown 
 over the necks of their steeds, or fall behind them, accord- 
 ing as the animal stands still suddenly, or starts off unex- 
 pectedly. A man jumping from a coach at full speed will 
 certainly fall prostrate on the ground, if he leaps down as 
 
 21. What illustrations are cited i 
 
 22. To what casualties does this render us liable f 
 
 23. What of jumping from a coach in motion ? 
 
EXAMPLES OF INERTIA. 
 
 15 
 
 if he were descending from a body at rest, to one which is 
 in the same state ; for when he makes the attempt, his 
 body has the same motion as the coach ; and when the 
 feet arrive at the ground, the motion in the lower part is 
 arrested, whilst it continues in the upper part ; and thus 
 he finds himself thrown from the perpendicular into the 
 horizontal position. 
 
 28. The following is a familiar example of the inertia 
 of matter : — upon the tip of the finger let a card be balanced, 
 and a piece of money — say a shilling — laid upon it. Let 
 the card then be smartly struck, and it will fly from be- 
 neath the coin, leaving it supported upon the finger. 
 This arises from the inertia of the metal being greater 
 than the friction of the card which passes from beneath it. 
 
 29. Coursing, or hare-hunting, affords a striking illus- 
 tration of inertia. In that field sport, the hare seems to 
 possess an instinctive consciousness of the existence of this 
 law of matter. When pursued by the greyhound, it does 
 not run in a straight line to the cover, but in a zig-zag one. 
 It doubles, that is, suddenly changes the direction of its 
 course, and turns back at an acute angle with the direction 
 in which it had been running. The greyhound, being 
 unprepared to make the turn, and therefore unable to 
 resist the tendency to persevere in the rapid motion which 
 it has acquired, is impelled a considerable distance forward 
 before it can check its speed and return to the pursuit. 
 But, in the mean time, the hare has been enabled to shoot 
 far ahead in the other direction ; and although a hare is 
 much less fleet than a greyhound, by this scientific ma- 
 noeuvring it often escapes its pursuer. Those who have 
 witnessed horse-racing, may have observed that the horses 
 shoot far past the winning-post before their speed can 
 be arrested. This is also owing to the inertia of their 
 bodies. 
 
 30. Common experience proving that matter does not 
 put itself in motion, we might be led to believe that rest is 
 the natural state of all inert bodies ; but a few consider- 
 
 24. What example is named ? 
 
 25. What of racing and hare-hunting ? 
 
IB 
 
 EXAMPLES OF INERTIA. 
 
 ations will show that motion is as much the natural state of 
 matter as rest, and that either state depends on the resist- 
 ance, or impulse, of external causes. 
 
 31. If a cannon-ball be rolled upon the ground, it will 
 soon cease to move, because the ground is rough, and 
 presents impediments to its motion ; hut if it be rolled on 
 the ice, its motion will continue much longer, because 
 there are fewer impediments, and, consequently, the same 
 force of impulse will carry it much farther. We see from 
 this, that, with the same impulse, the distance to which 
 the ball will move must depend on the impediments it 
 meets with, or the resistance it has to overcome. But 
 suppose that the ball and ice were both so smooth as to 
 remove as much as possible the resistance caused by fric- 
 tion, then it is obvious that the ball would continue to move 
 longer, and go to a greater distance. Next, suppose we 
 avoid the friction of the ice, and throw the ball through 
 the air, it would then continue in motion still longer with 
 the same force of projection, because the air alone presents 
 less impediment than the air and ice, and there is now 
 nothing to oppose its constant motion, except the resist- 
 ance of the air. 
 
 32. If the air be exhausted or pumped out of a vessel 
 by means of an air-pump, and a common top, with a small 
 hard point, be set in motion in it, the top will continue to 
 spin a considerable length of time, because the air does 
 not resist its motion. A pendulum, set in motion in an 
 exhausted vessel, will continue to swing, without the help 
 of clockwork, for a whole day, because there is nothing to 
 resist its perpetual motion but the small friction at the point 
 where it is suspended. 
 
 33. We see, then, that it is the resistance of the air, 
 and of friction, and of gravitation, which causes bodies once 
 in motion to cease moving, or come to rest ; and that dead 
 matter, of itself, is equally incapable of causing its own 
 motion, or its own rest. 
 
 26. Describe ihe motion of a ball upon the ground end upon the ice. 
 
 27. How is motion affected by excluding the air t 
 
 28. What agencies combine to bring bodies to rest ? 
 
ATTRACTION. 
 
 17 
 
 THE PROPERTIES OF MATTER CONTINUED. 
 
 ATTRACTION. 
 
 34. It is a fundamental law of nature, ascertained by Sir 
 Isaac Newton, that every atom or particle of matter has a 
 tendency to approach or to be attracted towards another 
 atom or particle. This forms one of the leading principles 
 in modern natural philosophy. Experience and observa- 
 tion demonstrate that this power of mutual attraction per- 
 vades all material things, and, though unseen except in 
 its results, is ever present with us ; is the cause of particles 
 of matter adhering to each other, and forming solid masses 
 — of these masses assuming in many instances a round or 
 globular form — of the falling of bodies to, and their stabi- 
 lity on, the earth — and is one of the causes of the whole 
 of the planetary bodies moving in their paths in the 
 heavens. 
 
 35. Attraction is of different kinds, although some of 
 these may be merely modifications of others, and has re- 
 ceived different names according to the circumstances under 
 which it acts. The force which keeps the particles of 
 matter together, to form bodies, or masses, is called attrac- 
 tion of cohesion. That which inclines different masses 
 towards each other, is called gravitation , or attraction <f 
 gravitation. That which causes liquids to rise in tubes, 
 or in very confined situations, is called capillary attraction. 
 That which forces the particles of different kinds to unite, 
 is called chemical attraction. That which causes the mag- 
 netic needle to point constantly towards the poles of the 
 earth, is magnetic attraction. And that which is excited 
 by friction in certain substances, is known by the name of 
 electrical attraction. 
 
 36. Attraction of cohesion acts only at insensible dis- 
 tances, as when the particles of bodies apparently touch 
 each other. 
 
 29. What of attraction, and how manifested ? 
 
 30. How many, and what kinds of attraction are named? 
 
 31. How does cohesion act, and in what forms of bodies ? 
 
18 
 
 ATTRACTION OF COHESION. 
 
 37. This kind of attraction may be described as the 
 quality in nature which causes matter to cohere or stick 
 together. It is much stronger in some bodies than in 
 others. It is stronger in the metals than in most other 
 substances, and in some of the metals it is stronger than 
 in others. In general, it is most powerful among the 
 particles of solid bodies, weaker among those of fluids, 
 and least of all, or almost entirely wanting, among elastic 
 fluids, such as air and the gases. 
 
 38. Thus, a small iron wire will hold a suspended 
 weight of many pounds, without having its particles sepa- 
 rated ; the particles of water are divided by a very small 
 force, while those of air are still more easily moved among 
 each other. These different properties depend on the 
 force of cohesion wdth which the several particles of these 
 bodies are united. 
 
 39. When the particles of a body can be suspended in 
 the air in a fluid state, they will, if not under the attractive 
 influence of some other body, arrange themselves by virtue 
 of the same law, around a centre, and take a spherical or 
 round form. Thus, a small quantity of dew suspended on 
 the point of a thorn or leaf, becomes a globule, because in 
 that case the attraction of the particles towards their own 
 centre is greater than the attraction of any neighbouring 
 body. Tears running down the cheeks, drops of rain, 
 and hail, are all examples of this tendency in insulated 
 fluid bodies to assume the globular form. When two 
 perfect globules of mercury are brought into contact, they 
 instantly unite together, and form one spherical drop. 
 The manufacture of shot is also a striking illustration. 
 The lead is melted and poured into a sieve, at the height 
 of about two hundred feet from the ground. Each stream 
 of lead, immediately after leaving the sieve, separates into 
 little globules, which, before they reach the ground, are 
 cooled and become solid : thus is formed the shot used by 
 sportsmen. To account for the globular form in all these 
 
 32. How is the difference illustrated ? 
 
 33. What of the globular or spherical form ? 
 
 34. How is this shown in shot- towers f 
 
CAPILLARY ATTRACTION. 
 
 19 
 
 cases, we have only to consider that the particles of matter 
 are mutually attracted towards a common centre, and in 
 liquids, being free to move, they arrange themselves ac- 
 cordingly. 
 
 49. In consequence of this law of nature, it is considered 
 probable that the planetary bodies, including our earth, 
 were originally in a fluid state — that, in that state, they 
 unavoidably assumed a spherical form, and were then 
 hardened into their present consistency. 
 
 CAPILLARY ATTRACTION. 
 
 41. The force by which small tubes, or porous sub- 
 stances, raise liquids above their levels, is called Capillary 
 Attraction, from capi/la, the Latin word for a hair. 
 
 42. In a wet tea-cup, or other vessel containing liquid, 
 you may perceive the liquid at the sides rising above the 
 level of that of the other parts of the surface ; this is 
 caused by attraction. 
 
 43. If two glass plates be brought very near each other, 
 so as to stand parallel with their flat sides in almost mutual 
 contact, and then their lower end be dipped into a vessel 
 of water, the fluid will rise up between the plates, and the 
 height to which it rises will be greater the nearer the 
 plates are to each other. The water rises very little on 
 the outsides of the plates, for this attraction is insensible 
 at even moderately small distances. If a glass tube, with 
 an exceedingly small or capillary bore, be dipped in water, 
 the fluid will rise in the interior of the tube; and the 
 smaller the bore, the higher does the water ascend. 
 
 44. A great variety of porous substances are capable 
 of this kind of attraction. If a piece of sponge or a lump 
 of sugar be placed, so that its lowest corner touches the 
 water, the fluid will rise up and wet the whole mass. In 
 the same manner, the wick of a lamp will carry up the oil 
 to supply the flame, though the flame is several inches 
 
 35. What inference is thence drawn of the original state of the 
 earth and other planets. 
 
 36. Define capillary attraction and give an instance. 
 
 37. What other illustrations are cited ? 
 
20 
 
 CHEMICAL ATTRACTION. 
 
 above the level of the oil. If the end of a towel happens 
 to be left in a basin of water, it will empty the basin of its 
 contents ; and, on the same principle, when a dry wedge 
 of wood is driven into the crevice of a rock, and after- 
 wards moistened with water, as when the rain falls upon 
 it, it will absorb the water, swell, and sometimes split 
 the rock. 
 
 45. It is this kind of attraction which is supposed to be 
 one of the causes of springs of water in the earth. The 
 water creeps up by capillary attraction through porous 
 beds of sand, small stones, and crevices of rocks, and in 
 this manner reaches the surface even at great heights. 
 The lower parts of the walls, and also the earthen floors 
 of cottages, are in the same manner apt to become damp, 
 by the attraction of the moisture upwards from the ground. 
 Hence the necessity for clearing away all wet earthy 
 matter from the foundations of houses. 
 
 CHEMICAL ATTRACTION. 
 
 46. The material world immediately under our obser- 
 vation, including such parts of the earth’s crust as have 
 been explored, the plants and animals upon the earth, 
 and the atmosphere which envelopes it, is found to consist 
 of fifty -four substances, just as all the words which, com- 
 pose a language are resolvable into a few letters. These 
 substances, having hitherto resisted all endeavours to 
 divide or resolve them into any others, are termed the 
 elements of matter , or simple bodies. From the earliest 
 stage of creation, most of them appear to have been in a 
 state of combination with each other ; they are scarcely 
 ever naturally found otherwise ; creation itself appears to 
 have consisted in putting them into the associations which 
 they have since commonly displayed. 
 
 47. Matter has ever been, and is now, undergoing per- 
 petual decompositions and recombinations ; some of which 
 take place upon an extensive scale, as part of the regular 
 functions and operations of nature, while others are affected 
 
 3 V . Between what portions of matter is chemical a'traciion exerted ! 
 3y. How many elements compose the universe ? 
 
CHEMICAL ATTRACTION. 
 
 21 
 
 by the ingenuity of man, to serve the purposes of his 
 ordinary economy. Of the fifty-four simple substances, 
 six are gases, forty-two are metals, and the remaining 
 bodies are reducible under no fixed class. The investiga- 
 tion of the laws under which these various elementary 
 bodies have formed the numerous compound substances 
 which we see in nature, and the means by which com- 
 pound substances can. be resolved into their original ele- 
 ments, or thrown into new combinations, are the objects 
 of the Science of Chemistry. 
 
 48. Chemical attraction, which is one of the leading 
 principles in chemistry, takes place when particles of dif- 
 f rent kinds of matter unite, and the particles thus formed 
 have properties in which they differ more or less from 
 those substances by whose union they were formed. This 
 species of attraction is also known under the name of 
 chemical affbriti/, because it is said that the particles of 
 substances, having an affinity for each other, will unite, 
 while those having no affinity, do not readily enter into 
 union. 
 
 4 ti. It might almost be supposed that there are such 
 things as preferences and dislikes among the particles of 
 matter. Thus, if a piece of marble be thrown into sul- 
 phuric acid, their particles will unite with great rapidity 
 and commotion, and there will result a compound differing 
 in all respects from the acid or the marble. But if a piece 
 of glass, quartz, gold, or silver, be thrown into the acid, no 
 change is produced on either, because their particles have 
 no affinity. 
 
 50. Shake sand and water in a bottle ; whenever the 
 agitation ceases, the sand falls ; the water has no chemical 
 action with it. 
 
 51. Suspend a piece of aqueous sulphate of copper 
 (common blue vitriol) with a thread in a glass full of 
 water. The particles of both combine, and form a stream 
 
 * See Reid’s Rudiments of Chemistry, forming parts of Cham- 
 bers’s Educational Course. 
 
 40. Describe these in classes. 
 
 41. What of chemical affinity, illustrate this ? 
 
22 
 
 MAGNETIC ATTRACTION. 
 
 of blue fluid, which descends from the points where they 
 are in contact. The solid is said to be dissolved. The 
 compound is called a solution of the solid. 
 
 52. Sulphur and quicksilver, when heated together, 
 will form a beautiful red compound, known under the 
 name of vermilion , and which has none of the qualities 
 of sulphur or quicksilver. 
 
 5:5. Oil and water have no affinity for each other, but 
 potash has an attraction for both ; and therefore oil and 
 water will unite when potash is mixed with them. In 
 this manner, the well-known article called soap is formed. 
 But the potash has a stronger attraction for an acid than 
 it has for either the oil or the water ; and, therefore, when 
 soap is mixed with an acid, the potash leaves the oil, and 
 unites with the acid ; thus destroying the old compound, 
 and at the same instant forming a new one. The same 
 happens when soap is dissolved in any water containing 
 an acid, as the water of the sea, and of certain wells. 
 The potash forsakes the oil, and unites with the acid, 
 thus leaving the oil to rise to the surface of the water. 
 Such waters are called hard , and are not good for wash- 
 ing, on account of the floating oil. 
 
 MAGNETIC ATTRACTION. 
 
 54. There is a certain ore of iron, a piece of which, 
 being suspended by a thread, will always turn one of its 
 sides to the north. This is called the Loadstone, or 
 natural Magnet ; and when it is brought near a piece of 
 iron, or steel, a mutual attraction takes place, and, under 
 certain circumstances, the two bodies will come together, 
 and adhere to each other. This is called Magnetic At- 
 traction. When a piece of steel or iron is rubbed with a 
 magnet, the same virtue is communicated to the steel, and 
 it will attract other pieces of steel, and if suspended by a 
 string, one of its ends will constantly point towards the 
 north, while the other, of course, points towards the south. 
 This is called an artificial magnet. The magnet ic needle 
 
 42. What experiments are here cited ? 
 
 43. Detine magnetic attraction, and its uses. 
 
ELECTRICAL ATTRACTION. 
 
 23 
 
 is a piece of steel, first touched with the loadstone, and 
 then suspended so as to turn easily on a point. By 
 means of this instrument, which is called the Mariner’s 
 Compass, the sailor is enabled to guide his ship through 
 the pathless ocean. 
 
 ELECTRICAL ATTRACTION. 
 
 55. All nature appears to be pervaded by a mysterious 
 affection, which bears the name of Electricity, in con- 
 sequence of its having been supposed by the ancients to 
 reside exclusively in electron, or amber. 
 
 56. In its ordinary state, electricity is invisible ; but 
 when excited, it assumes the appearance of a bright and 
 subtile fluid. It is sometimes excited in very tremendous 
 forms in the atmosphere ; but it can be produced in less 
 extent by mechanical means, particularly by the rubbing 
 of amber, glass, silk, and a few other bodies. 
 
 57. When a piece of glass, or sealing-wax, is rubbed 
 with the dry hand, or a piece of cloth, and then held to- 
 wards any light substance, such as hair, or thread, the 
 light body will be attracted by it, and will adhere for a 
 moment to the glass or wax. The influence which thus 
 moves the light body is called Electrical Attraction. 
 When the light body has adhered to the surface of the 
 glass for a moment, it is again thrown off, or repelled, and 
 this is called Electrical Repulsion. 
 
 58. It is the nature of electricity to remain in a state 
 of equilibrium or balance in all substances ; and when 
 one body happens to have more than its natural propor- 
 tion, while another has less, there is a tendency in the sur- 
 plus, in the one body, if sufficiently near, to rush to make 
 up the deficiency in the other. 
 
 59. Electricity is the cause of the phenomena of thun- 
 der and lightning. In particular states of the atmo- 
 sphere, generally in hot weather, the balance of electricity 
 among the clouds, or between the atmosphere and the 
 earth, is apt to become disturbed. If a cloud containing 
 
 44. What of electricif, and i's sources? 
 
 45. What of electrical attraction and repulsion ? 
 
 46. How is an equilibrium produced ? 
 
 47. What of lightning and thunder ? 
 
24 
 
 ATTRACTION OF GRAVITATION. 
 
 an overplus approaches or is attracted towards another 
 which is undercharged — in other words, if a cloud posi- 
 tively electrified approaches one negatively electrified — 
 the surplus flashes from the one into the other in the form 
 of lightning, with a noise stunning to the ear.* 
 
 ATTRACTION OF GRAVITATION. 
 
 60. As the attraction of cohesion unites the particles 
 of matter into masses or bodies, so the attraction of gravi- 
 tation tends to force those masses towards each other, to 
 form others of still greater dimensions. 
 
 61. The force of attraction increases in proportion as 
 bodies approach each other, and by the same law it must 
 diminish in proportion as they recede from each other. 
 
 62. Attraction, in technical language, is inversely as 
 the squares of the distances between the two bodies. 
 That is, in proportion as the square of the distance in- 
 creases, in the same proportion attraction decreases, and 
 so the contrary. Thus, if at the distance of 2 feet, the 
 attraction be equal to 4 pounds, at the distance of 4 feet 
 it will be only 1 pound ; for the square of 2 is 4, and the 
 square of 4 is 16, which is 4 times the square of 2. On 
 the contrary, if the attraction at the distance of 6 feet be 
 3 pounds, at the distance of 2 feet it will be 9 times as 
 much, or 27 pounds, because 36, the square of 6, is equal 
 to 9 times 4, the square of 2. 
 
 63. The intensity of light is found to increase and di- 
 minish in the same proportion. Thus, if a board a foot 
 square be placed at the distance of one foot from a candle, 
 it will be found to hide the light from another board of 
 two feet square, at the distance of two feet from the can- 
 dle Now, a board of two feet square is just four times 
 as large as one of one foot square, and therefore the light 
 at double the distance being spread over four times the 
 surface, has only one-fourth the intensity. 
 
 * Fur a further account of Magnetism and Electricity, see trea 
 tises on these branches of Natural Philosophy. 
 
 48. Define attraction of gravitation, and its laws. 
 
 49. What of the laws of the intensity of light? 
 
ATTRACTION OF GRAVITATION. 
 
 25 
 
 (54. The gradual diminution of attraction, as the dis- 
 tance increases, is exemplified in the following table. In 
 the upper line, the distance is expressed by progressive 
 numbers ; in the' lower corresponding squares, the dimi- 
 nution of attraction is indicated by the common arithme- 
 tical fractions. 
 
 Distance 
 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 and so on. 
 
 1 
 
 1 Attraction 
 
 i 
 
 1 
 
 J_ 
 
 4 
 
 1_ 
 
 9 
 
 16 
 
 25 
 
 36 
 
 49 
 
 64 
 
 and so on. 
 
 It is here seen, that, at the distance of 8, the attractive 
 force is diminished to a sixty-fourth part of what it was 
 
 at 1. 
 
 (55. The attractive force of matter is also in proportion 
 to the numbers of the atoms of matter which a body con- 
 tains ; the attraction therefore does not proceed from the 
 mere surface of a body, but from all the particles which 
 individually compose it. 
 
 t56. Some bodies of the same bulk contain a much 
 greater quantity of matter than others: thus, a piece of 
 lead contains about twelve times as much matter as a 
 piece of cork of the same dimensions ; and therefore a 
 piece of -lead of any given size, and a piece of cork 
 twelve times as large, will attract each other equally. 
 
 (57. The attractive power of any mass acts from the 
 centre. At all equal distances from the centre, the at- 
 tractive power is equal ; for instance, in a body per- 
 fectly spherical, the attraction to the centre would be the 
 same at all parts of the surface. The distance of the cen- 
 tre of a sphere from its surface is called the semi-diame/ei 
 of that sphere — that is, the half of its thickness. At a 
 point as far from the surface of a sphere as its semi- 
 diameter, its attractive power is diminished to a fourth. 
 At three distances, the attraction is a ninth ; at four dis- 
 
 50. Explain the table. 
 
 51. What of the number of atoms of a body f 
 
 52. What differences between bulk and quantity ? 
 
 53. How does the centre of attraction vary ? 
 
28 
 
 ATTRACTION OF GRAVITATION. 
 
 tances, a sixteenth ; and so on. When we wish, therefore, 
 to ascertain the relative amount of the attraction which any 
 mass of matter exercises over another, the rule is, to inquire 
 how many semi-diameters of the one the other is distant 
 from it, and then to multiply that number by itself. The 
 result shows how many times the attraction at this distance 
 is less than at the surface of the former. The moon, for 
 instance, is distant 240,000 miles from the earth ; or as 
 much as 60 semi-diameters of the earth ; 60 multiplied by 
 60 gives 3600 ; consequently, the attraction exercised by 
 the earth upon the moon is a 3000th part of what it would 
 exercise upon th • same mass at its own surface. 
 
 68. If the earth were a perfectly spherical body, its 
 attraction would be equal everywhere at the level of the 
 sea. As the surface at the pole is thirteen miles nearer 
 the centre than the surface at the equator, the attraction 
 is stronger at the former than at the latter place ; it gets 
 proportionally weaker as we advance towards the equator, 
 on account of the increase of distance from the centre. 
 Hence, a mass of iron which is considered a pound weight 
 in Britain, would be Jess than a pound on the coast of 
 Guinea, and more than a pound in Greenland, for weight 
 is only a result of attraction. If we ascend a mountain, 
 the effect is the same as if we proceed towards the equa- 
 tor: we are always getting farther from the centre of attrac- 
 tion, and consequently weights become lighter. On the 
 top of a hill four miles high, a ball of four thousand 
 pounds’ weight would be found to be two pounds lighter. 
 
 69. Pressure downwards, or weight, is in philosophical 
 language termed gravity, and under that head it is here- 
 after treated, in connection with the phenomena of falling 
 bodies. 
 
 70. In the set of large spheres constituting the Solar 
 System, the Sun is a central body of vast size, while the 
 Planets are comparatively small bodies, revolving round 
 him at different distances. If we take a stone in a sling, 
 and whirl it round, the stone will have a tendency, in the 
 
 54. By what rule is relative attraction found ? 
 
 55. How illustrated with the moon ? 
 
 56. Why does weight diminish toward the equator ? 
 
ATTRACTION OF GRAVITATION. 
 
 27 
 
 event of our slipping - the string, to fly off in a straight 
 line. This is called Centrifugal Force, that is, a force 
 operating so as to cause a body to fly from a centre. 
 When tb» planets received their first impulse, they had 
 the same tendency as a stone in a sling to fly off in a 
 straight tine into space; in which case, they would never 
 have come to a stop, till they fell under the attractive in- 
 fluence of some body of sufficient mass. But while im- 
 pelled thus to fly off from the sun, they were also under 
 the influence of his attraction, which, in this instance, is 
 called Centripetal Force — that is a force impelling a mass 
 to seek nr go to a centre. At once impelled from the 
 sun by their original motion, and drawn to him by his at- 
 traction, they took what may be called a middle course, 
 and began to revolve round him at mean distances adapted 
 to their rates of speed, and the force of the sun’s attrac- 
 tion. The same laws caused the satellites to revolve at 
 certain distances round the planets. 
 
 71. The attraction of bodies is mutual, and in propor- 
 tion to the quantity of matter they contain. Therefore, 
 any body, however small, exerts some degree of attrac- 
 tion upon the mass of the earth. Any body which comes 
 immediately under our observation, is so small in compa- 
 rison to the earth, that its attractive force is altogether un- 
 appreciable ; but if the body were of great density, and 
 of dimensions approaching to those of the earth, then we 
 should see the earth rise to meet the body, or fall towards 
 the body. The heavenly bodies, when they approach 
 each other, are drawn out of the line of their paths, or 
 orbits, by mutual attraction. 
 
 72. It is found by experiment, that a plumb-line sus- 
 pended in the neighbourhood of a mountain, is sensibly 
 attracted towards the mountain from the true vertical line. 
 
 72. The mutual attraction of matter is exemplified by 
 the diminution of the weight of bodies, as we penetrate 
 into the earth. At the depth of a mile, a body weighing 
 
 57. Explain centrifugal and ceniripetal forces. 
 
 58. How is the revolution of the planets perpetuated ? 
 
 59. How is the attraction of a mountain shown ? 
 
 60. What change in gravity by nearing the centre of the 
 
28 
 
 ATTRACTION OF GRAVITATION. 
 
 a pound would be found to be lighter than at the surface. 
 This is in consequence of the attraction of the matter of 
 the shell of the earth, which is exterior to the point, being 
 nothing, in consequence of the attractions of its particles 
 on this point counteracting each other ; and hence the 
 only efficient attraction on it arises merely from the smaller 
 sphere below the point, and, therefore, the nearer the point 
 is to the centre, the less is this internal sphere ; and the 
 less therefore is its attraction on the point. 
 
 74. Were we to proceed to the centre of the earth, we 
 should there find that weight altogether ceased, because 
 the attractive power would be equal on all sides. Were 
 there a cavity at the earth’s centre, the body would hang 
 suspended in space. 
 
 75. The attraction of the earth’s mass performs an im- 
 portant function, in binding the atmosphere, which is an 
 elastic fluid, around the surface of our planet, and of caus- 
 ing the air to perforate every open crevice and pore in the 
 superficial substances of the globe. The attractive force, 
 in this respect, produces what is called atmospheric pres- 
 sure , the air being pulled or pressed down by a force equi- 
 valent to about 15 lbs. on the square inch, at the level of 
 the sea, and diminishes in proportion to the distance above 
 that common level. The degree of atmospheric pressure 
 at any given height is ascertained by an instrument called 
 the barometer , which consists of a column of mercury in 
 a tube, and by the pressure of the air upon which, the 
 height above the level of the sea may be judged.* 
 
 70. Atmospheric pressure is, then, a result of attraction, 
 and as such produces divers phenomena in nature. It is 
 possible, by artificial means, to draw out the air from a 
 confined vessel, as in the case of the air-pump and its re- 
 ceiver, so as to produce a vacuum, or almost perfect ab- 
 sence of air and its pressure ; but it is not possible to di- 
 minish in any way the attraction of gravitation, which is 
 a property inherent and indestructible in all matter. 
 
 * See treatise on Pneumatics. 
 
 61. What effect has gravitation upon the air? 
 
 62. Name the average lorce of this pressure. 
 
 63. What instrument measures relative pressure ? 
 
REPULSIVE QUALITY IN MATTER HEAT. 
 
 29 
 
 77. Some bodies do not appear to be affected by attrac- 
 tion ; for instance, smoke and vapours rise, instead of fall- 
 ing to the ground; in all such cases, however, attraction 
 is present. Smoke consists chiefly of condensed vapour 
 and minute particles of soot, and is carried upwards by the 
 impulse of an ascending current of air, which is warmer, 
 and therefore lighter, than the surrounding atmosphere. 
 The sooty particles soon descend again, and the vaporous 
 particles are commonly dissolved by the atmosphere, 
 forming a transparent solution, and thus becoming invi- 
 sible. 
 
 THE REPULSIVE QUALITY IN MATTER— HEAT.* 
 
 78. While “attraction tends to unite and compress the 
 particles of matter, there is another and equally universal 
 principle, known in familiar language by the appellation 
 of Heat, the tendency of which is to keep the particles of 
 matter at a certain degree of expansion. Heat is often, 
 in scientific works, named caloric, from the Latin word for 
 heat. 
 
 79. Heat pervades ail things, but some in greater de- 
 grees than others. Even ice has been found to contain a 
 certain portion of heat. In fact, there is no such thing in 
 nature as positive cold. The things which seem cold to 
 us, are only under a low degree of heat. 
 
 80. The absolute nature of this universal principle is un- 
 known. We only know it by its effects, and the sensa- 
 tions it produces. Some have conjectured that it is a fluid ; 
 others think it is a quality or affection of matter, resulting 
 from electrical action. From its producing no sensible 
 difference in the weight of any substance, it has been called 
 an imponderable body. 
 
 * The operations and properties of Heat form a branch of know- 
 ledge sometimes called Pyronomics, a word signifying the Laws of 
 Fite. 
 
 64. How is gravitation proved without the air? 
 
 65. How is the ascent of smoke and vapour explained ? 
 
 66. What principle in matter produces repulsion ? 
 
 67. What of heat and of cold ? 
 
 68. By what name is it designated ? 
 
SO REPULSIVE QUALITY TV MATTER HEAT. 
 
 81. When the heat of any particular substance, as ice, 
 stone or wood, is not sensible to us, it is called latent that 
 is, concealed) heat. We may very readily detect its pre- 
 sence in a piece of wood or metal by rubbing or friction. 
 If a button, for instance, be rubbed on a table, it will soon 
 become too hot to be held by the fingers. In like manner, 
 the axle of any carriage-wheel soon becomes hot, unless 
 the friction is prevented by grease. 
 
 82. Heat, in its extreme form becomes fire. Thus, if an 
 ungreased wheel be rapidly turned for a long time on its 
 axle, so much heat will be excited that both wheel and 
 axle will burst into a flame. The effects of powerful fric- 
 tion are known to savage nations, among whom it is com- 
 mon to produce fire by rubbing two sticks together. 
 
 83. Two pieces of flint struck together, or^. flint struck 
 hard upon a piece of iron, evolve sparks of fire. By such 
 means, many important purposes are served ; for instance, 
 the discharge of fire-arms. Fire can also be evolved from 
 the common atmosphere, by compressing a quantity of it 
 suddenly in a tube, -at the bottom of which a piece of tinder 
 has been placed. 
 
 84. The evolution of heat by these means, and other 
 circumstances, lead to the conclusion that heat is an 
 element mixed up with the atoms of matter, which it 
 serves to keep at a lesser or greater distance from each 
 other. Thus, as we squeeze the pores of a sponge toge- 
 ther, and disengage the liquid which they held in cohesion, 
 so, when squeezing or rubbing a portion of matter, do we 
 disengage the heat which it retained amongst its compo- 
 nent atoms. 
 
 85. In all cases of the development of heat by pressure, 
 hammering, and friction, the cause is the squeezing to- 
 gether of atoms which nad been kept asunder by the latent 
 fluid, and which fluid must, as a matter of necessity, come 
 forth and make itself sensibly felt or seen. 
 
 69. What is meant by latent heat ? and how detected ? 
 
 70. In what ways is artificial fire produced i 
 
 71. How is this explained ? 
 
 72. What are the two great antagonist powers f 
 
 73. Of what use are these opposing agents ? 
 
REPULSION AND CONDUCT! ON OF HEAT. 
 
 31 
 
 REPULSIVE QUALITY OF HEAT. 
 
 86. Heat, then, is a principle of Repulsion in nature, 
 and in this capacity its uses are as obvious as those of ter- 
 restrial gravitation, to which it apparently acts as a coun- 
 terpoise. The force of attraction is so powerful, that un- 
 less for a counteracting principle of repulsion, all bodies 
 would hasten into close contact ; there would be no air, no 
 water, no vegetable or animal life ; all would be a uniform 
 dead solid mass, and the earth itself might perhaps be re- 
 duced to a small portion of its present bulk. 
 
 MODIFYING QUALITY' OF HEAT. 
 
 87. Heat, by pervading all things, modifies attraction, 
 and, according to circumstances, regulates the density or 
 solidity of bodies. Hence we possess in nature a beauti- 
 ful variety of substances, some solid and hard, like stone 
 and marble ; others soft, or of the jelly form ; a third class 
 liquid, like water; and a fourth kind aeriform, or gaseous. 
 Heat expands most bodies in proportion as it is increased 
 in quantity, and they become solid in proportion as it is 
 withdrawn. Water may thus be either expanded into the 
 form of vapour or steam, or hardened into ice. When 
 withdrawn, the process of cooling is said to take place ; 
 cold being simply a state of abstraction or comparative ab- 
 sence of heat. 
 
 CONDUCTION OF HEAT. 
 
 88. Heat is diffused or communicated by conduction 
 and radiation. When it passes slowly from one portion 
 of matter to another in contact with it, it is said to be con- 
 ducted ; and the process, in scientific language, is termed 
 the conduction of caloric. Metals are the best conductors, 
 then liquids, and, lastly, gases. Gold, silver, and copper, 
 are the best conductors among solids : glass, bricks, and 
 many stony substances, are very bad conductors ; and 
 
 74. How does heat modify bodies ? 
 
 75. What variety in nature is thus explained ? 
 
 76. Name the illustrations. 
 
 77. How is heat diffused ? illustrate this. 
 
32 RADIATION AND PRODUCTION OF HEAT. 
 
 porous spongy substances, as charcoal, hair, and fur, are 
 the worst. 
 
 89. Clothing is generally made of bad conductors, that 
 the heat of the body may not be conducted quickly to the 
 surrounding air. Furnaces, where great heat is required, 
 are built with porous bricks, which are very effectual in 
 preventing the escape of heat, and do not readily commu- 
 nicate the fire to adjacent bodies. 
 
 RADIATION OF HEAT. 
 
 90. Heat is said to radiate, when it is emitted from a fire 
 or from the rays of the sun, and affects the atmosphere or 
 substances at a distance from its source. Radiant heat is 
 absorbed when it falls upon bodies having painted or rough 
 surfaces, such as are presented by bricks and other porous 
 solids, by many kinds of stony matter, and numerous ani- 
 mal and vegetable substances, and makes them wanner 
 as it is taken up. But brilliant and polished metallic 
 surfaces absorb little heat ; they reflect or turn it back 
 again. 
 
 PRODUCTION OF HEAT. 
 
 91. Heat, as already mentioned, can be brought into 
 action in most substances, by percussion and rubbing. It 
 is also produced by the burning of certain inflammable 
 substances, as coal and wood : and in this manner its chief 
 purposes in domestic economy are effected. But the most 
 remarkable source of heat is the sun ; though whether this 
 luminary is a burning mass, throwing off warmth like a 
 common fire or red-hot ball, or produces the effect by 
 some peculiar and unknown operation, is as yet un- 
 certain. 
 
 92. Heat, besides being produced by the sun’s rays, 
 and by the friction and combustion of inanimate substances, 
 is evolved by chemical action, a familiar example of which 
 is observable in fermentation. It is by means of a natural 
 chemical action in connection with the circulation of the 
 
 78. Define and illustrate radiation. 
 
 79. Name the sources of heat. 
 
 80. Give examples of the chemical production of heat. 
 
DISTRIBUTION OF HEAT THE THERMOMETER. 33 
 
 blood, that heat is resident and sustained in most living 
 animals. A stoppage of the circulation of the blood, as 
 every one knows, leads to an absence of animal heat, or 
 a very considerable degree of coldness. On the contrary, 
 quick circulation of the blood, and active muscular motion, 
 as well as rubbing, produce heat. In these cases of mo- 
 tion and rubbing the heat seems to be in a great mea- 
 sure evolved by the momentary compression of the 
 parts. 
 
 GENERAL DISTRIBUTION OF HEAT. 
 
 93. Heat is unequally distributed over the globe. At 
 and near the equator, where the rays of the sun are sent 
 in the greatest degree of directness, the greatest heat pre- 
 vails. In the parts of the earth adjacent to the north and 
 south poles, he transmits his rays so slantingly as to have 
 little power ; and there, accordingly, the air is seldom of 
 a genial mildness. The higher we ascend in the air, the 
 colder it becomes ; the summits of very high mountains 
 are always covered with snow. In penetrating into the 
 body of the earth, after gaining a certain depth, the heat 
 becomes greater in proportion as we descend. The inte- 
 rior of the globe is by many believed to be at a very ele- 
 vated degree of heat, if not in a state of ignition. On the 
 surface, great expanses of sea tend to equalize and temper 
 the degrees of heat and cold in their neighbourhood, and 
 great continents have the contrary effect. 
 
 TEMPERATURE THE THERMOMETER. 
 
 94. The degrees of heat and cold in the atmosphere are 
 called its temperature ; and for ascertaining this correctly, 
 with reference to a standard, a very ingenious instrument 
 has been invented. This is called the thermometer (a 
 word signifying heat measurer). It is a glass tube with a 
 bulb at the bottom, into which mercury or quicksilver is 
 put, with a scale of figures along the tube to mark the 
 lising of the quicksilver. This instrument differs from 
 
 8) . What of the distribution of heat ? 
 
 82. Name causes of its inequality. 
 
 83. What of temperature and its measurement 7 ' 
 
34 
 
 TEMPERATURE-— THE THERMOMETER. 
 
 the barometer, inasmuch as the quicksilver is sealed up 
 close from the air. The atmospheric heat, however, affects 
 the metallic fluid in the bulb, and, according to its warmth, 
 causes it to expand and rise in the tube. The degree 
 of temperature is indicated by the figures to which it as- 
 cends. 
 
 95. Our common thermometer has a graduation from 
 No. 1, near the bulb, to 212, the degree of heat of boiling 
 water. In the scale of figures, 32 is marked as the freez- 
 ing point— that is to say, when the mercury is at the 
 height of 32, water freezes ; and the more it is below that 
 point, the more intense is the frost. 55 is reckoned mode- 
 rate heat, and 76 summer heat, in Great Britain. 98 is 
 the heat of the blood in the average of living men.* 
 
 96. The rising of mercury in the tube of the thermo- 
 meter offers a familiar example of the repulsive power of 
 heat in expanding or dilating bodies. Common experience 
 affords many such examples. A bar of iron is longer and 
 thicker when hot than when it is cold. The iron rim of 
 a wheel slips easily into its place when hot, and gripes or 
 binds fast when it becomes cool. When heated from 32 
 
 * Different nations adopt different graduations in the scale of ther- 
 mometers, which is a fertile source of error and confusion in estimating 
 and comparing the statements of temperature made by scientific men 
 in different countries. Where ever the English language prevails, the 
 graduation of a person called Fahrenheit is generally preferred. By 
 the Germans, Reaumur’s is used; and the French now adopt what 
 they term a centigrade thermometer. In the French centigrade ther- 
 mometer, 0 is the freezing point, and 100 the boiling point ; in Reau- 
 mur’s thermometer, 0 is the freezing point, and 80 the boiling point. 
 Each degree of Reaumur is equal to two and one-fourth of Fahrenheit. 
 [Of course this rule can only be accurately applied by adding the dif- 
 ference of 32° in all c mparisons between these two scales, the zero 
 of Fahrenheit being 32° below the zero of Reaumur.] It was at one 
 time imagined that the greatest cold could make the fluid in the ther- 
 mometer fall only 32° below the freezing point, the place to which it 
 then fell being zero , and therefore the noation commenced at that 
 place. But much greater degrees of cold exist at different parts of our 
 globe in winter, and may be produced artificially, so that the fluid in 
 the stem of the thermometer ofien descends below that point, and is 
 then said to be at so many degrees below zero. Thermometers in 
 common use, however, are not made with a stem and indications below 
 zero. 
 
 84. Describe this instrument. 
 
REPULSIVE ENERGY BOILING WATER. 
 
 35 
 
 to 212, air expands 3-Sths of its volume, alcohol l-9th, 
 water l-22d, and hammered iron l-273d. In these, and 
 all similar instances, the expansion arises from the fluid of 
 heat lodged among the atoms of matter pressing outwards 
 on all sides according as it is excited. 
 
 REPULSIVE ENERGY BOILING WATER. 
 
 97. The repulsive energy of heat is strikingly exem- 
 plified in the explosion of gunpowder. The particles of 
 powder on being ignited, and assuming the form of air, 
 are repelled with a force sufficient to lift immensely 
 heavy bodies, and to project shot to a distance of several 
 miles. 
 
 98. The repulsive energy of heat is also observable in 
 the case of boiling water. When water is placed in a 
 vessel on the fire, its particles become gradually heated. 
 Those nearest the fire are heated first ; being then of a 
 lighter or more expanded nature, they hasten or are re- 
 pelled to the surface, while the more cold and heavy par- 
 ticles sink downwards to the bottom, and are heated in 
 turn. In this manner the process of heating proceeds, 
 until all the particles are of a uniform temperature. 
 There is a limit beyond which, in ordinary circumstances, 
 they cannot be heated. This is when the water boils, and 
 is signified by the bubbling motion of the fluid. Boiling 
 takes place, as above mentioned, when the water readies 
 212 degrees in the thermometer. Nature has designed 
 that water should not become hotter by continued boiling, 
 the application of heat after reaching this point being ex- 
 pended in transforming the liquid into vapour or steam. 
 Hence it is not economical to boil any substance quickly 
 which may onty require exposure to a boiling temperature, 
 as all the heat that may be consumed in producing vapour 
 must cause an unnecessary expenditure of fuel. 
 
 99. The temperature of 212, at which water boils, is 
 only reached when the ordinary atmospheric pressure is 
 
 85. What examples ol the repulsion of heat are cited ? 
 
 86. N ame the illustrations g.ven of the force of repulsion. 
 
 87. How is this illustrated by boiling water ? 
 
 88. Does water become hotter by continuing the boiling ? 
 
VAPORIFIC POINT STEAM. 
 
 Q i» 
 
 ou 
 
 allowed to influence it. If the pressure be diminished or 
 entirely removed by the air-pump, the water will boil or 
 fly off in the vapour form at a much lower temperature. 
 At the summit of high mountains, where the pressure of 
 the atmosphere is less than at the common level of the 
 surface of the earth, water boils at a lower temperature 
 than 212. Thus, at the summit of Mount Blanc, the 
 highest peak of the Alps, which is 15,666 feet above the 
 level of the sea, it has been found that water boils at 187 
 degrees of the thermometer, or 25 degrees below the ordi- 
 nary boiling point. 
 
 100. An interesting experiment may be performed with 
 the view of exhibiting the boiling of water under the influ- 
 ence of a light pressure. Take a thin glass vessel, con- 
 taining a quantity of water ; hold it over a flame till it 
 boils, and then briskly and securely cork it, and remove it 
 from the flame so as to let it cool. It will at first cease to 
 boil, but the vapour will soon be condensed so as to form 
 a vacuum. By this means atmospheric pressure is par- 
 tially removed, and the water again begins to boil. By 
 pouring cold water on the vessel, the vacuum will become 
 greater, and the boiling will become more violent. When 
 at this stage in the process, pour boiling water on the ves- 
 sel, and the vapour will again rise and fill the vacuum, so 
 as to apply the pressure which was originally possessed, 
 and the boiling will cease, but may he again commenced 
 by a second application of cold water. 
 
 VAPORIFIC POINT STEAM. 
 
 101. Different liquids reach the boiling or vaporific 
 point at different degrees of temperature. AEther becomes 
 vapour at 10 1 degrees, alcohol or spirits at 175, water at 
 212, and mercury at 602. 
 
 102. Steam is transparent, colourless, and invisible like 
 the air. The white cloudy-looking matter which is emit- 
 
 sy. What becomes of the superfluous heat ? 
 
 yo. How is the boiling point of liquids affected by the atmospheric 
 pressure ! and how is this shown ? 
 
 91. What simple experiment exhibits the differences ? 
 
 92. What of the boiling point of liquids ? 
 
 93 Des'-nbe s eam, and ihe extent of the expansion. 
 
SPONTANEOUS EVAPORATION. 
 
 37 
 
 ted in the form of vapour, is moisture produced by the 
 partial condensation of the steam in the atmosphere. A 
 cubic inch of water produces almost exactly a cubic foot of 
 steam, or 1728 cubic inches. In proportion as we increase 
 the heat which produces steam, and do not suffer it to 
 escape, so do its repulsive properties become more appa- 
 rent. It will burst the strongest vessels in which it may 
 be generated or confined. When the force with which it 
 expands is carefully regulated, so as to produce motion in 
 machinery, it forms the most powerful engine which man 
 has invented, namely, the steam-engine. 
 
 103. When steam is exposed to cold, it condenses into 
 water, giving out all the heat by which it was produced ; 
 and hence the severe scald it produces when condensed on 
 any part of the body. 
 
 104. Distillation consists in the production of vapour by 
 heat ; the spirituous particles of the liquid are carried off 
 and condensed, by passing through a tube immersed in cold 
 water. 
 
 SPONTANEOUS EVAPORATION. 
 
 105. Spontaneous evaporation is the term usually em- 
 ployed when vapour is produced slowly from a fluid, and 
 without ebullition, as when water disappears from any 
 moist surface. Evaporation, to a lesser or greater extent, 
 is in constant exercise over the whole earth. The ocean, 
 lakes, rivers, fields, are ever yielding up water in this in- 
 visible form to the atmosphere ; and plants and vege- 
 tables, as well as living creatures, are also giving forth ex- 
 halations. 
 
 106. The atmosphere is thus a great receptacle for the 
 moisture of the earth. When the temperature of the air 
 is high, moisture in the atmosphere is not generally per- 
 ceptible near the ground. But when the temperature is 
 low, the air is felt to be damp or humid, in which condi- 
 tion it is unwholesome. Sometimes the humidity becomes 
 
 94. Explain the effects and manner of condensing steam. 
 
 95. What of distillation ? 
 
 96 Explain spontaneous evaporation, wiih examples. 
 
 97 What natural phenomena depend upon it ? 
 
38 
 
 FROST FREEZING POINT. 
 
 so great, that the watery particles in the atmosphere are 
 observable in the form of mist or fog. At night, when the 
 plants lose their heat which they have contracted during 
 the day, the moisture of the atmosphere is condensed upon 
 them in the shape of dew, which, in very cold nights, be- 
 comes hoar-frost. When aqueous vapours are carried 
 high into the atmosphere, or are formed there, they receive 
 the name of clouds. 
 
 107. The invisible steam or vapour constantly arising 
 from the pores in the skin of living animals, and exhaled 
 in breath from the lungs, may be observed to condense into 
 liquid on the insides of panes of glass in windows, and on 
 the walls of apartments. This, however, only occurs when 
 the walls are comparatively cold, or when the outer atmo- 
 sphere affecting the glass is colder than the atmosphere 
 within ; and in proportion to the degree of external cold, 
 so is the condensation and deposition of liquid greater. 
 
 FROST FREEZING POINT. 
 
 108. When the temperature of the atmosphere falls be- 
 low the freezing point, 32, which it does principally from 
 the weakness of the sun’s rays in winter, the phenomenon of 
 frost, or freezing, ensues. Freezing is a process of conge- 
 lation, or properly crystallization, produced by the with- 
 drawal of heat, and by which water assumes the form of 
 ice. When the temperature of the atmosphere rises above 
 the freezing point, the ice melts, and is resolved into its 
 original element. 
 
 109. When the temperature of the atmosphere is be- 
 low the freezing point, the particles of water which are 
 upheld in the clouds are frozen in their descent, and reach 
 the earth in the form of flakes of snow. If this freezing 
 take place after the particles have become united into rain- 
 drops, we have hail instead of snow. When the descend- 
 ing flakes of snow come into a temperature above the freez- 
 ing point as they approach the earth, they are apt to melt, 
 
 98. What familiar example of condensed vapour is cited? 
 99 Explain freezing, snow, hail, sleet, &c. 
 
 100. Describe equilibrium with an example. 
 
EQUILIBRIUM OF TTEAT AND COLD. 39 
 
 and, in such a case, fall in the shape of sleet, which is half- 
 melted snow or hail. 
 
 EQUILIBRIUM OF HEAT AND COLD. 
 
 110. Heat has a constant tendency to preserve an equili- 
 brium in all situations ; and hence its diffusion through 
 nature, and many of the ordinary phenomena in relation to 
 temperature. When we touch a cold substance with our 
 hand, a portion of the heat of the hand rushes into the 
 substance, and leaves the hand so much deficient of its 
 former heat. On the same principle, when we touch a 
 substance which is warmer than the hand, some of the heat 
 rushes into the hand, and renders it hot. When we pour 
 a quantity of hot water into that which is cold, an equal- 
 ization of the two temperatures immediately ensues. When 
 the air at any particular place becomes heated or rarified, 
 it ascends by virtue of its greater lightness, leaving a 
 vacancy which the neighbouring air rushes in to supply. 
 This is one of the chief causes of winds. The same prin- 
 ciple is observable in the case of heated apartments. If 
 the door of a heated room be thrown open, a current of 
 cold air immediately rushes in to supply the deficiency in 
 the rarified atmosphere. 
 
 111. Evaporation is always accompanied by the with- 
 drawal of heat, or production of cold, when no heat is 
 directly applied ; the heat necessary for the production 
 of the vapour is then derived or radiated from surround- 
 ing objects, as is mentioned above in the case of dew form- 
 ing on plants. 
 
 1 12. Examples of spontaneous evaporation producing 
 cold, are familiar to most persons. Bathe the temples 
 with spirits, and the quick evaporation of the fluid will 
 produce a feeling of considerable cold. A current of air, 
 when not loaded with moisture, promotes evaporation ; 
 hence the rapidity with which a wet surface generally 
 dries on a windy day. 
 
 101. How does this explain winds ? 
 
 102. What of evaporation, and how illustrated ? 
 
40 
 
 ARTIFICIAL FREEZING TEMPERATURE. 
 
 ARTIFICIAL FREEZING APPARATUS. 
 
 113. The circumstance of evaporation absorbing heat, 
 and so producing cold, has led to the discovery of a plan 
 by which water may be frozen into ice by simple artificial 
 means, even in a warm room. The apparatus for per- 
 forming the operation consists of an air-pump and its re- 
 ceiver. The receiver is a spacious glass vessel standing 
 with its open end downwards on a flat dish, and which 
 can be exhausted of air by the pump. In the dish a 
 quantity of sulphuric acid is placed, and in the centre of 
 the dish stands a cup or a tripod holding some water. 
 The air being pumped from the receiver, the atmospheric 
 pressure is removed from the water ; evaporation rapidly 
 ensues ; the vapour as it rises is absorbed by the sulphuric 
 acid, by which a vacuum is kept up ; the temperature of 
 the water sinks to the freezing point, and soon exhibits a 
 cake -or mass of ice. A powerful air-pump operating on 
 several receivers will produce six pounds of ice in about 
 an hour. Instead of sulphuric acid, highly toasted and 
 dried oatmeal will answer the purpose of absorption. 
 
 GRADUAL ALTERATION OF TEMPERATURE. 
 
 114. In the great operations of nature, the withdrawal 
 of heat to produce intense cold, and the application of heat 
 to produce great warmth, ordinarily take place gradually. 
 Thus, although water freezes at a temperature of 32, it is 
 some time before frost is completely effectual in changing 
 the aspect and condition of liquid bodies ; and when the 
 temperature rises a few. degrees above 32, after a frost, 
 the ice and snow which have been formed do not vanish 
 immediately ; indeed, ice will remain unthawed for several 
 days after the temperature has risen some degrees above 
 the freezing point. By this slow process, either in the 
 absorption or evolution of heat, the animal and vegetable 
 worlds are not liable to the injury which would ensue 
 
 103. How is artificial freezing explained i 
 
 104. What of changes of temperature ? 
 
EXPANSION IN COOLING DENSITY IN WATER. 41 
 
 from instantaneous changes in the condition of their ele- 
 mentary fluids. 
 
 EXPANSION IN COOLING CRYSTALLIZATION. 
 
 115. It has been observed that heat expands most bodies 
 in proportion as it is increased in quantity. There are 
 also instances in which substances expand in cooling as 
 well as in heating. These substances are water, iron, 
 antimony, bismuth, and many salts, in which solidification 
 takes place by crystallization. In the cooling of melted 
 lead, gold, or silver, the atoms solidify into a dense com- 
 pact mass, leaving no visible pores between them. But 
 when the atoms of water, melted iron, and other sub- 
 stances, solidify, they arrange themselves in the form of 
 crystals, or minute needle-like parts shooting out in all 
 directions, and leaving pores or vacant spaces in the mass. 
 Thus, by the incorporation of pores, the bulk of the body 
 is increased. Crystallization produces beautiful and 
 regularly formed bodies, the forms being obviously the 
 result of certain fixed laws, which, however, are not yet 
 very well defined or understood. 
 
 POINT OF GREATEST DENSITY IN WATER. 
 
 116. The point of temperature at which water is most 
 dense, is 46 degrees (or, according to some authors, 39|). 
 When the temperature is reduced below this point, the 
 volume increases till it reach 32, when the liquid freezes. 
 When the temperature is raised above 40, the voiume 
 increases till it reach the boiling point. Therefore, at any 
 temperature below 40, as at 35, its volume is the same 
 as for a temperature as many degrees above 40, that is, 
 at 45. 
 
 117. When the surface of a body of water, whose 
 temperature exceeds 46, is exposed to a lower tempera- 
 ture, the water at the surface, when it is reduced in the 
 least degree, becomes heavier than the water beneath, and 
 
 10e. What substances expand on cooling? 
 
 10n. What differences in the solidification of bodies ? 
 
 107. How does certain temperature affect the density of water? 
 
42 
 
 EFFECTS OF FROST. 
 
 it consequently descends, its place being now occupied by 
 a stratum of higher temperature, which is n >xt cooled down 
 and descends like the former ; and this process continues 
 till the temperature of the whole mass is reduced to 40 
 degrees. After the temperature has reached this point, 
 the water at the surface becomes lighter than the sub- 
 jacent mass, and it consequently remains stationary. If 
 the temperature be lowered to or below 32, congelation 
 takes place ; and as ice, from its porosity, is lighter than 
 water, it floats on the surface. From this circumstance, 
 the process of congelation is retarded ; for the latent heat 
 or caloric of the water, which is in contact with the lower 
 surface of the ice, evolved during congelation, instead of 
 being quickly carried off by the atmosphere, as it would 
 be were there no ice over it, must pass through the ice, 
 which is a bad conductor of heat ; and this circumstance 
 consequently causes a delay in the process of congelation. 
 Were it not for this evolution of latent caloric during con- 
 gelation, and the buoyancy of ice, rivers would frequently 
 be converted into one solid mass. 
 
 EFFECTS OF FROST. 
 
 118. The circumstance of water being increased in 
 volume by congelation, explains the ordinary phenomenon 
 of the bursting of water-pipes, and other similar occur- 
 rences, during frost. When a vessel of moderate strength 
 is filled with water, its expansion, when it is converted 
 into ice, by exposure to a freezing temperature, causes 
 the vessel to burst. If the vessel is not brittle, but pos- 
 sessed of considerable tenacity, as a leaden water-pipe, 
 the rupture will seldom be observed during the continu- 
 ance of the frost while the water remains in a solid state, 
 but it readily appears when thaw takes place, as the water 
 is then forced out with a velocity corresponding to the 
 vertical height of the column of water in the pipe. The 
 
 108. Explain the phenomenon of freezing water. 
 
 109. What explains the buoyancy of ice ? 
 
 110. What becomes of the latent heat ? 
 
 111. Illustrate the expansion of water by freezing. 
 
EFFECTS OF FROST. 
 
 43 
 
 fissures of rocks, too, are widened by the freezing of the 
 water which may happen to lodge in them before frost ; 
 and this process, therefore, is a powerful agent in the 
 disintegration of rocks. Portions of steep banks, also, 
 from a similar cause, tumble down after thaw; for the 
 moisture in them expands when frozen, and thus rends 
 them to pieces, which, however, during the frost, are 
 bound together as by cement, and fall down whenever 
 thaw dissolves the moisture. On the same principle may 
 be explained the mouldering of soils which are turned 
 over and exposed to the winter frosts. The moisture in 
 the soil is frozen, which rends it into minute portions, 
 which remain firmly united during frost, but crumble 
 down whenever thaw takes place. It may also be fre- 
 quently observed, that footpaths, especially when com- 
 posed of a mixture of earth and gravel, are considerably 
 raised during frost by the expansion of the frozen mois- 
 ture in them, and they consequently become very soft 
 after thaw. The husbandman is well acquainted with 
 these effects, and takes advantage of them by turning up 
 the soil, and thus exposing it to the influence of the winter 
 frosts, which easily produce effects that w'ould otherwise 
 require a great amount of mechanical labour, skilfully ap- 
 plied, to accomplish. 
 
 119. To prove that water expands in freezing, place a 
 phial full of water, and well corked, in a situation exposed 
 to frost. In a short time the phial will be observed to be 
 cracked all over by the expansion. If the cork be left 
 out, it will be observed that an expansion has taken place 
 upwards, and a mass of ice, resembling a cork in figure, 
 has been projected above the mouth of the phial. 
 
 120. As ice thaws, it gives forth the air which it had 
 incorporated in its pores ; and this air, being of a highei 
 temperature than the surrounding water, buoys up bubbles 
 or air globules on the surface. Hence the froth on the 
 surface and margins of lately frozen brooks. 
 
 112. What effects upon the soil? 
 
 113. What simple experiment is cited ? 
 
 1 14. Explain the results of a thaw. 
 
44 
 
 SHRINKING OF BODIES BY HEAT. 
 
 SHRINKING OF BODIES BY HEAT. 
 
 121. Heat has a powerful effect in causing certain 
 bodies to shrink and diminish in volume. This happens 
 with those substances which do not liquify, such as wood 
 and clay. The contraction arises from the heat carrying 
 off the watery particles from the bodies, and thus allowing 
 the constituent atoms to come more closely together. As 
 wood becomes drier, its fibres are sometimes split asunder, 
 so as to emit loud cracking noises, which, in the case of _ 
 household furniture, are ascribed by the ignorant to super- 
 natural causes. 
 
 IGNITION OF BODIES FIRE. 
 
 122. Most bodies which are not convertible into vapour 
 by the application of heat, as in the case of the wood just 
 mentioned, are ignitible, and become luminous in the dark, 
 when heated to 800 degrees, or about 1000 when heated 
 in the day-light. This is observed equally in combustible 
 solids, as charcoal, and in stony or other matters which do 
 not flame. Combustible bodies, when in the state of 
 luminous heat, are said to be on fire, or ignited. 
 
 123. From a state of simple ignition, heat may be aug- 
 mented in intensity to a very high degree, till it exhibit, 
 as is observable in furnaces, a white luminous appearance, 
 at which height of temperature most metals and other sub- 
 stances are melted, and, if not removed and cooled, they 
 are in a certain time destroyed. Fire is active in propor- 
 tion to the combustibility of the substances on which it 
 acts, and to the quantity of atmospheric air which is 
 afforded to it. When fire is deprived of air, it speedily 
 ceases, and is extinguished. 
 
 124. The principal effects produced by heat or caloric 
 have now been mentioned ; namely, repulsion of atoms or 
 expansion, liquefaction, vaporization, evaporation, and igni- 
 tion ; also the effects produced by its withdrawal, namely, 
 
 115. What bodies contract by heat, and why? 
 
 1 16. What of ignition, and at what temperature ? 
 
 1 17. What of combustible bodies ? 
 
DENSITY OF WATER. 
 
 45 
 
 condensation, cold, freezing, and crystallization. A further 
 consideration of the subject, particularly as regards com- 
 bustion, belongs to Chemistry. Under the beads Pneu- 
 matics and Meteorology, some of the leading properties 
 of heat will be recurred to, in connection with atmospheric 
 phenomena. 
 
 ACCIDENTAL PROPERTIES OF MATTER. 
 
 125. While the beautiful and extensive variety of form 
 in bodies — solid, liquid, gaseous and the different modifi- 
 cations of these — are to be traced to the operation of chiefly 
 two great leading principles in nature, attraction and re- 
 pulsion, the peculiar forms or characters which bodies 
 assume from the influence of these or other causes, are 
 usually described as the accidental properties of 
 matter, for they depend on circumstances and are sus- 
 ceptible of variation. The following is a summary of 
 these accidental properties : — Density, Porosity or Rari- 
 ty, Compressibility, Elasticity, Dilatation, Hardness, 
 Brittleness, Malleability, Ductility, and Tenacity. 
 
 DENSITY OF BODIES. 
 
 126. Density signifies closeness of texture, or com- 
 pactness. Bodies are most dense when in the solid state, 
 less dense when in the condition of liquids, and least dense 
 of all when gaseous or aeriform. In this manner the 
 degree of density is in agreement with the closeness of the 
 atoms to each other. The density of bodies may generally 
 be altered by artificial means, as is afterwards mentioned. 
 The metals, in particular, may have the quality of density 
 increased by hammering, by which their pores are made 
 smaller, and their constituent particles are brought nearer 
 to each other. 
 
 127. The more dense in substance that a body is, it is 
 the more heavy or weighty. In speaking of the density 
 of different solid and liquid bodies, the term specific gravity 
 
 118. Name the accidenml properties of matter. 
 
 119. Detine density. ..rid its peculiarities. 
 
4G DENSITY SPECIFIC GRAVITY OF LIQU' 
 
 is used to denote the comparison wmcti is made. Thus, 
 the specific gravity of a lump of lead is greater than an 
 equal bulk of cork ; or the specific gravity of water is greater 
 than that of an equal quantity of spirituous fluid. For 
 the sake of convenience, pure distilled water, at a tempera- 
 ture of 62 degrees, has been established as a standard by 
 which to compare the specific gravity or relative weights 
 of bodies. Water, as the standard, is thus said to be 1. 
 When, therefore, any body, bulk for bulk, is double the 
 specific gravity of water, it is called 2, and so on to 3 and 
 4 times, up to 22 times, which is the specific gravity of 
 platinum, the heaviest known substance. In almost every 
 case of comparison there are fractional parts, and these are 
 usually written in figures, according to the following ar- 
 rangement : Fractional parts are divided into tens, hun- 
 dreds, thousands, and so on. If, in addition, to the figure 
 expressing the main part of the specific gravity, there be 
 one other figure, with a dot or point between them — thus 
 2-5 — the additional figure signifies tenths, and the body is 
 two times and five-tenths parts of a time more dense or 
 heavy than water. If two figures occur — thus, 10-40 — 
 hundredths are signified, and the body is ten times and 
 forty-hundredth parts of a time heavier than water. If 
 there be three figures, thousandths of parts of a time are 
 meant ; if four figures, ten thousandth parts ; and so on. 
 Common air is sometimes taken as a standard with which 
 to compare gases, being a more simple mode of comparing 
 the relative weights of aerial substances. But all the 
 solids and liquids are estimated with reference to water as 
 the standard. 
 
 128. Any body of greater specific gravity than water, 
 will sink on being thrown into water ; but it will float on 
 the surface, if its specific gravity be less than that of 
 water. A body, such as a piece of wood, after floating a 
 certain length of time on water, will imbibe such a 
 quantity of liquid that its specific gravity will be gradually 
 
 120. What is specific gravity ? 
 
 121. How is this quality measured ? 
 
 122. What of fractional parts > 
 
 123. By what standard ate gases weighed ? 
 
SPECIFIC GRAVITY OF LIQUIDS. 
 
 47 
 
 increased, and in the coarse of time it may sink to the 
 bottom. 
 
 129. The density of liquid bodies is liable to be altered 
 by intermixture ; for an increase or diminution of bulk 
 often attends the combination of two different ingredients. 
 Thus, a cubic inch of alcohol, a strong spirituous fluid, 
 mixed with a cubic inch of water, will produce a measure 
 less than two cubic inches ; in mixing strong spirits with 
 water, a diminution of about 4 gallons in the 100 takes 
 place. The diminution in all such cases is occasioned by 
 the mutual penetration of the particles of spirits and water; 
 each liquid fills up the interstices in the other. An ex- 
 ample of a combination of two bodies producing a body 
 larger than the two bodies were individually, is seen in 
 the case of incorporating tin with lead, by which an in- 
 crease of bulk takes place. 
 
 130. Water is of a greater density or specific gravity 
 than spirits ; consequently, spirits are apt to float on the 
 surface of water, unless the two liquids be well mixed, so 
 as to produce a mutual incorporation of parts. A body 
 which will float on water may sink in spirits. Although 
 water has thus the greatest power of buoying up, it is in 
 ordinary language called weak ; and spirits, the lighter 
 they are, are called the more strong. A knowledge of 
 this relative power of buoying up has led to methods for 
 discovering the strength of spirits. Small hollow glass 
 beads, marked of different weights, are thrown into spirits ; 
 and the lighter, that is, the stronger, the fluid, the less 
 weight of bead will be sustained. An instrument, con- 
 sisting of a loaded hollow brass ball, and a rod with a 
 graduated scale of figures rising from it, called a hi/dro- 
 me'er, answers the same purpose. The ball, on being 
 let into the fluid, sinks in proportion to the lightness of the 
 spirits, and the degree of strength is indicated by the 
 figure to which the liquid rises on the graduated scale. 
 There is a certain point of strength called propf. below 
 
 124. Wha varieties in the density of bodies occur on mixture ? 
 
 125. How is i he strength ot spiri s resied? 
 
 126. Describe a hydrometer , and its use. 
 
48 
 
 SPECIFIC GRAVITY OF SOLIDS. 
 
 which all liquids of a spirituous nature are legally 
 prohibited. 
 
 131. In making calculations of the strength and specific 
 gravity of spirits, by the above or any other means, atten- 
 tion must be paid to the degree of temperature of the fluid. 
 Heat expands the liquor, and renders it lighter ; all spirits 
 are therefore more bulky, in proportion to their weight, in 
 summer than in winter, and also apparently stronger, not 
 really so. A cubic inch of brandy will weigh 10 grains 
 less in summer than in winter; and what measures 33 
 gallons of spirits in summer, will measure only 32 in 
 winter. Thus, if a person purchase spirits in winter, by 
 measure only, and sejl them again in summer, by measure 
 only, he will profit to the extent of one gallon in 32. To 
 effect sales of spirits on a principle of fairness, both to 
 buyer and seller, the fluid must not only be measured, but 
 its specific gravity established in connection with its de- 
 gree of temperature. The standard heat of water, by 
 which the specific gravity of liquids is compared, is, as 
 already mentioned, 62 degrees, being the medium tempe- 
 rature all over the globe. If, therefore, spirits be above 
 62 in temperature, a corresponding deduction must be 
 made from their estimated and apparent strength. 
 
 132. The relative specific gravity of solid bodies of 
 precisely the same volume, is simply ascertained by 
 weighing them in opposite scales of a balance, and the 
 heavier of the two is the more dense, or has the greater 
 specific gravity. This process, however, will not deter- 
 mine the true intrinsic value or character of any given 
 substance. For instance, if a man were to bring a piece 
 of metal to a goldsmith for sale, calling it a pound of gold, 
 and the goldsmith put it in a balance and found that it 
 really weighed a pound, there would be no certainty that 
 the mass was wholly gold ; it is possible that a portion of 
 it might be lead, silver, copper, or any other inferior metal. 
 How, then, should this difficulty be adjusted ? All such 
 questions, in relation to the specific gravity of bodies, are 
 
 127. What of proof spirits t 
 
 128. How are the effects of temperature manifest ? 
 
 129. How is the relat.ve specific gravity of bodies tested! 
 
POROSITY COMPRESSIBILITY. 
 
 49 
 
 solved by having recourse to the hydrostatic balance, an 
 instrument which acts upon a principle discovered by 
 Archimedes, an ancient philosopher. The principle is, 
 that the specific gravity of any solid may be determined 
 by the bulk of water which a similar solid of the same 
 weight displaces when plunged into it. The goldsmith 
 above mentioned, by knowing, in the first place, how 
 much water a pound of pure gold displaces, would try 
 the metal brought to him by that standard ; in other 
 words, he would see whether it displaced the quantity of 
 water proper for a pound of gold ; if it displaced more 
 than what was proper, then it contained alio} 7 , was too 
 bulky for a pound weight, and would be rejected accord- 
 ingly- 
 
 POROSITY. 
 
 133. Porosity is the quality opposite to density, and 
 means that the substance to which it is applied is porous; 
 that is, full of small pores or empty spaces between the 
 particles, and that the body is comparatively light. The 
 instances of porosity are numerous in every department of 
 the material world, but those which are connected with 
 animal and vegetable bodies are the most remarkable. 
 Bone is a tissue of pores or cells, and, when seen through 
 a microscope, may be said to resemble a honeycomb. 
 Wood is also a tissue of cells or tubes. If the end of a 
 cylinder of straight wood be immersed in water, whilst the 
 other is forcibly blown into, the air will be found to pass 
 through the pores of the wood, and rise in bubbles through 
 the water. When a gas is comparatively light, it is said 
 to be rare, or to possess rarity. 
 
 COMPRESSIBILITY. 
 
 134. By compressibility is meant that quality in virtue 
 of which a body allows its volume to be diminished, 
 without the quantity or mass of matter being diminished. 
 It arises, of course, from the the constituent particles being 
 
 130. What of the hydrostatic balance ? 
 
 131. Define poros ty with examples. 
 
50 
 
 ELASTICITY. 
 
 brought nearer to each other, and is effected in various 
 ways. All bodies are less or more capable of being 
 diminished in bulk, which is a conclusive proof of tneir 
 porosity. 
 
 135. Liquids are less easily compressed than solid 
 bodies ; nevertheless they, to a small extent, yield, and go 
 into smaller bulk by great pressure. The water at the 
 bottom of the sea, by being pressed down by the superin- 
 cumbent water, is more dense or compact than it would 
 be at the surface. 
 
 136. Atmospheric air and gases are much more easily 
 compressed than liquids, or even than many solids. Air 
 may be compressed into a hundredth part of its ordinary 
 volume. When at this state of compression, it has a great 
 tendency to expand and burst the vessel in which it is 
 confined. This is exemplified in the air-gun, in which a 
 hundred pints of air are pressed into the size of one pint ; 
 and it is the force with which the confined and compressed 
 air hastens to resume its former bulk, that causes the shot 
 to be projected. When air is compressed to a much 
 greater degree than the hundredth part of its ordinary 
 bulk, the particles of matter of which it is composed col- 
 lapse, and become so dense as to form a liquid of an oily 
 nature ; in which case, as in all other instances of com- 
 pression, the heat which held the particles in suspension 
 is forced out, and is felt to give warmth to the instrument 
 or vessel in which the operation takes place. 
 
 ELASTICITY. 
 
 137. Some bodies have the power of resuming their 
 former volume or shape when the force which diminished 
 it is withdrawn. This quality is termed elasticity. Steel 
 is one of the most elastic of metallic bodies, but its elasti- 
 city is not nearly so great as that of India-rubber, which, 
 though twisted, drawn out, or compressed in d iff rent 
 ways, always resumes its original form. The aeriform 
 
 132. What of compressibility, and i f univeis: lity ? 
 
 133. What of this property in air. a id its effec » i 
 
 134. What of the extreme compression of air 1 
 
 135. Define elasticity with examples. 
 
HARDNESS, BRITTLENESS, MALLEABILITY. 
 
 51 
 
 fluids, such as atmospheric air, and the gases, are all ex- 
 ceedingly elastic ; and so are liquids, such as water, but 
 to a smaller extent. 
 
 DILAT ABILITY. 
 
 158. Dilatability is that quality of bodies by which 
 they are enabled to be expanded or enlarged in their di- 
 mensions, without any addition being made to their sub- 
 stance. 
 
 HARDNESS. 
 
 139. Hardness is the quality which is the opposite of 
 softness, and does not depend so much on the density of 
 the substance, as the force with which the particles of a 
 body cohere, or keep their places. For instance, glass is 
 less dense than most of the metals, and it is so hard that 
 it is capable of scratching them. Some of the metals are 
 capable of being made either hard or soft. Steel, when 
 heaLed to a white heat, and then suddenly cooled, as by 
 immersion in water, becomes harder than glass ; and when 
 cooled slowly, it becomes soft and flexible. 
 
 BRITTLENESS. 
 
 140. Brittleness is that quality by which bodies are 
 capable of being easily broken into irregular fragments ; 
 and it belongs chiefly to hard bodies. Iron, steel, brass, 
 and copper, when heated and suddenly cooled, become 
 brittle. 
 
 MALLEABILITY. 
 
 141. Malleability is the quality by which bodies are 
 capable of being extended by hammering. Some of the 
 malleable metals are gold, silver, copper, zinc at the tem- 
 perature of boiling water, lead, iron, and some others. 
 Some of the metals possess the opposite quality of brittle- 
 
 136. Explain dilatability. 
 
 137. Upon what does hardness depend ? examples. 
 
 138. Explain brittleness, with examples. 
 
52 SUMMARY OF PROPERTIES IN BODIES. 
 
 ness. Gold is the most, malleable of all metals, and it 
 may be hammered so thin as to be translucent, or perme- 
 able to light. 
 
 DUCTILITY. 
 
 142. By ductility is understood that property by which 
 metals may be drawn into wire. The most malleable 
 metals are not the most ductile. Tin and lead may be rolled 
 into thin leaves, but cannot be drawn into wire. The 
 most ductile metal is platina, which can be drawn into 
 Avire as fine as the threads of a cobweb. 
 
 TENACITY. 
 
 143. Tenacity is the quality by which bodies are not 
 easily torn asunder. Steel is the most tenacious of all 
 substances ; a wire of this metal, the hundredth of an inch 
 in diameter, will support a weight of 134 lbs. ; while one 
 of the same size of platina will sustain only 16 lbs., and 
 one of lead only 2 lbs. 
 
 SUMMARY OF PROPERTIES. 
 
 We have now presented a definition of all the proper- 
 ties or qualities usually ascribed to matter, and, for the 
 sake of fixing them in the mind of the pupil, we shall 
 here shortly recapitulate them. 
 
 144. The essential properties of matter are Impenetra- 
 bility, Extension. Figure, Divisibility, Inertia, and Attrac- 
 tion. Attraction is an essential property only when un- 
 der the character of attraction of gravitation, or terrestrial 
 attraction, as it is sometimes called. When exhibited 
 under its supposed modifications in relation to cohesion, 
 capillary attraction, chemistry, magnetism, and electricity, 
 it is not an essential, but an accidental property, for it acts 
 only according to circumstances. These modifications 
 may be shortly styled Accidental Varieties of Attraction. 
 
 139. What of malleability and ductility ? 
 
 140. What of tenacity, with an example ? 
 
 141. Recapitulate the summary. 
 
MOTION AND MATTER. 
 
 53 
 
 1 15. The repulsive or expansive quality in matter is 
 termed Heat, or Caloric. 
 
 ■ 14H. The accidental properties of matter are Density, 
 Porosity or Rarity, Compressibility, Elasticity, Dilatation, 
 Hardness, Brittleness, Malleability, Ductility, and Tena- 
 city. 
 
 MOTION AND FORCES— GENERAL EXPLANA- 
 TIONS. 
 
 147. Motion is the changing of place, or the opposite 
 of rest. 
 
 148. Matter, according to the definitions which have 
 been given of its properties, is substance devoid of life 
 and volition, and which is perfectly passive, or inert. It 
 has been described as possessing the property of inertia, 
 and in this respect it is said to possess an unwillingness 
 or reluctance to move ; but these phrases are only figura- 
 tive, and are used for the purpose of conveying a forcible 
 idea of the passiveness of its character. It is also, in 
 consequence of this property of inertia, or passiveness to 
 submit to any condition to which it is subjected, that a 
 body, when once in motion, will continue to move conti- 
 nually with the same velocity and in the same direction, 
 till it be disturbed by some external cause. 
 
 149. Any instance of rest which comes under our ob- 
 servation, is only rest in a relative , not an absolute, sense ; 
 that is, it is rest as relates to the earth, but not rest as re- 
 lates to the universe ; for though the stone which falls to 
 the ground lies at rest on the earth, the earth is always in 
 motion, and therefore the stone is no more at rest than 
 the insect which sits upon a moving wheel is at rest. 
 Hence, in speaking of bodies coming apparently to a state 
 of rest, we must always recollect, that it is only relative, 
 not positive or absolute rest. It is supposed that there is 
 no such thing as absolute rest in creation. All the planets 
 
 142. Define motion and matter. 
 
 143. What is ascribed to inertia ? 
 
 144. What is said of absolute rest ? 
 
54 
 
 MOTION IN MATTER. 
 
 are in motion round the sun ; the sun itself has a motion 
 on its own axis ; it is also believed by many astronomers 
 that the sun has an onward or progressive motion in 
 space, besides its rotary movement ; and thus, perhaps, 
 revolves round some distant centre, with all its planets in 
 its train. 
 
 150. Common experience would lead to the conviction 
 that rest is more natural for matter than motion : but this 
 conviction is founded on a limited consideration of circum- 
 stances. The reason why we see ordinary moving bodies 
 coming to a state of rest — such as a wheel stopping after 
 having been whirled on its axle, a ball stopping after roll- 
 ing on the ground, or an object falling to the earth after 
 being thrown upwards — is, that they are sooner or later 
 arrested in their progress by the earth’s attraction or their 
 own gravity, by the friction or rubbing against some other 
 body, or by the opposition presented to them by the at- 
 mosphere. Except for these three pr vailinc causes of 
 impediment and stoppage,' all bodies once set in motion 
 would go on moving for ever. Taking this expanded 
 view of things, and dismissing the erroneous impressions 
 arising from what is obvious only to pur limited experi- 
 ence, we find that there is nothing more remarkable in 
 perpetual motion than in perpetual rest. 
 
 151. It is only, however, in the great works of creation, 
 or the heavenly bodies, that perpetual motion is observ- 
 able. The planetary bodies are under the ever-acting 
 impulses of centrifugal and centripetal forces, and are not 
 impeded by friction, or by the atmosphere, for they move 
 in space, or in a comparative vacuum. Many ingenious 
 attempts have bi en made to produce perpetual motion on 
 mechanical principles in terrestrial objects, but they have 
 all necessarily failed, as no human effort can destroy gravity 
 in bodies, or altogether prevent friction in movement. 
 
 152. In regard to bodies on the earth, of which a state 
 
 145. Why does rest seem to be the natural state of matter ? 
 
 146. What agencies obstruct motion? 
 
 147. What examples have we of perpetual motion? 
 
 148. Why have all experiments failed to discover perpetual motion 
 in machinery ? 
 
FORCES OR TOWERS. 
 
 55 
 
 of rest is the ordinary condition, motion is produced by 
 ceriain agencies, or impelling causes, either belonging to 
 the phenomena of nature or to art. The property of ca- 
 pillary attraction causes a motion in liquids under certain 
 circumstances; the winds blow, and cause motion; rivers, 
 in flowing down their channels, and the action of the tides, 
 likewise produce motion ; thus, there exist many natural 
 causes of motion, which are taken advantage of by man 
 in the economy of arts and manufactures. Motion in the 
 animal economy is produced by a principle of life ; but 
 of the nature of this kind of motion mankind are ignorant, 
 and nothing here requires to be said regarding it. The 
 causes of motion which have to engage our attention are 
 those which consist o i forces, whether natural or artificial, 
 and which forces have the property of impelling inani- 
 mate objects from a state of rest to a state of motion, of 
 stopping them when in motion, or of altering the character 
 of their motion. These forces are also called powers. 
 
 153. Motion, according to the mode in which the force 
 acts, is susceptible of innumerable variations. According 
 as the moving body is affected, it may move rapidly or 
 slowly ; proceed in a straight line, turn in a circle or 
 curve ; it may move with uniform or irregular speed, or 
 be retarded or accelerated. The body may also move 
 upon or in respect of another body which is also moving. 
 Some of these peculiarities in motion will immediately 
 engage our attention ; meanwhile. it has to be explained, 
 that, for the sake of convenience in language, and accu- 
 racy in the application of terms, certain words are used 
 to define the nature of motion in bodies, and the forces 
 affecting them. 
 
 154. Motion is said to be common to two or more bodies 
 when they move in contact or together ; or when, though 
 not in contact, they are carried along in a similar manner, 
 and with the same velocity ; that is, when they have a 
 motion in common, or participate in the same motion. 
 Motion is said to be absolute, w hen a body actually moves 
 
 149. What phenomena of motion are produced in nature? 
 
 150. What of the varieties of motion ? 
 
 151. Define common motion. 
 
MOMENTUM. 
 
 56 
 
 from one point of space to another, or when it moves to- 
 wards, or when it passes, another which is at rest. There- 
 fore, setting aside the idea of the earth moving, we should 
 say that a vessel moving on the sea has an absolute mo- 
 tion, while the land is fixed or stationary. Motion is said 
 to be relative-, when the motion of one moving body is 
 considered in reference to that of another movjng body. 
 Thus, if two bodies move in the same direction, their rela- 
 tive motion is the difference of their motions ; if they 
 move in opposite directions, it is the sum of their separate 
 motions. 
 
 155. When a force, applied to any material object, is 
 resisted or counteracted, so that no motion ensues, it is 
 called a pressure ; and forces so counteracted are said to 
 balance each other, or to be in equilibrium. 
 
 156. The degree of speed in the motion of bodies is 
 called velocity. Velocity is measured by the space or 
 distance passed over, with an invariable motion, and in a 
 given time, as one second. Thus, if a body, in one second, 
 with an invariable motion, pass over twenty feet, its velo- 
 city is said to be twenty feet per second. 
 
 157. When a motion is invariable, it is said to he uni- 
 form ; if it be gradually increasing, it is said to he accel- 
 erated ; and if it gradually decrease, it is said to be re- 
 tarded. A force is said to be an accelerating or retarding 
 force, according as it produces an accelerated or retarded 
 motion. 
 
 15b. Forces are either instantaneous or continued. The 
 former is an impulse, like a stroke ; the latter acts without 
 intermission. When a continued force remains always 
 of the same intensity, it is called a constant force. Other 
 continued forces are said to be variable. 
 
 159. A body, in moving, possesses a force which is 
 called its momentum, or motal force. Momentum is very 
 different from velocity. A light body and a heavy body 
 may move at the same velocity, but the momentum of the 
 light body will be small in comparison with that of the 
 
 152. Define relative and absolute motion. 
 
 153. Define pressure, balance, velocity, &e. 
 
 J54. Name varieties in velocity ? 
 
PHENOMENA OF FALLING BODIES. 
 
 57 
 
 heavy one. The light one, on coming to a state of rest, 
 will perhaps fall harmlessly on the ground, while the 
 other, by its momentum, will strike forcibly on the earth, 
 or destroy any object which opposes it. Momentum is 
 proportionate to the mass and velocity of bodies, and, by 
 multiplying the weight by the number of feet moved over 
 per second, we find that the momentum is the product. 
 Thus, if a body of twelve ounces move with a velocity of 
 twenty feet per second, its momentum is (twelve times 
 twenty) two hundred and forty. In ordinary language, 
 the term impetus is used to signify the violent tendency 
 of a moving body to any point. 
 
 Before entering upon a consideration of motion as pro- 
 duced by ordinary forces, it will be appropriate to describe 
 the effects produced upon bodies when simply falling — 
 that is, moving downwards towards the earth, when the 
 supports which upheld them are withdrawn. 
 
 THE PHENOMENA OF FALLING BODIES— WEIGHT. 
 
 160. Attraction, as already explained, is a force inherent 
 in nature, by which particles and masses of matter are 
 drawn towards each other. This force, it has also been 
 stated, increases in proportion to the quantity of matter 
 which the attracting body contains, and it also increases as 
 th’e^bodies approach each other. 
 
 161. Further, it has been mentioned that this powerful 
 and subtile quality in matter is the cause of the falling or 
 drawing of bodies downwards towards the earth, and thus 
 produces what is termed weight or gravity. Gravity, 
 then, is simply the tendency which any substance has to 
 press downwards in obedience to the law of attraction, as 
 exemplified in the phenomena of bodies failing from 
 heights to the ground, when the supports which upheld 
 them are removed. 
 
 162. All falling bodies tend directly towards the centre 
 of the earth, in a straight line from the point where they 
 are let fall. If, then, a body be'let fall in any part of the 
 
 155. What of momentum ? 
 
 156. Define gravity, and illustrate. 
 
58 
 
 PHENOMENA OF FALLING BODIES. 
 
 world, the line of its direction will be perpendicular to the 
 earth’s centre. Consequently, two bodies falling on op- 
 posite sides of the earth, fall towards each other. 
 
 164. Suppose any h dy to be disengaged from a height 
 opposite to us, on the other side of the earth, its motion 
 in respect to us would be upward, while the downward 
 motion from where we stand, would be upward, in respect 
 to those who stand opposite to us, on the other side of the 
 earth. 
 
 104. In like manner, if the falling body be a quarter, 
 instead of half the distance round the earth from us, its 
 line of direction would be directly across, or sidewise, 
 that is, at right angles with the lines already supposed. 
 
 165. It will be obvious, therefore, that what we call up 
 and down are merely relative terms, and that what is down 
 in respect to us, is up in respect to those who live on the 
 opposite side of the globe. Consequently, down every- 
 where means towards the centre of the earth, and up sig- 
 nifies from the centre of the earth. 
 
 166. The velocity or rapidity of every falling body is 
 uniformly accelerated, or increased, in its approach towards 
 the earth, from whatever height it falls, if the resistance 
 of the atmosphere be not reckoned. 
 
 167. If a rock be rolled from the summit of a steep 
 mountain, its motion is at first slow and gentle, but .^s it 
 proceeds downwards, it moves with perpetually increased 
 velocity, seeming to gather fresn speed every moment, 
 until its force is such that every obstacle is overcome; 
 trees and rocks are dashed from its path, and its motion 
 does not cease until it has rolled to a great distance on the 
 plain. 
 
 148. The same principle of increased velocity in bodies, 
 as they descend from a height, is illustrated by pouring 
 treacle, honey, or any thick syrup, from an elevated ves- 
 sel. The bulky stream, which is perhaps two inches in 
 diameter where it leaves the vessel, is reduced to the size 
 of a straw or a thread on reaching its destination ; but 
 
 157. What of the antipodes, and other positions ! 
 
 158. How are we to unders and down and up > 
 
 159. How is momentum and velocity increased, and why ? 
 
VELOCITY OF FALLING BODIES. 
 
 59 
 
 what it wants in bulk is made up in velocity, for the small 
 thread-like stream at the bottom will fill a vessel just as 
 soon as the large and slow moving stream at the outlet ; the 
 velocity is indeed so great, that the stream has not time to 
 sink at once into the mass below, but falls in overlaying 
 folds. 
 
 1(59. From the same principle, a person may leap 
 from a chair without danger; but if he jump from the 
 house-top, his velocity becomes so much increased, be- 
 fore he reaches the ground, as to endanger his life by the 
 fall. 
 
 170. It is found by experiment, that the motion of a fall- 
 ing body is increased, or accelerated, in regular arithmetical 
 progression. In other words, in every second of time during 
 its descent, it acquires an additional rate of speed, the rate 
 regularly increasing by the accumulation of the preceding 
 additions. 
 
 171. It is ascertained that a dense or compact body, wh en 
 fallingfreely,passesthroughaspace of 10 feet 1 inch during 
 the first second of time. Leaving out the odd inch for the 
 sake of even numbers, we find that the space fallen through 
 in a given time is determined by the following arithmetical 
 computation. 
 
 173. Ascertain the number of seconds which a body oc- 
 cupies in falling. Take the square of that number (that is, 
 the number multiplied by itself), and multiply the square 
 by Id, which is the number of feet fallen during the first 
 second, and the result is the amount of feet which the body 
 altogether falls. For example, if a ball occupy 3 seconds 
 in falling, we take the square of 3, which is 9 ; then we 
 multiply 9 by Id, which gives 144 as the result, and that 
 is the number of feet fallen. Again, if we find that the ball 
 occupy 4 seconds in falling, we take the square of 4, which 
 is Id, and multiply 16 by 1 0, the result is 256, which is the 
 number of feet fallen. And so on, always following the same 
 rule of computation. 
 
 1G0. What examples are given ? 
 
 16], In what proportion does velocity increase ? 
 162. Give examples of the calculation 
 
VELOCITY O' FALLING BODIES. 
 
 CO 
 
 17.3. It is not always easy, by the above mode of calcu- 
 lation, to arrive at a correct result as to the height fallen by 
 bodies, and all that can be expected is an approximation 
 to a true result. This arises from bodies being of different 
 bulks, and receiving different degrees of opposition from 
 the atmosphere in their descent. It is a common suppo- 
 sition that large and heavy bodies fall more quickly than 
 small and light ones. This opinion, which was maintained 
 even by philosophers, until Galileo rectified the mistake, 
 perhaps originates in the error of confounding momentum 
 with velocity. Be this as it may, it is now an ascertained 
 truth in science, that all bodies, of whatever density, fall 
 with the same velocity. Thus, a ball containing a pound 
 of lead falls with the same velocity as a bail containing an 
 ounce. This equality in the rate of falling is, however, 
 disturbed by the quality of figure and bulk of bodies. A 
 solid ball of gold will fall more quickly than the same quan- 
 tity of gold beat out into a thin leaf, because in the case of 
 the leaf the resistance from the atmosphere on a large 
 surface impedes the descent. Thus the atmosphere pre- 
 vents bulky and porous substances from falling with the 
 same velocity as those which are compact. 
 
 174. If the atmosphere were removed, all bodies, whether 
 light or heavy, large or small, would descend with the same 
 velocity. This fact is ascertained by experiments performed 
 with the air-pump. 
 
 1 15. When a piece of coin, for instance a guinea, and 
 a feather, are let fall at the same instant of time, from a 
 hook which has held them at the top of the exhausted re- 
 ceiver of an air-pump, they are observed to fall at an equal 
 rate, and to strike the bottom at the same moment. Hence 
 it is demonstrated, that were it not for the resistance of the 
 atmosphere, a bag full of feathers, and one of coins, would 
 fall from a given height with the same velocity, and in the 
 same space of time. 
 
 1/6. It has been stated that the attraction of gravitation 
 
 163. What mistake results from confounding momentum with ve- 
 locity? 
 
 164. How is it affected by bulk and figure, and why ? 
 
 165. What of the air-pump ? 
 
THE CENTRE OF GRAVITY. 
 
 61 
 
 increases in proportion to the quantity of matter which the 
 attracting body contains. Thus, the mass of our planet, 
 the earth, exerts a force of attraction which produces the 
 phenomena of weight, and the falling of bodies with a cer- 
 tain velocity. 
 
 177. In consequence of the different size and density 
 of the sun and planetary bodies, attraction is much stronger • 
 in some of them than others, and consequently the weight 
 of bodies differs in each. On the surface of the sun, our 
 pound weight would weigh upwards of 27 pounds, and a 
 body would fall upon it 434 feet the first second. On the 
 surface of Jupiter, our pound would weigh about 2 pounds 
 4 ounces. And on the surface of the moon, our pound 
 would weigh only the fifth part of a pound. 
 
 178. As a body in descending to the earth receives in- 
 creasing accessions to its velocity during every successive 
 second, so when a body is projected upwards from the 
 surface of the earth, its velocity decreases in the same pro- 
 portion, till it comes to a state of momentary rest, when it 
 instantly begins to descend with a gradually increasing 
 velocity, which at any point in the descent is equal to its 
 velocity at the same point when ascending. In this cal- 
 culation, however we omit the influence of the atmosphere, 
 which would cause the final velocity in the descent to be 
 less than the original velocity with which the body was 
 projected upwards. 
 
 THE CENTRE OF GRAVITY. 
 
 179. Terrestrial gravitation, as already explained, does 
 not act on the mere surface of bodies, or according to their 
 bulk, but is exerted in reference to all the particles or 
 atoms individually which compose the mass of a body. 
 As the earth is nearly of a spherical form, its attraction is 
 the same nearly as if it proceeded entirely from the centre. 
 On account of the great size of the earth, compared with 
 that of any ordinary body at its surface, its attractive force 
 
 166. How is gravitation increased by quantity of matter? 
 
 167. What of weight on the different planets ? 
 
 168. What of the velocity of bodies thrown upward ? 
 
62 CENTRE OF GRAVITY. 
 
 acts in straight lines, sensibly parallel, proceeding from the 
 earth’s centre. In the case of liquids, in which the atoms 
 slightly cohere, the atoms have liberty to spread them- 
 selves over the earth, and to seek the lowest situation for 
 repose. In the case of solids, a different operation is ob- 
 servable. In them, the particles of matter stick so closely 
 together, that they are not at liberty to obey the law of 
 gravitation individually, but rally, as it were, round a 
 common centre, upon which the force of attraction may 
 be considered to act for the general behoof. This centre 
 is called the centre of gravity, the centre of inertia, or 
 the centre of parallel forces. 
 
 180. Every solid body or dense mass possesses a centre 
 of gravity, which is the point upon or about which the 
 body balances itself, and remains in a state of rest, or 
 equilibrium, in any position. 
 
 181. The centre of gravity may be described as a point 
 in solids which always seeks its lowest level, in the same 
 manner that the lowest level is sought for by water ; for it is 
 only by propping up the body, that the centre of gravity is 
 prevented from displaying the same mode of action. 
 
 182. The centre of gravity in round, square, or other 
 regular shaped bodies, oh uniform density in ail their 
 parts, is the centre of these bodies. 
 
 183. When a body is shaped irregularly, or when there 
 are two or more bodies connected, the centre of gravity is 
 the point about which they will balance each other. 
 
 184. Any square or angular body 
 which we may place on the ground, 
 will remain stationary, or safely at 
 rest, provided an ideal 'ine, drawn 
 from its centre of gravity, and pass- 
 ing to the ground in a direction per- 
 pendicular to the earth’s surface, fall 
 within its base, as in figure 1. A 
 point below A is the centre of gravity ; 
 and from that point the line of direc- 
 
 Fig. t. 
 
 169. What is meant by the cenire of gravity, & c. ? 
 
 170. Describe its variation in different bodies 
 
CENTRE OF GRAVITY. 
 
 6-1 
 
 lion goes downward to B, which is within the edges of the 
 base. An object of this form, and so placed, will stand. 
 
 Fig. 2 . 185. If the line of direction from 
 
 the centre of gravity fall without the 
 outer edge of the base, as in figure 2 , 
 from A to B. then the object will not 
 remain balanced on its base ; it wi i 
 fall over, and attain some position in 
 which the line of direction falls within 
 the boundary of the base on which it 
 stands. 
 
 188. By keeping this simple prin- 
 ciple in view, stability and safety will generally be secured 
 m the erection of objects of art. such as houses, monu- 
 mental edifices, spires, and obelisks, as well as in the lad- 
 ing of coaches, carts, and other vehicles, and the piling 
 of timber or any kind of goods in heaps. In every 
 instance, the base ought to be sufficiently broad to admit 
 of the line of direction from the centre of gravity falling 
 within it. 
 
 187. A small degree of experience -seems to point out 
 the propriety of erecting all kinds of structures with a 
 base wide enough to secure stability ; nevertheless, in 
 opposition both to experience and the simple principles 
 of science, we often find that stage-coaches are laden in 
 such a manner that their centre of gravity is liable to too 
 great a change of position, and that they are overturned, 
 to the personal injury, and even loss of life, of the pas- 
 sengers. The error in these instances consists in raising 
 the centre of gravity too high. At first, perhaps, the 
 centre of gravity is so comparatively low, that, in the case 
 of swaying to a side, the line of direction would fall within 
 the edge of the wheel, and no danger would ensue ; but it 
 is common to go on piling masses of goods or luggage, or 
 placing a number of passengers, on the roof of the vehicle, 
 so that the centre of gravity becomes considerably elevated ; 
 
 171. What of the line of direction ? 
 
 172. Wha: practical examples are cited ? 
 
 173. Explain the upsetting of a vehicle. 
 
CENTRE OF CR WTTY. 
 
 F s ! so high, indeed, that when the 
 
 carriage is swayed or jolts to 
 one side, the line of direction 
 is thrown beyond the wheel, 
 and the vehicle will conse- 
 quently fall over. In the an- 
 nexed cut, figure 3, a loaded 
 vehicle is represented cross- 
 ing an inclined plane, or we 
 may suppose that its wheel 
 on one side has come in con- 
 tact with a stone S. which has raised it above the level of 
 the other wheel, so as to incline the body of the vehicle 
 very considerably from the horizontal. The centre of 
 gravity is represented in two different positions, a lower- 
 with the line of direction L C, and a higher with the line 
 of direction U C. Had the vehicle not been high laden, 
 the line of direction would have remained as L C, and as 
 it falls within the wheel or base, the vehicle would have 
 maintained its balance, but being now laden to a consider- 
 able height, the line has risen to about the place where it 
 is marked descending from C to U, beyond the base; con- 
 sequently the vehicle must overturn. 
 
 188. Children who have not gained 
 experience of the tendency which bodies 
 have to be overturned when their centre 
 of gravity is wrong placed, frequently 
 receive falls and personal injuries by 
 tumbling from pieces of furniture. In 
 the annexed cut, figure 4, a little boy is 
 represented standing on a chair, and 
 leaning over its back. So long as the 
 line of direction from A falls within the 
 base at B. he is safe; but if he lean 
 much farther over, and cause the line to 
 fall beyond the base, to C, he must 
 
 Fig 4. 
 
 174. Explain (he drawing. 
 
 175. What other examples are cited ? 
 
CENTRE OF GRAVITY. 
 
 G5 
 
 183. Drunken men, who reel to and fro, are observed 
 to have considerable difficulty in preserving their erect 
 position, in consequence of the perpetual disturbance of 
 their centre of gravity. Persons who feel themselves fall- 
 ing, instinctively throw out an arm, or try to lean in an 
 opposite direction, so as to recover their balance. For 
 the same reason, rope-dancers, in trying to balance them- 
 selves, use a pole loaded at each end with a hall of lead ; 
 and by inclining the pole in the direction opposite to that 
 to which they feel themselves falling, they preserve their 
 equilibrium. Some dexterous rope-dancers, by the use 
 of their arms only, are able to maintain their balance. 
 
 luO. There are instances in which bodies will not be 
 overturned, although the line of direction falls consider- 
 ably beyond the base. These exceptions to a common 
 rule are observable in the case of rapidly and smoothly 
 moving bodies, in which centrifugal force acts as a counter- 
 poise to the weight of the body. A fami iar example of 
 this kind occurs in the case of skaters, in making their 
 circular turns on the ice, in which they bend or lean 
 greatly beyond the perpendicular position without falling. 
 A notice of this peculiarity in moving bodies will engage 
 our attention, under the head Centrifugal Force. 
 
 191. The tendency which leaning bodies have to fall, 
 may also be counteracted in some measure by the cohe- 
 sion of parts. Thus, there are many instances of walls, 
 steeples, and towers, inclining sensibly from the vertical 
 line, and yet, by the strength of the cement which binds 
 them, they have stood for ages. 
 
 192. Whatever raises the centre of gravity, or narrows 
 the base, allows the line of direction to pass more easily 
 without it, and diminishes the stability. Hence the im- 
 prudence of rising up in carriages or boats, when in 
 danger of being upset ; and hence, as we have just 
 mentioned, the danger of high-loading of vehicles. Lately 
 an improvement has been effected in stage-coach build- 
 ing, by which a chief part of the load is placed as low as 
 
 176. What exceptions are named? 
 
 177. What useiul hints are given to avoid danger ? 
 
66 
 
 CENTRA OF GRAVITY. 
 
 <he axle of the wheels ; and by this means the danger of 
 overturning is almost entirely averted. 
 
 193. The centre of gravity of a body is not always in 
 the substance of the body. Thus, the centre of gravity 
 of a circular ring is in the centre of the circle ; of an ellip- 
 tic or oval ring, in 'the centre of the ellipse ; and of a hol- 
 low cylindric tube, it is in the imaginary axis of the tube. 
 In a drum, for instance, the centre of gravity is a point in 
 the centre of the drum, where there is nothing but air. 
 
 194. When a circular object is placed on level ground, 
 or a horizontal plane, it remains at rest on a point of its 
 surface, because the line of direction from its centre, which 
 is its centre of gravity, falls perpendicularly downwards 
 to the point on which it is in contact with the earth and 
 at rest ; and because it could not possibly get its centre 
 of gravity nearer the earth by changing its position. 
 
 195. When a similar circular object is placed on an 
 inclined plane, it will not remain at rest, but roll over, 
 because the line of direction from its centre of gravity falls 
 perpendicularly downwards in front of the point on its 
 surface which touches the plane. On this account it rolls 
 over, as if it were seeking a spot on which it might have 
 the line of direction from its centre of gravity passing 
 through its point of contact with the earth. Hence a 
 circular body continues rolling down an inclined plane till 
 it find a level spot on which the line of direction passes 
 through its point of rest. 
 
 190. In a bar ol iron, six feet long, and of equal breadth 
 and thickness, the centre of gravity is just three feet from 
 each end, or exactly in the middle. If the bar be sup- 
 ported at this point, it will balance itself, because there 
 are equal weights on both ends. This point, therefore, is 
 the centre of gravity. 
 
 197. If a bar of iron be loaded at one end with a ball 
 of a certain weight, then the centre of gravity will not be 
 at the middle, but situated near the heavy end of the bar. 
 But if we attach a ball of the same weight to both ends, 
 the centre of gravity is again in the middle of the bar. 
 
 178. VVh:.t variations in the centre of gravity ? 
 
 179. Name the examples. 
 
CENTRE OF GRAVITY. 
 
 67 
 
 198. A remarkable illustration of the principles now de- 
 tailed, is exhibited in the case of the earth and moon. The 
 earth revolves round the sun, in consequence of a cause 
 already explained, namely, the sun’s attraction; but in- 
 stead of the centre of the earth describing the oval or el- 
 liptic orbit round the sun, it is the centre of gravity of the 
 earth and moon that describes it. We shall briefly ex- 
 plain the reason for this. The earth, in its course, is en- 
 cumbered with the moon, a body about the 79th of its mass ; 
 in other words, the moon is like a small ball stuck at one 
 end of a bar, having the earth or a larger ball at the other 
 end — the bar between being the mutual attraction of the 
 earth and moon. On this account, the centre of gravity 
 of the earth and moon is at a point somewhere between the 
 centres of the earth and moon. This point lies not far be- 
 low the earth’s surface. Therefore, if the earth were to 
 fall towards the sun, it would be this point which would 
 proceed most directly towards it. 
 
 199. In suspending an irregularly shaped body from 
 different points successively, we may learn where the 
 centre of gravity of the body is placed, by observing that 
 
 the line of direction in each case 
 passes through the same point, 
 which point is the centre of gra- 
 vity. For example, let a paint- 
 er’s palette, which is an irregu- 
 larly shaped body, be suspended 
 from the thumbhole, as in the an- 
 nexed cut, figure 5, and the line 
 of direction will necessarily be 
 from A to B. Next suspend it 
 from a point at D, and anew line 
 of direction will be obtained, cross- 
 ing the line A B. The place where the two lines inter- 
 sect, is thus the centre of gravity. The point of suspension, 
 on being removed to C, will give the same place of inter- 
 section in the original line of direction ; and a similar result 
 will follow any other change of the suspension point. 
 
 180 What is said of the earth and moon ? 
 181. Explain the drawing- 
 
68 
 
 CENTRE OF GRAVITY . 
 
 200. In the various natural structures displayed in the 
 animal and vegetable kingdoms, the centre of gravity s 
 always so situated as to produce a just equilibrium and a 
 harmony of parts. Every animal is properly balanced on 
 its limbs, and every tree has a tendency to grow in a di- 
 rection perpendicular to its base, whether it grow from a 
 level or an inclined plane. Some animals are enabled to 
 move in opposition to the law of gravity, as, for instance, 
 flies creeping on the ceiling of an apartment ; but in such 
 cases, other powers in nature are exerted to preserve the 
 secure footing of the animals. 
 
 201. Our perceptions and appreciations of the beautiful, 
 both in nature and art, appear very much to depend on the 
 objects we contemplate being constructed in reference to 
 the preservation of their equilibrium or balance. An er ct 
 or properly balanced man, wall, steeple, and pillar, are 
 more grateful to the sense of sight, than if they were lean- 
 ing to a side. We feel as if an object in leaning were 
 doing a violence to nature. Thus, the sight of lines and 
 objects swayed from the perpendicular, in a ship agi- 
 tated by the waves, disturbs all our preconceptions of 
 what is consistent with nature, and powerfully assists 
 in bewildering our senses, and rendering us sea-sick. 
 
 202. In consequence of this strong perception of the 
 beautiful and pleasing, not to speak of the absolute utility, 
 in perpendicularly erected structures, allartizans employed 
 in building are anxious to preserve the true line of per- 
 pendicularity. For this purpose they have continual re- 
 course to what they call a plumb-line ; that is, a cord with 
 a small ball of lead, or plummet, at its lower end, hung in 
 a wooden frame; and this being applied to the edges of 
 the structure as it proceeds, shows whether the true per- 
 pendicular line is preserved. Walls leaning from the 
 erect position, are, from this useful instrument, said to be 
 off the plumb-line. 
 
 182. What is said of animal and vegetable structure 1 
 
 183. What of beauty in nature and art ? 
 
 184. How is sea-sickness accounted for in part ? 
 
 185. How is perpendicular secured by builders ? 
 
THE PENDULUM. 
 
 69 
 
 THE PENDULUM. 
 
 203. Gravity, which causes bodies to fall, also causes 
 them to swing backwards and forwards, when suspended 
 freely by a string or rod, from a point, and when once 
 moved to a side, to give them an occasion of falling. A 
 body suspended in this manner is called a Pendulum. 
 
 204. Pendulums usually consist of a rod or wire of 
 metal, at the lower end of which a heavy piece or ball of 
 brass or other metal is attached. When a pendulum swings, 
 it is said to oscillate or vibrate ; and the path which its ball 
 pursues in swinging, from its resemblance in figure to an 
 inverted arch or how, is called its arc. 
 
 205. In the accompanying cut, figure 6, a pendulum 
 
 Fig. g. of the most common construction is 
 
 the pendulum is at rest, it hangs perpendicularly, as here 
 represented, and the place which the ball is seen to occupy 
 is called the point of rest. 
 
 206. The pendulum remains at rest till its bail is drawn 
 aside to allow it an opportunity of swinging on its axis. 
 Being raised to any height on one side, and set at liberty, 
 the ball, by the force of gravity, has a tendency to fall to 
 the ground, but being confined by the suspending rod, it 
 is compelled to make a sweep to that point where it was 
 formerly hanging at rest, immediately beneath the point 
 of suspension. But it does not stop here ; it has acquired 
 a velocity sufficient to carry it onward in an ascending 
 course to nearly as high a point on the opposite side as 
 that from which it was let fall. Of its own accord, it 
 
 A 
 
 represented. A is the axis or point 
 of suspension. B is the rod. C is 
 the ball, or a round flatfish piece of 
 metal, which is fastened to the rod by 
 a screw behind, and by which screw 
 
 B 
 
 Q 
 
 
 ✓ -it can be raised or lowered on the rod. 
 D D is the path or arc which the 
 ball traverses in swinging. When 
 
 186. Define a pendulum, and expldn the drawing. 
 181. What of its motion, and way does it cease ? 
 
70 
 
 ISOCHRON’S}! IN PENDULUMS. 
 
 again falls downwards in the same arc, and rises ro near 
 the point where it set off; and thus, of itself, c niinu s to 
 swing to and fro, or vibrate, for a certain length of time, 
 till its force is expended, and it finally comes to a state of 
 rest in its original dependent situation under the point of 
 suspension. 
 
 217. At every sweep of the pendulum (when not med- 
 dled with, or assisted by any external force), the length 
 of the path or arc traversed by the ball is in a small degree 
 diminished. This arises from two causes — the obstruction 
 offered by the atmosphere, and the friction on its axis or 
 point of suspension. These causes, therefore, sooner or 
 later, bring the pendulum to a state of rest, unless external 
 force of some kind continues to be applied to urge it to sus- 
 tain its action. 
 
 208. The ball of a pendulum in swinging, as has been 
 mentioned, describes the figure of an arc. This arc is a 
 certain porth n of a circle. The extent of this portion de- 
 pends on the force exerted in setting the pendulum in mo- 
 tion, or in drawing it aside to let it fall. A circle being 
 divided by mathematicians into 3 0 degrees or parts, the 
 ball may be made to swing over five, ten, twenty, or any 
 other number of degrees under ISO, which is half a circle. 
 The extent of the arc traversed under ordinary circum- 
 stances, is from ten to twenty degrees. 
 
 209. When the ball of a pendulum traverses an arc not 
 exceeding four or five degrees, it is observed to possess 
 what is called the property of isochrortism — that is, it 
 passes over its point of rest always at the same interval of 
 time (or very nearly the same interval), whether it traverse 
 one, two, three, four, or five degrees ; thus always accom- 
 plishing its excursion in precisely the same space of time. 
 At first sight this seems doubtful ; but a consideration of 
 circumstances shows that it is perfectly correct. The 
 cause of the phenomenon is, that the pendulum which 
 goes over a greater exent of arc, has a greater speed than 
 that which goes over a smaller extent. It should, how- 
 ever, be clearly understood, that the comparison as to 
 
 188. What of isorhronisns T 
 
rt.O'M PENDUl.TTMS. 
 
 71 
 
 lengths of time occupied in vibration, alluded to here, ap- 
 plies only to any given length of rod — that is to say, we 
 must not compare the time occupied by a long rod with 
 the time occupied by a. short rod ; but, in every case, hold 
 to only one rod, whatever be its length. 
 
 210. A pendulum with a long rod vibrates slower than 
 one with a short rod. The time does not become longer, 
 however, in exact proportion, as we extend the rod. The 
 vibration it must always be recollected, is analogous to the 
 falling bodies. The spaces fallen through by a body in 
 1, 2, 3, or 4 seconds, are not in proportion to 1, 2, 3, 4, 
 and so on, but in the proportion of 1, 4, 9, 16, 25, and 
 so on, or the squares of the time occupied in falling. 
 In the case of pendulums, it is found that their lengths 
 are as the squares of the times of vibration. Thus, if the 
 times occupied by one vibration of two pendulums be 1 and 
 2 seconds respectively, the lengths of the pendulums will 
 be as 1 and 4 ; so if the time of one vibration of several pen- 
 dulums be as 1, 2, 3, 4, their lengths are as 1, 4, 9, and 16. 
 
 211. The vibrations of the pendulum being produced by 
 terrestrial gravitation, it follows, as a natural result, that if 
 the force of gravitation be weakened, so will the tendency 
 of the ball of the pendulum to fall or swing be weakened. 
 This result is distinctly observable in different parts of the 
 earth. At the equator, the earth, as already mentioned, 
 
 , bulges out to a thickness of 26 miles on the diameter, or 
 13 miles from the surface to the centre ; and as the attrac- 
 tion of gravitation proceeds from the centre, the force of 
 this attraction is consequently weaker at the surface at the 
 equator than it is at the surface at the poles. At every 
 part of the surface between the equator and poles, there is 
 a proportionate increase of gravity. Besides the effect 
 produced by the greater distance of the surface from the 
 centre at the equator, centrifugal force, which is strongest 
 at the equator, assists in weakening the attractive force at 
 that place. 
 
 212. In consequence of these combined causes, a pen- 
 
 189. How does the length of rod affect time ? 
 
 190. What difference occurs over the equator and whv ? 
 
 191. By what rule is the length of the pendulum varied? 
 
72 
 
 CENTRE OF OSCILLATION'. 
 
 dulum of a given length vibrates more slowly at the equa- 
 tor than at the poles. In proportion as we advance on the 
 surface of the earth from the equator towards the poles, so 
 does the pendulum swing or vibrate more quickly. In 
 order, therefore, to preserve uniformity of speed in pendu- 
 lums at different parts of the globe — that is, in order that 
 they may all vibrate in one second, their length must be 
 regulated according to the distance of the places from the 
 equator. Thus, each degree of latitude has its own length 
 of pendulum. 
 
 213. The uniform vibration of the pendulum has ren- 
 dered it useful in regulating the motion of clocks for mea- 
 suring time. In the common clock, a pendulum, con- 
 nected with the wheel-work, and impelled by weights, oi 
 a spring, regulates the motions of the minute and hour 
 hands on the dial-plate, by which the time of day is pointed 
 out. If no pendulum were employed, the wheels would go 
 very irregularly. The pendulum is regulated in length, 
 so as to vibrate sixty times, each time being a second, in 
 the space of a minute. At each vibration, it acts upon 
 the tooth of awheel, which turns the rest of the machinery. 
 In order that the pendulum may vibrate neither quicker 
 nor slower than sixty times a minute, in the latitude of 
 London it must measure 39 inches and about the 7th of 
 an inch from the point of suspension to the centre of os- 
 cillation. A pendulum at Edinburgh would require to be 
 
 a small degree longer. The greatest possible nicety is ’ 
 required in the adjustment of the length ; for a difference 
 in extent amounting to the 1000th part of an inch, would 
 cause an error of about one second in a day. Therefore, 
 to make a pendulum go slower by one second a day, it 
 must be lengthened by the 1000th part of an inch ; and to 
 make it go quicker, it must be shortened in the same pro- 
 portion. 
 
 214. It is possible to cause short pendulums to regu- 
 late the movement of clocks the same as long pendulums : 
 and this is done in -cases where long pendulums would be 
 inconvenient, or inelegant in appearance. This is accom- 
 
 192. Des ribe he use of pendulums in clock- and iheir varie y. 
 
CENTRE OF OSCILLATION. 
 
 73 
 
 plished by shortening the pendulum to a fourth of its or- 
 dinary length, by which it beats or vibrates twice instead 
 of once in a second. The wheel-work is constructed to 
 suit this arrangement. 
 
 215. The pendulums of clocks being made of a rod of 
 metal, they are liable to be extended by the heat of sum- 
 mer and shortened by the cold of winter ; and by this 
 means the uniformity of their motion is destroyed. Vari- 
 ous contrivances have been adopted in order to compen- 
 sate this effect on the motion of the clock, and pendulums 
 constructed for this purpose are called compensation pen- 
 dulums. The parts of the rods of these pendulums are 
 so constructed and arranged that when one of them ex- 
 pands downwards, another at the same time expands up- 
 wards, by which any variation from temperature is greatly 
 diminished. 
 
 216. In the moving mass of every pendulum, there is 
 a point which is called the centre of oscillation. The 
 centre of oscillation may be in the rod or in the ball, or 
 even below the pendulum, according to circumstances. 
 To- understand this, it will be necessary to remember, that, 
 if each particle of matter in the swinging body were at 
 liberty to swing separately, those particles which are near 
 the axis would swing more rapidly than those which are 
 farther rem -ved from it. Although the various compo- 
 nent particles, from their intimate connection with each 
 other, are not at liberty to obey this tendency, still the 
 tendency exists. The nearer particles are retarded by 
 those more distant, and those which are distant are accele- 
 rated by those which are nearer. There is thus a mutual 
 exchange of influences among the particles of the swing- 
 ing body. But there is a point or spot somewhere in the 
 mass, where the mutual exchange is so completely equal- 
 ized, that the influences or momenta neutralize each other, 
 and the particle of matter situated at this point con- 
 sequently swings as if unconnected with any other par- 
 ticle in the body. This point is the centre of oscillation. 
 
 193. Whence the necessity of compensation pendulums ? 
 
 194. Whai of the centre of oscillation ? 
 
74 
 
 CENTRE OF OSCILLATION. 
 
 217. The centre of oscillation in a pendulum is disco- 
 verable in the following manner. Take a common p n- 
 dulum and set it a-swinging. Next, take a small ball of 
 lead and suspend it by a fine thread from the same axis 
 as that of the pendulum. This ball and thread form what 
 is called a simple pendulum. It is simple, because the 
 weight of the thread may be reckoned as nothing, and 
 the ball vibrates with the smallest possible resistance or 
 impediment; by which means it is well lilted for experi- 
 ments. This simple pendulum is set a-swinging in front 
 of the common pendulum, and its thread must be length- 
 ened or shortened, as may be necessary, to cause the 
 leaden ball to move at precisely the same pace or velocity 
 as that of the common pendulum. Having rendered the 
 two velocities exactly uniform, then stop both the pendu- 
 lums, and the centre of the spot on the common pendu- 
 lum, which the ball covers (supposing the ball to he per- 
 fectly circular), is the centre of oscillation. 
 
 218. It is to be noted, that the discovery of the centre 
 of oscillation is not a matter of practical utility, as far as 
 regards common or clock pendulums, but is interesting in 
 a philosophical point of view, from the mechanical truths 
 connected with it. For example, if we take a straight 
 and uniformly thick bar of wood or metal, and suspend it 
 in the character of a pendulum, we shall, by the means 
 just pointed out, ascertain that its centre of oscillation is 
 at a certain spot. If we then take the pendulum from its 
 axis, reverse it, and suspend it from the spot indicated, 
 we shall perceive, that, on being set in motion, it will 
 again swing in agreement with the leaden ball and thread. 
 The centre of oscillation and the point of suspension are 
 thus said to be controvertible, without producing any 
 change in the rate of vibration. How this result should 
 follow, appears at first rather strange, but on consideration 
 it will be found, that, by reversing the pendulum, there is 
 a portion necessarily placed above the axis; wherefore, 
 the speed which would ensue from the shortening of the 
 
 195. How is this centre ascertained ? 
 
 196. Of what importance is this experiment ? 
 
LAWS OF MOTION. 
 
 75 
 
 pendulum is counterbalanced by the retarding influence 
 of the portion placed above the axis. 
 
 THE LAWS OF MOTION. 
 
 219. Motion, as already mentioned, is the changing of 
 place or the opposite of rest.* 
 
 220. According to the general explanations which have 
 been given, it appears that motion in bodies is as natural 
 as rest, and that matter passively submits to remain in 
 either of these states in which it may be placed, provided 
 no external force or obstacle interfere to cause an alteration 
 of condition. 
 
 221. These and other fundamental laws of nature, in 
 relation to rest and motion of matter, are laid down by 
 Sir Isaac Newton in the following three propositions : — 
 
 1st, Every body must persevere in its state of rest, or of 
 uniform motion in a straight line, unless it be compelled 
 to change that state by forces impressed upon it. 
 
 2d, Every change of motion must be proportional to the 
 impressed force, and must be in the direction of that 
 straight line in which the force is impressed. 
 
 3d, Action must always be equal and contrary to reac- 
 tion : or the actions of two bodies upon each other must 
 be equal, and their directions must be opposite. 
 
 222. These propositions we shall treat separately. In 
 the first of the series there are three points requiring con- 
 sideration, namely, the permanency, the uniformity, and 
 the straight line of direction, of motion in bodies. 
 
 UNIFORM MOTION IN A STRAIGHT LINE. 
 
 223. As was formerly observed, it is impossible to 
 show either permanency or uniformity of motion in bodies 
 
 * In scientific language, the nature and laws of motion form a branch 
 of knowledge called Dynamics (a word signifying power or force) ; 
 while the principles of forces in equilibrium are classed under the term 
 Statics (a word signifying to stand or be at rest). 
 
 197. Name Newton’s three propositions. 
 
 198. What considerations are important in the first ? 
 
 199. Where are the laws of motion most clearly illustrated ? 
 
 200. Define Dynamics and Statics. 
 
70 UNIFORM MOTION IN A STRAIGHT LINE. 
 
 upon or near the earth ; for all moving- bodies are sooner 
 or later brought to a state of rest by the force of attrac- 
 tion, friction, and the opposition of the atmosphere. It is 
 only, therefore, in the case of the great works of nature 
 or planetary bodies, that the laws of motion are most 
 clearly and fully illustrated. In them, motion is uniform 
 and permanent. The earth, for example, moves at the 
 present moment with the same regularity, the same pla- 
 cid steadiness, that it did thousands of years ago. On 
 account of this regularity and permanency of motion, as- 
 tronomers are able to calculate eclipses of the sun, moon, 
 or other heavenly bodies, at any distance of time. They 
 can foretell, to an instant of time, at what part of their orbits 
 the earth or moon will be a thousand years hence. The 
 motions of the planetary bodies also afford a standard 
 wherewith to reckon the course of time.* We call the 
 space of time occupied by a revolution of the earth in its 
 orbit round the sun, a year — that of a revolution of the 
 earth on its axis, a day — that of a revolution of the moon 
 round the earth, a month ; and these periods we divide 
 into weeks, hours, minutes, and seconds. Thus, time is 
 sectioned and computed with unerring accuracy. The 
 inhabitants of the different planets, in all likelihood, take 
 advantage of the same means of reckoning their time, each 
 planet, however, having its own peculiar length of year and 
 day, according to the period occupied in its revolution 
 round the sun or on its axis. In Jupiter, the year is 
 nearly 12 of our years, and the length of the day nearly 
 10 hours. In Mars, the year is 1 of our years and 321 
 days, and the day 24 hours and 39 minutes. In Venus, 
 
 * The motions of the planetary bodies are here spoken of as being 
 uniform or regular; this is not strictly correct. When we come to 
 treat of Astronomy, it will be shown that there are certain irregulari- 
 ties in the motions of the planets, caused by their action on each other ; 
 but as these irregularities are the subject of calculation, and do not 
 disturb the harmonious permanency of motion in the system of the 
 universe, it has been thought unnecessary to advert to them in the above 
 popular definition. 
 
 201 . How is time reckoned by the motions of the planets! 
 
 202. What of motion in a straight line ? 
 
CENTRIFUGAL FORCE AND CIRCULAR MOTION. 77 
 
 the year is only 224 of our days, and the day 23 hours and 
 21 minutes. 
 
 224. The tendency of a body to move in a straightdine 
 from the point whence it set out, is as much a property of 
 matter as the uniformity of motion. If we conceive the 
 idea of a body impelled into a state of motion by any given 
 force, and at the same time conceive the idea that there is 
 no obstacle to interrupt it, no attractive force to bend it 
 aside, we shall then fully understand that a moving body 
 must, as a matter of necessity, from its property of inertia, 
 proceed in a straight line of direction — it must go on an 
 even path for ever. 
 
 CENTRIFUGAL FORCE AND CIRCULAR MOTION. 
 
 225. Bodies in flying round a centre have a tendency 
 to proceed in a straight line, and this principle of motion, 
 as already mentioned, is termed centrifugal force. Ex- 
 amples of this tendency are very familiar to our observa- 
 tion. When we whirl rapidly a sling with a stone in it, 
 and suddenly allow the stone to fly off, it proceeds at first 
 in a straight line, but is gradually pulled to the earth by 
 attraction. In turning a circular grinding-stone rapidly 
 with water in contact with it, we perceive a rim of water 
 first rising on the stone and next flying off ; and the more 
 rapidly we turn the stone, so does the water fly off with 
 the greater force. I'n grinding corn by two rapidly turn- 
 ing stones playing on each other, the grain poured in at 
 an opening at the centre is quickly shuffled towards the 
 edges of the stones and expelled in the condition of meal 
 or flour. If we put some water in a vessel, and rapidly 
 turn it in one direction, we shall find that the water en- 
 deavours to escape, and rises up to the edges of the vessel, 
 leaving a deep hollow in the middle. The tendency to fly 
 off from a centre is made use of in the manufacture of pot- 
 tery : Soft clay being placed on a revolving wheel, it quick- 
 ly spreads towards the circumference of the machine, and 
 is guided or moulded by the hand of the potter into the 
 
 203. What of centrifugal force ? examples. 
 
 204. What manufactures are on this principle ? 
 
78 CENTRIFUGAL FORCE AND CIRCULAR MOTION. 
 
 required form. In forming common crown or window 
 glass, advantage is also taken of the principle of centrifugal 
 force. A thick round mass of glass, softened by heat and 
 fixed at the middle on an iron rod, being made to turn ra- 
 pidly round first in one direction, and then in the opposite, 
 and continuing this alternating rotary motion till the glass 
 becomes cool, is found to spread out into a large, thin, cir- 
 cular plaie. From this plate, square panes of glass are 
 afterwards cut. 
 
 226. Equestrians, in performing their feats of horseman- 
 ship, always incline their bodies inwards when standing 
 on a horse which is running round a circle. Centrifugal 
 force having a tendency to impel them outwards, is thus 
 counteracted by the inward leaning, and forms a species 
 of support to their overhanging bodies. A horse running 
 in a circle, or quickly turning a corner, naturally adopts 
 the same count., racting posture, and leans inwards. A 
 skater, in moving in a circular or curvilin ar path on 
 smooth ice, also leans inwards, so much so, that if he 
 were to stand still in this posture, he would inevitably fall 
 on his side ; but centrifugal force, which has a tendency 
 to impel his body outwards from the curve, or in a straight 
 line of motion, sustains him, as it does the equestrian, and 
 he therefore moves gracefully and safely in the circular 
 path which his fancy directs. In this and other instances, 
 we find the force of gravity overcome by centrifugal force. 
 It is in obedience to this principle, that the earth bulges 
 out to the thickness of 2(5 miles upon the circumference 
 at the equator, where the whirling motion is most rapid. 
 
 227. Thus centrifugal force is the tendency to fly ofF 
 in a straight line, or at a tangent, from motion round a 
 centre; and the power which prevents bodies from flying 
 off, and draws them towards a centre, is, as already men- 
 tioned, called centripetal, or centre- seeking force. All 
 bodies moving in circles are constantly acted upon by these 
 opposite forces, as may be exemplified by the annexed cut, 
 fig. 7. A is a point to which a string with a ball at the end 
 
 205. Name the o : her illustrations here cited. 
 20; >. What of centripetal force ? 
 
REVOLVING BODIES. 71) 
 
 of it, B, is attached. On forcing 
 the ball B into motion, it will de- 
 scribe a circle round the point A, 
 in which, case the string is the 
 centripetal force. The ball in 
 whirling, however, having a con- 
 tinual tendency to fly off, if it be 
 disengaged from the string at C, 
 will go in a straight line C D ; if 
 at E, it will go in the line E F ; if 
 at G, in the line G H ; and soon, 
 at every point in the circle. 
 
 228. The mutual action of centrifugal and centripetal 
 forces, in the case of circular motion, proceeds according 
 to a certain ratio. If the mass of the revolving body be 
 increased, its distance from the centre and velocity remain- 
 ing the same, its centrifugal force will be increased in the 
 same proportion. If the distance from the centre be in- 
 creased, while the mass and the time of revolution remain 
 the same, the centrifugal force will also be increased in 
 the same proportion. If the number of revolutions per- 
 formed in a given time be twice as many, the distance and 
 mass being unchanged, the centrifugal force will be four 
 times as great ; if three times as many, the force will be 
 nine times as great ; if four times as many, it will be six- 
 teen times as great ; and so on in the same proportion. 
 The masses of the planets, and their distances from the 
 sun, being various, the forces which affect them are also 
 similarly varied. 
 
 229. The line round which a body performs a motion 
 of rotation, is called an axis. This axis may be only ima- 
 ginary, like that of the earth ; or real, as the axle of a 
 wheel. The body may revolve about two projecting pins 
 or pivots resting in sockets, in which case its axis is a 
 straight line joining the pivots ; or it may turn on a cylin- 
 drical rod of small diameter, passing through the body, like 
 a wheel on its axle. It is evident that every point of the body, 
 
 Fig. 7. 
 
 207. Explain the diagram. 
 
 203. What of the mutual action of these two forces ? 
 209. What ot the axis ? 
 
80 
 
 REVOLVING BODIES. 
 
 during its revolution, will describe a circle, the centre of 
 which is a point in the axis of the body. 
 
 230. In the turning of a wheel 
 on its axis, that part which is at the 
 greatest distance from the centre 
 has the greatest velocity ; and at 
 this extremity of the circumference, 
 the centrifugal force is greatest. For 
 example, in the representation of a 
 wheel with arms radiating from a 
 centre, (figure 8,) the velocity is 
 greater at the extremity of the arm 
 at A, than it is at B, half tin- distance from the centre. But 
 the point B goes round as often as the point A. having a 
 smaller circle to traverse. 
 
 231. In this manner, the velocity of revolving bodies 
 must always, as a matter of necessity, increase in propor- 
 tion to the distance from the centre of motion. Hence a 
 comparatively small centrifugal force near the centre, is 
 prodigiously increased towards the circumference. By in- 
 creasing the force, and adding to the velocity of a revolv- 
 ing body, the centrifugal force becomes so great that it 
 will in some cases overcome the cohesiveness in the ma- 
 terial of the body, and cause it to break and fly off in 
 pieces. When grinding-stones are thus whirled with great 
 rapidity, they are apt to be destroyed, flying in pieces to the 
 extreme danger of those who are using them. 
 
 232. The power of centrifugal force in rapidly whirl- 
 ing bodies, may be rendered so great as to overcome the 
 force of gravity. In whirling a sling with a stone in it, 
 the stone does not fall out of its place in the sling. The 
 following is a more striking example : — Place a jug of 
 water on the inside of the rim of a wheel a few feet in 
 diameter; then, beginning gradually, set the wheel in 
 rapid motion, and it will be observed that the jug retains 
 its place, whirling round in a perfectly stable manner, and 
 that even the water in it is not spilled. Thus, gravity, or 
 the tendency to fall downwards, is overcome by centrifugal 
 
 210. Explain the diagram. 
 
 211. What of increased velocity ? 
 
 Fift 8. 
 
REVOLVING BODIES. 
 
 81 
 
 force. If the jug were placed in a situation in the wheel, 
 near the centre of motion, where the centrifugal force is 
 weak, it would at once fall to the ground. 
 
 233. When the axis of a revolving body is imaginary, 
 it is sometimes in motion itself, like the axis of the earth. 
 In most cases of rotary motion, the axis is immovable, 
 and the motion always in one direction, as the wheels of 
 watches, clocks, and machinery ; and in some cases the 
 motion is alternating or reciprocating, as the vibrations of 
 a pendulum, the oscillations of the balance-wheel of a 
 watch or chronometer, or the working-beams of steam- 
 engines ; in which cases the motion continues in one direc- 
 tion only for a short period, and is then reversed. This 
 alternating motion is called oscillation or vibration. 
 
 234. When a body, which is quiescent and free, as a 
 ball lying on a perfectly smooth plane, is acted on by an 
 instantaneous force, and in the direction of its centre of 
 gravity, the body will be impelled with a uniform motion 
 in the direction of the stroke, having only this motion of 
 translation, as it is called, without any motion of rotation. 
 If the impulse given to the body be not in the direction of 
 its centre of gravity, it will still receive the same motion 
 of translation, but it will also have communicated to it a 
 motion of rotation about its centre of gravity. In this case, 
 each of the two motions will be exactly the same as if the 
 other did not exist.; that is, the progressive motion is the 
 same as if the direction of the impulse passed through the 
 centre of gravity, and the motion of rotation is just what 
 would be produced by the same impulse, if the body had 
 a fixed axis through its centre of gravity, and about which 
 it whirled. 
 
 235. There is a point at a certain distance from the 
 axis of a revolving body, at which, if all its matter were 
 concentrated, it would give exactly the same resistance 
 to the communication of rotary motion, as the whole body 
 itself does, supposing that in both cases the same impulse 
 is given, and at the same distance from the axis. This 
 
 212. Will this force overcome gravity ? 
 
 213. Describe oscillation and other forms of rotary motion. 
 
 214. What is a motion of translation, and how complicated ? 
 
LAWS OF PROJECTILES. 
 
 b2 
 
 point is called the centre of gyration, and its distance 
 from the axis is called the radius of gyration. This centre 
 of gyration is analagous to the centre of oscillation in vibrat- 
 ing bodies. The product of the number representing the 
 mass or weight of a body into th#t denoting the square of 
 the length of this radius, is called the moment of inertia. 
 For example, let a wheel be 10 pounds in weight, and its 
 radius of gyration 2 feet, the square of which 2 is 4 ; then 
 multiply 10 by 4, and 40 is given as the moment of inertia. 
 The word moment, used in this sense, is a contraction of 
 momentum, a term which in this respect is now disused, 
 in order to prevent its being confounded with momentum 
 in ordinary moving bodies. 
 
 236. If the parts of a body be symmetrically distributed 
 around an axis of rotation, that is, if equal portions of the 
 body be placed at equal distances from it, and in directly 
 opposite directions, the opposing centrifugal forces will 
 balance each other, and there will be no pressure on the 
 axis, and the body would revolve permanently about it. 
 Thus, a sphere of uniform density would revolve perma- 
 nently about any of its diameters. A cylinder of uniform 
 density would also revolve permanently about its axis. If 
 the revolving body be not uniform, or fairly balanced on its 
 imaginary axis, it will possess an irregular or hobbling 
 motion, and come sooner to a state of rest by friction 
 than would be the case if it were of regular density, 
 or properly balanced. Examples of this are very fami- 
 liar. 
 
 LAWS OF PROJECTILES. 
 
 237. Bodies, on being projected by any impulsive 
 forces, are called projectiles, and are observed to pursue a 
 curvilinear or bent line of direction in their motion. The 
 bending from the straight line is produced by the force of 
 gravity, and “the change is proportional to the impressed 
 force.” 
 
 215. Explain the centre and radius of gyration. 
 
 216. What of the moment of inertia? 
 
 217. What of the uniformity of a revolving body ? 
 
 218. What of projectiles ? 
 
LAWS OF PROJECTILES. 
 
 83 
 
 238. A ball projected from a cannon, a stone thrown by 
 the hand, and water spouted from a confined vessel, furnish 
 familiar examples of curvilinear motion. 
 
 239. It is a remarkable law of motion, that, whether 
 the force which projects a body be great or small, the body, 
 if thrown horizontally, will reach the surface of the earth 
 from the same height, in the same space of time, not cal- 
 culating resistance of the air. For example, if two guns 
 are fired from the same spot at the same instant, and. in a 
 horizontal direction, one of the balls falling half a mile, 
 and the other a mile distant, it will be found that the ball 
 which proceeds the greatest distance takes precisely the 
 same time to reach the ground which the other does. 
 
 240. The time of flight, as it is called, of two balls, 
 will be the same in whatever directions and with whatever 
 velocities they are fired, provided they reach the same 
 height. 
 
 241. The reason for the same length of time being oc- 
 cupied in falling by both balls, is, that they are both car- 
 ried downward at the same rate by gravity. Hence, a 
 ball dropped perpendicularly from the top of a high tower, 
 does not reach the ground sooner than a ball shot from the 
 same height to the distance of one or more miles in a hori- 
 zontal direction. 
 
 242. In projecting bodies through the atmosphere, great 
 advantage, in point of distance, is gained by impelling 
 them from heights, because a ball thrown from a high 
 situation to a lower, reckoning its whole course, is more 
 aided than retarded by gravity. When the ball is pro- 
 jected from a lower situation to a higher, it is in the first 
 place retarded by gravity in its ascent, and the accelera- 
 tion afterwards by gravity being less than this previous 
 retardation, it consequently does not go so far, or has not 
 such a wide range, as if projected from a height. Skilful 
 generals, in bombarding towns at a safe distance, take ad- 
 vantage of this law of projectiles. 
 
 219. Give examples of curvilinear direction. 
 
 220. What law of motion is shown by cannon balls 1 
 
 221. Why this similarity of time 1 
 
LAWS OF PROJECTILES. 
 
 S4 
 
 We are now prepared for the consideration of one of 
 the most important principles in Dynamics, namely, the 
 law of motion which governs a body after receiving a pro- 
 jectile impulse. 
 
 243. A projectile exhibits a composition of motion, 
 namely, a horizontal motion forward, when thrown in that 
 direction, produced by the impressed force ; and a descend- 
 ing motion, produced by gravity, or the earth’s attraction. 
 These two motions are unequal; they are not at the same 
 velocity. The horizontal motion is uniform, while the 
 descending motion, according to the law of gravitation in 
 relation to falling bodies (see 170), is accelerated. The 
 consequence is, that the projectile, as already mentioned, 
 pursues a curved line of direction, the convex side of the 
 curve being uppermost. 
 
 244. The degree of curvature of the h'ne of motion 
 depends on the amount of the original projectile force. 
 The law is, the greater the projectile force, or the greater 
 the original velocity of the object, so is the sweep of the 
 curve proportionally greater. 
 
 245. Let us suppose that the projectile force is sufficient 
 to carry a cannon ball ten miles; this will give a very 
 wide curve, allowing that the ball is shot from a lofty situa- 
 tion. But let us add to the projectile force, and send the 
 ball double the distance, and the curve is now exceedingly 
 wide. If we in this manner go on adding to the projec- 
 tile force, vve at length give the ball such a moial force 
 that it will go quite round the world; instead of describing 
 portions of curves, it will describe a whole circle. 
 
 246. This conducts us to a most extensive result. We 
 have at once placed before us a reason why the planetary 
 bodies should have assumed curvilinear paths in relation 
 to the sun. The original projectile force which they re- 
 ceived, in connection with the force of gravitation, has 
 obliged them to pursue curved lines in their motion ; and 
 once being disengaged, they have, by a balance of centri- 
 
 222. What law of projectiles is useful in military operations ? 
 
 223. What of the compound motion of projectiles ? 
 
 224. How is this law of projectiles illustrated ? 
 
 225. What important bearing has this upon astronomy ? 
 
ACTION AND REACTION. 
 
 85 
 
 fugal and centripetal forces, continued to travel in circular, 
 or, properly speaking, elliptical orbits — the ellipticity being 
 caused by a want of exact uniformity between the forces 
 which affect them. 
 
 A calculation of these forces belongs properly to Mathe- 
 matics, and will engage our attention when treating of 
 Astronomy. 
 
 ACTION AND REACTION. 
 
 We proceed to a consideration of the first clause in the 
 third proposition of Newton — “Action must always be 
 equal and contrary to reaction.” 
 
 247. Action is the impression of force. A blow is action ; 
 pressure is action. Reaction is resistance ; but the word 
 resistance does not fully convey the meaning of reaction, 
 which properly signifies the action of striking or pressing 
 back, even although the body struck or pressed upon do 
 not move. 
 
 ' 248. When a man strikes a hammer upon a fixed stone, 
 the stone strikes the hammer at the moment of contact as 
 much as the hammer strikes it. But if the stone be not 
 fixed, and be liable to be easily upset, then its reaction is 
 less, and it acquires a momentum. When a boy throws 
 his ball against the wall of a house, the wall reacts on the 
 ball, and causes it to rebound ; but if the boy throw his 
 ball at a pane of glass with the same force, the glass, having 
 the power to resist only a portion of the force, gives way 
 before it. In this case, if we suppose the ball to possess 
 the action or force of 4, and the glass to possess the reac- 
 tion of 2, the ball in passing through the glass loses 2 in 
 its force, and retains the remaining 2. If it then came 
 against another pane possessing a reactive power of 2, 
 it would not break the glass, and, its force being now spent, 
 it would fall to the ground. Thus, “ action and reaction 
 are equal.” 
 
 249. A story is told of a person who, from his know- 
 ledge of the law of action and reaction, betted that he 
 
 226. Define action and reaction, and their relation. 
 
 227. What illustra'ions are cited ? 
 
 228. What examples in proof are given ? 
 
86 
 
 ACTION AND REACTION. 
 
 would lie down on the ground and allow an anvil to be 
 placed upon his breast, and that any one might strike the 
 anvil with as much force as he was pleased to exert. In 
 this case, the person who made the offer was quite safe, 
 provided he could support the weight of the anvil ; for if 
 a blow were given with the utmost force by a comparatively 
 light body, as a hammer, though it would communicate 
 nearly double its momentum to the anvil, yet the anvil, 
 being so heavy, would acquire so small a velocity that the 
 shock given to the person would be insensible. Were 
 a freestone of the same weight as the anvil used, it would 
 give a still less shock, for the action and reaction of per- 
 fectly elastic bodies are twice as great as that of inelastic 
 bodies. Iron has more elasticity than stone. 
 
 250. It is by reaction acting contrary or in opposition 
 to action, that the movements of living objects are rendered 
 effectual. When we walk on the ground, the ground 
 resists the pressure, and we feel ourselves steadied. A 
 bird in flying pushes itself onward by the flapping of its 
 wings against the partially resisting medium of the atmo- 
 sphere. The partially resisting force of water, in the same 
 manner, allows a fish to propel itself by its 'tail and fins. 
 A sailor in rowing a boat causes the oars to push against 
 the water, and, the water partially resisting the force, 
 motion is communicated to the boat. In pushing a boat 
 from the shore, the firm ground has such a power of reac- 
 tion, that we are able to give the boat much greater mo- 
 mentum than if we pushed only against water. If we 
 go into the boat, and try to move it, by merely pressing 
 against some part of its fabric, no motion whatever is pro- 
 duced, for the action and reaction are equal. The whole 
 force employed must be rendered greater than the reaction, 
 otherwise no motion can be communicated to the body. 
 
 251. When two bodies come into collision with each 
 other, as in case of two bodies moving in a straight line, 
 but opposite course to each other, the law of action and 
 reaction being equal, will not be clearly illustrated, unless 
 the collision be in the direction of the centre of gravity or 
 
 229. What of the movements of living objects ? 
 
MOTION IN ELASTIC BODIES. 
 
 87 
 
 inertia of the two — in common language, unless the blow 
 be fair. The centre of gravity, in cases of this kind, is 
 called the centre of action, or percussion. For example, 
 when we strike a ball with a club, fairly against its side 
 opposite to its centre of gravity, it is impelled to a con- 
 siderable distance ; but if we strike it above this central 
 point, a part of'the force is expended in vain, or lost, and 
 the ball moves but a comparatively short distance. Expe- 
 rience has demonstrated that the centre of action in ham- 
 mers should be in the head or striking part ; and, there- 
 fore, in striking with these instruments, the blow may be 
 given with every advantage. But when an attempt is 
 made to strike with an object in which the centre of action 
 is at a place short of its extreme point, for instance, a com- 
 mon iron poker, a part of the action is expended towards 
 the hand of the person who strikes, and he feels a dis- 
 agreeable jarring sensation in his arm. 
 
 252. This definition of the centre of action applies only 
 to the motion of bodies in a straight line. In the case of 
 revolving bodies, the. centre of action or percussion is a 
 point in it, to which if an immovable obstacle be applied, 
 the body will remain at rest without any tendency to move 
 in any direction, and the axis will receive no shock. In 
 straight rods, or bodies of any form, suspended as pendu- 
 lums, the centre of oscillation is the same as the centre of 
 action in revolving bodies. 
 
 MOTION IN ELASTIC BODIES. 
 
 252. In reference to the effects of collision, bodies are 
 divided into three classes — hard, soft, and elastic. A hard 
 body is one that suffers no change of form by the action 
 of any force. A soft body is one that undergoes a change 
 of form by this means. An elastic body suffers a momen- 
 tary change of form by the action of any force impressed 
 upon it, and immediately springs back, or recovers its 
 original form. The first two classes are styled inelastic 
 bodies. 
 
 230. What of the centre of percussion ? 
 
 231. What difference in the kind of motion? 
 
 232. Define inelastic bodies. 
 
88 
 
 REFLECTED MOTION. 
 
 254. If two equal inelastic bodies bp moving with equal 
 velocities in opposite directions, and come in collision, 
 each will destroy the onward motion of the other, and, 
 consequently, both will be reduced to a state of rest. 
 
 255. If there be any elasticity in the bodies, they will, 
 according to their degree of elasticity, rebound from each 
 other, and a positive process of reaction will be exhibited. 
 By this means there will be at once a counteraction and 
 transmission of force. As above stated, when the bodies 
 are perfectly elastic, the action and reaction are double 
 those of inelastic bodies. 
 
 256. An example of the transmission of force or motion 
 from one body to another, while the transmitting bodies 
 remain at rest from their mutual counteraction of the force 
 communicated, may be seen in the case of a row of bil- 
 liard balls, which possess a certain elasticity. Place six 
 billiard balls in a row on a smooth plane, and let them be 
 all pretty close to each other, or even in contact. Then 
 give a smart blow to the first bail, or, as we may call it, 
 No. 1 ; it will instantly strike against No. 2, which will 
 
 Fi s- 9 - communicate the force to No. 3, and from 3 it 
 , will be given to 4, and from 4 to 5, and from 
 5 to 6. None of the balls, however, will sen- 
 sibly move from the spot in which it rests, 
 except the last of the row, which, having no 
 ball to impinge upon, will roll away, and thus 
 expend the force communicated by the blow 
 upon No. 1. An experiment of this kind is 
 generally performed upon a number of elastic balls of a 
 small size, suspended in a row by threads, as in figure 9, 
 in which case there is no friction to interrupt the process 
 of action and reaction. 
 
 666 
 
 REFLECTED MOTION. 
 
 257. A body projected by a single force proceeds in a 
 straight line till a new force act upon it, and send it on a 
 
 233. Name the experiment with the billiard halls. 
 
 234. What of reflected motion, with examples? 
 
REFLECTED MOTION. 
 
 80 
 
 row line of direction When amoving body is thus im- 
 pelled into a new line by striking against some body, its 
 motion is said to be reflec’ed. 
 
 258. Examples of reflected motion are very common; 
 as, for instance, when a rolling ball encounters an opposing 
 stone in its path, in which case it flies off obliquely in a 
 new direction ; when we throw a thin piece of slate along 
 the surface of a river, and make it skip from point to 
 point ; or when an apple, in falling from a tree, touches a 
 lower branch in its descent, and rebounds in a slanting 
 direction to the ground. 
 
 256. It is found by experiments, that moving bodies 
 observe certain laws in respect to the line of direction 
 they pursue in rebounding or being reflected from any 
 impediment with which they happen to come in contact. 
 
 260. In the accompanying cut, figure 10, the line A B is 
 
 a level marble slab. C is 
 
 c an ivory ball, which, being 
 thrown towards the slab in 
 the direction of C E, is 
 B reflected in the direction 
 ED. Thus, the two angles 
 F and G are exactly equal; and it is. demonstrated, that 
 a perfectly elastic ball striking a smooth wall or floor makes 
 the same angle in leaving the point where it strikes that 
 it does in approaching it. 
 
 261. Whatever be the angle at which the ball strikes 
 the smooth fixed surface, the same rule will be observed to 
 
 be followed. This is exem- 
 p ified in figure 11. If the 
 ball be dropped perpendicu- 
 larly from L to K, it will re- 
 bound and return to L. If 
 sent in the line H K, it will 
 rebound or be reflected to I. 
 The angle which a ball makes 
 with the perpendicular line in goingfrom H to K, is call d 
 
 235. Explain the diagram. 
 
 236. Explain the diagrams, and angle ot incidence. 
 
90 COMPOSITION OF MOTION AND FORCES. 
 
 the angle of inci fence; and the angle which it makes in 
 rebounding from the point at K to I, is called the angle 
 of reflection. These angles are always equal. 
 
 262. A calculation of the angles of reflected motion is 
 necessary in the case of presenting a shield or other object 
 to ward off a missile or blow from the person. If the 
 angle be too acute, that is, if the blow be too point-blank, 
 the shielding object may be damaged, or perhaps destroyed ; 
 while, if the angle be obtuse, the object which gives the 
 blow will slide off harmlessly. In playing at the game of 
 billiards, the greatest exactness is required in the calcula- 
 tion of the forces and their directions according to the 
 principles of reflected motion ; and a similar kind of skill 
 is required by those who handle the bat in the game of 
 cricket. 
 
 THE LAWS OF MOTION CONTINUED. 
 
 COMPOSITION OF MOTION AND FORCES. 
 
 263. Hitherto we have spoken only of the motion of a 
 body as produced by a single impulsive force, and turned 
 aside or reflected by another force acting upon it ; we have 
 now to consider the subject of compound motion and force, 
 or motion and force produced -by two or more forces acting 
 on a body in different directions at the same time. 
 
 264. If two or more forces act on a given point of a 
 body, at certain angles, a single force may be found which 
 would produce the same effect. This single force is tech- 
 nically called the resultant or equivalent. For instance, 
 a wind blowing from the north-west, and a current setting 
 from the north-east, both acting on a ship and tending to 
 carry it with equal velocities in their own directions, the 
 ship will be found to move in an intermediate direction, as 
 if it were acted on by a single force, like a breeze, from 
 due north. 
 
 It is usual, in treating of combinations of mechanical 
 forces, to represent them by diagrams, the various lines of 
 which are significant of the quantity or intensity of the 
 
 237. What use is the calculation of the angles of reflection? 
 
 238. What of compound forces, and the resultant? 
 
COMPOSITION OF FORCES. 
 
 SI 
 
 forces, of the directions in which they act, and of the 
 effects produced by them. This explains the reason for 
 illustrating the action of forces by the following figures: 
 
 265. In figure 12, we have an example of motion pro- 
 
 Fig.12. duced by two forces in different 
 
 directions acting on a body. . A is 
 a ball, which, having received a 
 c blow at B, is proceeding onward to 
 C. At the point A, while on its 
 course, it receives a blow equal to 
 the former, which second blow 
 would have been alone capable of 
 carrying it to E in the same time 
 f that the first blow would have car- 
 ried it to C. This new force, by changing the direc- 
 tion of the original motion, causes the ball to move in a 
 line towards F, and the effect is the same as if the ball had 
 been at first sent in the direction of A F by a single force. 
 Practically- it would be difficult to regulate blows with such 
 nicety as to produce this line of motion, but in the theory 
 of forces the law is as it has been stated. The line A F 
 in the figure here drawn is termed the diagonal of (he 
 square. 
 
 266. Should the constituent forces be of different mag- 
 nitudes, then the figure described maybe a parallelogram, 
 or oblong, as in the annexed cut, fig. 13. The force here, 
 in the direction A B, is double that of the cross force C D, 
 
 Fig. is. by which means the ball describes 
 
 a diagonal line to F, and so forms 
 a parallelogram, when we draw 
 all the lines connected with the 
 experiment. The parallelogram 
 thus formed is called the paral- 
 lelogram of forces. The two 
 given forces acting in the direc- 
 tions E B, E D, are called components, and the single 
 force in the direction E F is the resultant. The process 
 
 239. Explain the first diagram, and the diagonal of the square. 
 
 240. Describe the second, and the italicised terms. 
 
92 
 
 COMPOSITION OF FORCES. 
 
 of finding a single force equivalent to two or more forces, 
 is called the composition of forces. 
 
 267. The process of finding forces which will produce a 
 motion equal to that of a single force, is called the resolu- 
 tion of forces. 
 
 The following are examples of the resolution of forces : — 
 
 268. If a boat DEM floating on a river be pressed 
 downwards in the line M C by a current, two forces P and 
 
 F'g- 14. _ Q,, acting in the di- 
 
 rections M P, M Q., 
 may be found that 
 will counteract the 
 
 
 
 
 
 
 R C, 
 
 D 
 
 M / 
 -U- =5 ^-- 
 
 
 R' 
 
 
 E 
 
 
 
 
 
 rent, and keep the 
 boat stationary. F or, 
 make M C to repre- 
 Q sent R, the force of 
 
 the current, and make MC' equal to M C, and find M A 
 and M B as before, they will respectively represent P and 
 Q,. If two men, therefore, pull two ropes in the directions 
 M P, M Q., with forces denoted by M A, M B, they would 
 keep the boat at rest. If the ropes be tied to two posts at 
 P and Q., the forces M A, M B, will represent their reac- 
 tions. 
 
 269. Let HM be a canal boat, M P the rope by which 
 it is drawn by a horse attached to it at P. Thy force of 
 
 the draught being 
 denoted by M P, it 
 may be resolved into 
 M A and M B, of 
 which only M A is 
 effective in drawing 
 
 Fig-. 15. 
 
 D 'sFl 
 
 
 the boat forward ; the other force M B tends to turn the 
 head of the boat in the direction M B. This last force must 
 therefore be counteracted, which is effected by means of 
 the helm H E turned to an oblique position. When the 
 boat is in motion, the water, being at rest, produces a re- 
 
 241. What is the first diagram ? 
 24 Q. Explain the record. 
 
composition of forces. 
 
 93 
 
 sistance or pressure against the helm. If C D denote the 
 resistance, it may be resolved into H D and H C, of which 
 H D produces no effect on the helm ; therefore C H is the 
 only effective pressure. Again, C H may be resolved into 
 C F and F H, the latter of which tends to turn the stern 
 of the boat in the direction F H, and thus counteracts the 
 force M B, by tending to turn the boat round in an oppo- 
 site direction ; and the part C F tends to move the boat 
 backwards, and thus, counteracting a part of the force M A, 
 it retards the progress of the vessel. The two forces F H, 
 M B, would move the boat sideways, or laterally, to the 
 side of the canal ; but this can be prevented by giving the 
 helm a little more obliquity, for, from the length and shape 
 of the vessel, it is much more easily moved in 'the direc- 
 tion of its length than of its breadth. 
 
 270. Let TP be a ship, S L its sail, W A the direction 
 of the wind and its pressure on the sail. W A can be re- 
 solved into A B perpendicular to the sail, and B W 
 parallel to it, the latter of which has no effect in pressing 
 on the sail ; therefore A B is the effective pressure on the 
 sail. Were the vessel round, it would move in the direc- 
 tion B A. Let B A be resolved 
 into C A and B C, the former C A 
 acting in the direction of the keel 
 or length of the vessel, or in the 
 direction C'A, and the latter per- 
 pendicular to it, or in the direction 
 of the breadth. The former pres- 
 sure C A is the only pressure that 
 
 moves the vessel forward, the other BC makes it move 
 sideways. From the form of the vessel, however, this lat- 
 ter force BC produces comparatively little lateral motion ; 
 any that it does occasion, is called leeway. By turning 
 the helm, the vessel may be made to turn round in any 
 direction by the pressure of the water upon it, if the vessel 
 has also at the same time progressive motion. 
 
 271. The suspension of a kite in the air is another 
 
 243. Explain the diagram. 
 
94 
 
 COMMON MOTION. 
 
 interesting' illustration of the eff ct of the pressure of a 
 current of air, the explanation of which belongs to Pneu- 
 matics. 
 
 THE LAWS OF MOTION CONCLUDED. 
 
 COMMON MOTION. 
 
 272. Motion, as has been stated (154), is called common, 
 when participated in by two or more bodies. Thus, all 
 things on the earth, including the atmosphere, have a mo- 
 tion in common with the earth ; a person riding in a chaise 
 has a motion in common with the chaise ; a person in a mov- 
 ing vessel at sea has a motion in common with the vessel. 
 
 For convenience, we shall, in treating of this branch of 
 our subject, use the terms larger and smaller body — the 
 larger being understood to be the body on which the force 
 to produce motion is immediately impressed, and the 
 smaller being the body which is carried along by the body 
 which has received this impression of force. 
 
 273. A large body is in motion ; it is moving in a cer- 
 tain direction, at a certain velocity ; every thing on it, or 
 small body connected with it, partakes in its motion, and 
 has a tendency to proceed in the same direction, and at 
 the same velocity. 
 
 274. It appears strange that there should be a com- 
 munication of motion from the larger body to the 
 smaller, without the immediate intervention of impressed 
 force on the smaller ; but a little examination shows that 
 such must necessarily be the case. The larger body has 
 received the impulse to move, and this impulse is trans- 
 mitted through the whole mass of the body, including all 
 the small objects on its surface, and those which are any 
 way connected with it in its propulsion. When a man is 
 walking on the deck of a ship which is moving at the rate 
 of ten miles an hour, he perhaps imagines that he has no 
 more motion than if he were walking on the solid ground. 
 But it would be incorrect for him to think so. His body. 
 
 244. What of common motion, with examples ? 
 
 245. How is it accounted for ? 
 
COMMON MOTION. 
 
 95 
 
 ' and every thing about his person, have received an im- 
 pulse from the vessel ; he possesses a velocity of ten miles 
 an hour as much as the planks of the vessel do ; and this 
 onward motion he cannot divest himself of, as long as the 
 ship continues to move at this rate of speed, or as long as 
 he continues in connection with it. 
 
 275. On account of this participation of motion in ail 
 bodies moving in connected masses, it is observed that all 
 objects whatever keep their proper places in or about the 
 large moving bodies with which they are in contact, and 
 hence no confusion takes place in the relative situation 
 of objects on the earth by its motion. For example, when 
 we leap from the ground, the earth does not slip away 
 from below us ; if we ascend in a straight line of direction, 
 we fall down exactly upon the same spot whence we arose. 
 When a man falls from the top of a mast of a moving ves- 
 sel, he falls upon the deck upon a spot directly under the 
 point whence he fell ; the vessel does not leave him. 
 When we are sitting in the cabin of a moving vessel, and 
 let a small object drop from our hand to the floor, it falls 
 on a point on the floor immediately below, the same as if 
 it had been dropped in a house on solid ground ; the floor 
 does not leave it behind. When we are sitting in a 
 rapidly moving coach, and, in a similar manner, let an 
 object fall, it descends in the same manner to the bottom 
 of the coach. The reason for these phenomena is that 
 already mentioned — the small objects possess a motion 
 derived from the larger ; this common motion, or motal 
 inertia , as some authors call it, is retained by the small 
 objects during their descent, so that, while descending, 
 they are also going forward ; in other words, they display 
 a composition of motion — a horizontal motion and a de- 
 scending perpendicular motion. 
 
 276. One of the most beautiful examples of common 
 motion, is that which is exhibited by an equestrian stand- 
 ing on a horse which is running round a circle, while he 
 it the same time throws oranges from his hand and catcfus 
 ’mm in their descent. Notwithstanding his rapid motion, 
 
 246. Name the familiar examples of this motion. 
 
96 
 
 COMMON MOTION. 
 
 the oranges which an j thrown into the air do not fall be- 
 hind ; they return regularly to his hand. To counteract 
 centrifugal force, he leans greatly inward ; but this does 
 not alter the law of motal inertia, which causes the oranges 
 to return. He throws them almost sidewise in an inward 
 slanting direction, and yet they come readily back to him. 
 The reason for these phenomena is. that the oranges par- 
 ticipate in the forces by which he himself is impelled and 
 sustained. 
 
 277. Small bodies which have derived a motal inertia 
 from a larger, continue to possess this motal inertia, after 
 leaving the larger, untl they meet with some new impres- 
 sion of force sufficient to alter their condition. If they 
 were not pulled to the earth by attraction, and were not 
 opposed by the atmosphere, they would go on moving in 
 a straight line for ever. 
 
 27S. When we drop a ball from the window of a moving 
 coach, it continues to go forward, as if it were still in the 
 coach, till it meet the ground, when it is stopped ; thus, 
 its motal inertia :s destroyed. If we attempt to leap from 
 a moving body, such as a coach or a boat, we continue to 
 possess the motion which we previously had until we 
 touch the earth, when we receive a shock by the destruc- 
 tion of our motal inertia. But if we leap from one moving 
 body to another moving body which is going near it, on 
 the same level, in the same direction, and at the same ve- 
 locity, we sustain no shock, because the body upon which 
 we leap possesses the same condition of motion as that 
 which we possess. 
 
 279. When a man standing on the ground shoots at a 
 bird on the wing, he requires to follow its motion by keep- 
 ing his gun moving when presented at it ; but if he be 
 standing on the deck of a ship sailing at the rate of ten 
 miles an hour, and point his gun at a bird flying in the 
 same direction and at the same velocity as the ship, then 
 he is placed in the same condition as the bird ; he does 
 not require to move his gun, as if following the bird. In 
 
 247. Repeat and explain the illustrations cited. 
 
 248. Describe the uses of understanding this law. 
 
COMMON MOTION. 
 
 9/ 
 
 taking aim at a bird on the wing from the solid ground, it 
 requires considerabJe skill to prevent the shot from pro- 
 ceeding to a point behind the bird, because the shot is 
 entirely destitute of rnotal inertia on being fired, unless it 
 be previously put in motion. But a bullet on leaving a 
 gun which is moving at the same rate as the bird, and in 
 the same direction, keeps going on in the direction of the 
 bird, because it retains the motion it had in common with 
 the gun. The bullet in this case does not go in the 
 direction of the gun, but obliquely, so as to keep up with 
 the motion of the bird, so that the same effect is produced 
 as if the shot had been fired from a fixed gun on land to a 
 fixed point in the air in advance of the bird. Should the 
 bullet be fired from a gun in a moving vessel, for instance 
 a ship sailing westward to a fixed point on land, then a 
 certain allowance must be made for the motal inertia of 
 the bullet ; it must be fired a little eastward, and the motal 
 inertia will carry it westward to the object. 
 
 280. Objects falling from bodies moving in an onward 
 direction to those which are at rest, are regulated by the 
 same law that governs projectiles. The falling objects, as 
 formerly mentioned, are affected by two motions — one in 
 a horizontal and the other in a descending direction. 
 When these motions are unequal, the falling body de- 
 scribes a curve in its descent, the convex side of the curve 
 being uppermost. Thus, motal inertia and the motion pro- 
 duced by projectile impulse are the same thing ; and hence, 
 powerful centrifugal force in the sun, sufficient to disen- 
 gage a portion of its mass, would be equivalent to a projec- 
 tile impulse from it as a fixed body. 
 
 281. In consequence of the general participation of 
 common motion in all things connected with a moving 
 body, there can be no consciousness of motion in the living 
 beings carried about by it, provided the motion be perfectly 
 smooth, and there be no means of observing bodies which 
 are at rest. Thus, on account of our possessing a motion 
 in common with the earth, which moves with perfect 
 smoothness, we can neither see nor feel the earth moving. 
 
 249. When are we consci ms of p ir'icipaiing in this motion ? 
 
98 CONCLUSION OF LAWS OF MOTION. 
 
 We, however, see the sun, which seems to us to be in 
 motion in reference to the earth, but which, by various 
 means, we know to be at rest ; and hence we are assured 
 of the earth’s diurnal rotation on its axis, and its annual or 
 planetary motion round the sun. In the same manner, a 
 person sitting in the cabin of a smooth-sailing ship, and 
 not looking out at the windows, cannot, by his mere sen- 
 sations, tell that the vessel is moving ; but if he look at the 
 shore, which is at rest, he is immediately sensible of the 
 progressive motion of the vessel. 
 
 2&2. In looking from a moving body, as from the earth 
 to the sun, from a ship to the shore, or from a coach to 
 objects on the wayside, a delusive feeling prevails that it 
 is not the body you are upon, but the body which is at 
 rest, that is ready moving — going in a direction contrary 
 to that of the body you are connected with. This is in 
 consequence of our possession of motion in common with 
 the moving body. We are under an influence, or in a 
 condition, that renders us incapable of seeing our own 
 motion : and, hence, the error which the sense of vision 
 leads us to commit, is left to be rectified by an exertion of 
 the understanding. 
 
 The subject of the next Book is Mechanics, or a treatise 
 on Mechanical Powers and Machinery, being the ap 
 plication of the laws above demonstrated to contrivances 
 for lessening and aiding human labour. 
 
 250. Why are we not so, and when 1 
 
 251. To what mistakes are we liable, and why ? 
 
 THE END. 
 
 STEREOTYPED BY L. JOHNSON AND CO. 
 PHILADELPHIA. 
 
ELEMENTS 
 
 OF 
 
 NATURAL PHILOSOPHY. 
 
 PART II. 
 
 MECHANICS. 
 
 CHAMBERS’ EDUCATIONAL COURSE. 
 

 . 
 
 - 
 
 
 ■ 
 
 
 i 
 
 
 
INTRODUCTORY OBSERVATIONS 
 
 BY 
 
 THE AMERICAN EDITOR. 
 
 This second book of Natural Philosophy is designed to fol- 
 low the work on Matter and Motion, which is introductory to 
 practical Mechanics, and should first be made familiar to both 
 the teacher and scholar. The catechetical questions upon 
 every page of both these volumes are designed to furnish such 
 an analysis of every topic as shall render the acquisition of 
 the elements of these departments of science so easy that 
 none may be deterred from their cultivation ; and if the sug- 
 gestions of the preface be acted upon, and the learners be en- 
 couraged to construct, with their own hands, simple and rude 
 apparatus, which shall illustrate the principles taught, no 
 study will be more delightful to children than the departments 
 of nature and art to which these sciences introduce them. 
 
 Nothing can be more gratifying to the philanthropist, than 
 to witness the march of mind, characteristic of the present 
 age, as exemplified in the diffusion of scientific knowledge 
 among the masses of the people, by the adaptation of the 
 teachings of philosophy to the young and rising generation. 
 Instead of locking up knowledge in these higher walks of 
 science in cloisters and academic groves, accessible only to a 
 favoured few, the teachings of philosophy are now disrobed 
 of all their mystery, and by cheap publications they are ra- 
 pidly becoming the property of all. 
 
 The educational series, of which this little volume forms a 
 part, is calculated to initiate the young into the elements of all 
 
 3 
 
4 
 
 INTRODUCTORY DBS K RVATIONS. 
 
 the sciences, even in the common school. The poorest chil- 
 dren of the present generation may thus become wiser than 
 their parents, and understand more of philosophy and science 
 than was the lot of any in the previous century, except those 
 whom fortune favoured with wealth and thorough collegiate 
 training, extending to adult years, and even consuming the 
 greater part of life in the seclusion of study. And a taste for 
 such pursuits being thus early acquired, and the habit of in- 
 vestigation into the nature and causes of things becoming, as 
 it will, a part of their mental constitution, it is impossible to 
 predict, or to limit, the practical improvements and useful dis- 
 coveries which will result, or the amount of increase to hu- 
 man progress and happiness which this generation shall 
 witness. 
 
 The admirable “ Lectures of Dr. Lardner on Science and 
 the Useful Arts,” now in the course of publication, are so 
 well adapted to the popular mind, that as a sequel to these 
 volumes, they cannot fail to be appreciated, and they will be 
 eminently useful in proportion as they are read by those who 
 are trained in their schools to estimate the importance and 
 necessity of philosophy in every department of art, and in the 
 economy of human life. 
 
 Let parents and teachers then avail themselves of this series 
 and other kindred publications to cheapen knowledge, and 
 diffuse it abroad far and wide among the masses, in conform- 
 ity with the spirit of the age. 
 
 D. M. R. 
 
PREFACE. 
 
 The present Treatise, comprehending' Mechanics, the Ele- 
 ments of Practical Machinery; and Moving Forces, forms 
 the second department of Natural Philosophy, according to 
 the arrangement described in the Preface to the Laws of 
 Matter and Motion. 
 
 A passage of that preface, as of general application, may 
 appropriately be repeated here: — “In exercising a class in 
 this and other departments of Natural Science, it will be 
 found to be of considerable importance to cause each para- 
 graph to be mastered or thoroughly understood before pro- 
 ceeding to what follows ; for the whole constitutes a structure 
 in which each part rests on what has gone before it. The 
 pupil should, also, not only read, but be induced to think on 
 the nature of the principles which are unfolded, and led to 
 find examples of their action in the every-day concerns of life, 
 and the common phenomena of the universe.” It is further 
 suggested, that pupils should, by the aid of small pieces of 
 wood, cord, and other easily procured materials, endeavour to 
 work out, with their own hands, the various principles of Me- 
 chanics which are demonstrated in the following pages. It is 
 believed, that by no other means could these valuable princi- 
 ples be so well fixed in the memory, or have such a powerful 
 effect in cultivating the understanding. 
 
 In the present, as in the preceding Treatise, very great pains 
 have been taken to render the language simple and intelli- 
 gible, so that the learner may find at least no technical diffi- 
 culty in his path. Those who are desirous of pursuing the 
 study of Dynamical and Mechanical science, beyond the 
 
6 
 
 PREFACE. 
 
 limits of these elementary works, and who possess a know- 
 ledge of Algebraic and Mathematical formulae, are recom- 
 mended to have recourse to the excellent “ Treatise of Me- 
 chanics, Theoretical and Practical, by Olinthus Gregory 
 the “ Introduction to Natural Philosophy, bf William Nichol- 
 son or to the Treatises of Wood, Leslie, and Whewell 
 No popular and comprehensive treatise on the properties of 
 matter and doctrines of forces, excels the well-known Ele- 
 ments of Physics, by Dr. Neil Arnot. There are also a few 
 compendious productions of American writers which may be 
 consulted, particularly those of Gale, Comstock, and Bigelow, 
 to which the Editors have to acknowledge themselves indebted 
 for some useful hints. Engineers, mill-wrights, and other 
 artisans, who require to make practical calculations, will find 
 a small work, entitled “ Burton’s Compendium of Mecha- 
 nics,” worthy of their attention. 
 
CONTENTS. 
 
 Page 
 
 CrENEit-iL Definitions 9 
 
 Of Levers 11 
 
 First kind of Lever 12 
 
 Second kind of Lever 20 
 
 Third kind of Lever 22 
 
 Of Compound and Bent Levers 24 
 
 Compound Levers 24 
 
 Bent Levers 26 
 
 Levers of oblique action 27 
 
 Recapitulation of Lever Powers, and Animal Levers 30 
 
 Animal Levers 31 
 
 Of the Wheel and Axle 35 
 
 Wheels ........ 35 
 
 Wheel and Axle 36 
 
 Of Cords and Pulleys 39 
 
 Fixed Pulleys 39 
 
 Moveable Pulleys 40 
 
 Principle of the Pulley Power 42 
 
 Combinations of Pulleys 43 
 
 Practical application of Pulleys 45 
 
 Of the Inclined Plane 45 
 
 Standards of comparison for Inclinations 46 
 
 Principle of the Power of Inclined Planes 47 
 
 Rules for calculating the Power of Inclined Planes. 48 
 
 Examples... 49 
 
 O the Wedge 52 
 
 Rules for calculating the Powers of the Wedge 53 
 
 Examples of Wedge Powers 53 
 
 ? 
 
8 CONTENTS. 
 
 Page 
 
 Of the Screw 54 
 
 Powers of the Screw 55 
 
 Rules for calculating the Powers of the Screw 57 
 
 Examples of Screw Powers 59 
 
 Mechanical combination and structure 60 
 
 Arched Structures 64 
 
 Elements of practical Machinery 67 
 
 Wheels 70 
 
 Wheels and Pinions 70 
 
 Practical Examples 73 
 
 Working of Toothed Wheels 74 
 
 Altering the Direction of Motion 74 
 
 Bevel Wheels 75 
 
 Transmission of Power by Belts 75 
 
 Shafts and Pulleys 77 
 
 Changing Velocity 78 
 
 Preserving regularity of Motion .by a Variable Force 79 
 Alternate or reciprocating Motion — Eccentric Wheels 80 
 
 Oblique action 83 
 
 Cranks 84 
 
 Ratchet Wheels 84 
 
 Engaging and disengaging Machinery 85 
 
 Practical Machinery continued — of accumulating and 
 
 equalising Power 85 
 
 Accumulation 85 
 
 Equalisation — Fly Wheels. , . . . . 88 
 
 Practical Machinery continued — Obstacles to Motion 89 
 
 Friction 89 
 
 Uses of Friction 93 
 
 Resistance of Air and Water 93 
 
 Practical Machinery concluded — Moving Forces 94 
 
 Human Labour 95 
 
 Horse’s Power — Draught 98 
 
 Water Power 103 
 
 Steam Power 104 
 
NATURAL PHILOSOPHY. 
 
 MECHANICS. 
 
 GENERAL DEFINITIONS. 
 
 1. The application of the laws of motion and foices to 
 objects in nature or contrivances in the arts, forms the 
 branch of Natural Philosophy usually treated under the 
 head Mechanics, Mechanical Powers, or Elements of 
 Machinery. 
 
 2. The original signification of the word machine , which 
 is the root of the various terms mechanic , mechanical, and 
 so forth, was art, contrivance, or ingenuity. 
 
 3. When the term mechanic, or mechanical, is applied to 
 the action of forces — as mechanical powers — it is meant 
 that certain powers are exerted, or motion produced, by the 
 action of particles or masses of matter, solid or fluid, one 
 upon another. Thus, mechanical action is applied to the 
 action of forces that produce no change in the constitution 
 of bodies, and is therefore distinguished from chemical or 
 any other species of action.* 
 
 4. In Natural Philosophy, machines are spoken of as 
 being of two kinds — simple and complex. A simple ma- 
 
 * In scientific works, the term mechanics is usually restricted to the 
 action of solids, while mechanical or mechanically is applied to the ac- 
 tion of both solids and fluids. For example, the wearing away of stone 
 by the action of water, is said to be mechanical action, or that the wa- 
 ter acts mechanically . 
 
 1. Define the science of Mechanics, and the word itself. 
 
 2. How is mechanical distinguished from chemical force ? 
 
 3. How are machines divided primarily 1 
 
 9 
 
10 
 
 MECHANICAL POWERS. 
 
 chine is equivalent to a tool or instrument, and a complex 
 machine is an engine, in which different parts combine to 
 produce the required effect. In common phraseology, 
 these distinctions are not very minutely attended to. 
 
 5. Machines are, under all denominations or circum- 
 stances, only instruments through which power may be 
 made to act. They only convey, regulate, or distribute, 
 the force or power which is communicated to them from 
 some source of motion, and never create or generate power. 
 But although a machine does not create power, or give 
 more power than it has received, it practically applies the 
 power which has been communicated to it, in so conve- 
 nient and easy a manner, that a result ensues almost as 
 surprising as if it had actually generated the whole or a 
 portion of the power it exhibits. 
 
 6. The main purpose required in mechanical operations 
 is to overcome, oppose, or sustain, a certain resistance or 
 force. 'This purpose is obtained by applying another species 
 of force. According to the usual phraseology, the resist- 
 ance or force to be overcome is called the weight, and the 
 force which is applied is called the power. 
 
 7. The ability of applying force by the human hands, 
 without the aid of instruments or machines, is very limited. 
 In almost all our operations of art, it is found necessary to 
 call in the aid of instruments or machines of some kind. 
 All the instruments which mankind have adopted for their 
 use — from a piece of stick with which the savage scratches 
 the ground as a plough, to the most elegant piece of mech- 
 anism — act upon certain fixed principles in nature, which 
 a long course of experience and scientific investigation has 
 developed. 
 
 8. The mechanical powers, which exhibit the working of 
 these principles, are strictly only three in number, namely — 
 
 1. The Lever. 
 
 2. The Pulley, or Cord. 
 
 3. The Inclined Plane. 
 
 4. What part do they enact ? 
 
 5. What is the main purpose of mechanical operations 1 
 
 6. Define the weight and power in this relation. 
 
 7. The importance and variety of machinery. 
 
MECHANICAL POWERS. 
 
 11 
 
 These may be called the Primary Mechanical Powers ; 
 and from two of them, the Lever and Inclined Plane, other 
 three are formed, as follow — 
 
 1. Wheel and Axle, from the Lever. 
 
 2. Wedge, from the Inclined Plane. 
 
 3. Screw, from the Inclined Plane. 
 
 These may be called the Secondary Mechanical Powers. 
 The six altogether form the elements of every species of 
 machinery, however complex. 
 
 OF LEVERS. 
 
 9. The lever is one of the most important and exten- 
 sively used of all the mechanical powers, and its operation 
 exhibits some of the leading principles in mechanics. 
 
 10. A lever is a rod, or bar of iron, wood, or any other 
 material which is moveable upon or about a prop or ful- 
 crum, or about a fixed axis. It is called a lever, from a 
 French word signifying to raise, and has been applied to 
 instruments for raising or lifting weights. 
 
 11. Three elements contribute to the operation of the 
 lever — the power , the fulcrum, and the weight. The power 
 is the force applied, the fulcrum is the prop or support, and 
 the weight is the resistance or burden to be lifted. The 
 terms power and weight have merely a reference to the 
 manner in which the machine is used ; strictly, both the 
 power and the weight are forces the same in character and 
 action. 
 
 12. There are three kinds of levers, differing according 
 to the relative situation of the power, fulcrum, and weight. 
 Each of these kinds consists of a straight bar, and in theo- 
 retical calculations is supposed to be in itself destitute of 
 any gravity or degree of heaviness. In theory, also, the 
 forces which are applied are supposed to act at right angles 
 to the fulcrum. 
 
 S. Name the primary mechanical powers, and the secondary. 
 
 9. Whence are the latter derived ? 
 
 10. Define a lever. 
 
 11. What elements are concerned in its action ? 
 
 12. Define each of these and which are forces. 
 
 13. Varieties of levers, and theory of their action. 
 
12 
 
 FIRST KIND OF LEVER. 
 
 13. In the first or most simple kind of lever, “ the ful- 
 crum is disposed between the power and the weight.” In 
 the second kind, “ the weight is disposed between the 
 power and the fulcrum.” In the third kind, “ the power is 
 disposed between the weight and the fulcrum.” 
 
 FIRST KIND OF LEVER. 
 
 14. In the first kind of lever, “ the fulcrum is disposed 
 between the power and the weight.” Figure 1, is an ex- 
 
 Figure l. ample. A to B is a straight 
 
 =gf bar, resting on a prop or ful- 
 i crum F. From A to F is the 
 w « long arm of the lever, and from 
 F to B is the short arm. P is the power, or a certain force 
 drawing down the extremity of the long arm at A. W is 
 the weight suspended from the extremity of the short arm 
 at B.* The object is, to cause P, which is supposed to be 
 a small weight, to balance or overcome W, which is sup- 
 posed to be a weight much heavier. Practically, the force 
 of a man pressing upon the extremity of the handle of the 
 lever at A, will effect with ease, in lifting the heavy weight 
 W, what it would require a much greater force to accom- 
 plish by pressing upon the long arm at a point half way 
 betwixt A and the fulcrum.t 
 
 15. This is more clearly exemplified in figure 2, which 
 
 represents a lever placed 
 conveniently for raising a 
 square block W, which is 
 the weight. On pressing 
 down the extremity of the 
 long arm of the lever at 
 
 * Some authors call the long arm the arm of the power, and the short 
 arm the arm of the weight. 
 
 t Note 1. — Properly speaking, the power does not sustain the weight, 
 for both are supported by the fulcrum ; the power, in the case of equi- 
 librium, only prevents the weight from producing a motion of rotation. 
 
 Note 2 . — In every machine, simple or complex, besides the power 
 required to balance the resistance, there must be some additional 
 power applied in order to produce motion, or overcome the inertia of 
 rest of the body. 
 
 14. Define each of the three in the arrangement of the forces. 
 
 15. Explain the diagram, and the notes. 
 
 Figure 2 
 
FIRST KIND OF LEVER. 
 
 13 
 
 A, the point of the short arm B raises the block. F is 
 an object lying on the ground to press against as the ful- 
 crum. As in the case of figure 1, “ the force of a man 
 pressing upon the extremity of the handle at A, will effect 
 with ease, in lifting the weight W, what it would require a 
 much greater force to accomplish by pressing upon the long 
 arm at a point half way betwixt A and the fulcrum.” 
 
 1G. The principle in mechanics which produces this 
 phenomenon is very simple, and is explained by what is 
 called the Law of Virtual Velocities, or, from its gene- 
 ral application, the Golden Rule of Mechanics. 
 
 17. This law or rule is, that a small weight, descend- 
 ing a LONG WAY, IN ANY GIVEN LENGTH OF TIME, IS EQUAL 
 IN EFFECT TO A GREAT WEIGHT DESCENDING A PROPORTION- 
 ABLY SHORTER WAY IN THE SAME SPACE OF TIME. In Other 
 
 words, what is gained in velocity or time, is lost in expen- 
 diture of power. 
 
 18. Another way of stating this important law is as 
 follows: — In the case of equilibrium, if a motion be 
 
 GIVEN TO THE MECHANICAL POWER, THEN THE POWER MUL- 
 TIPLIED BY THE SPACE THROUGH WHICH IT MOVES, IN A 
 VERTICAL DIRECTION, WILL BE EQUAL TO THE WEIGHT MUL- 
 TIPLIED BY THE SPACE THROUGH WHICH IT MOVES IN A 
 VERTICAL DIRECTION. 
 
 19. This principle, which applies to every mechanical 
 movement in the case of equilibrium, has been illustrated 
 by a reference to the property of attraction of gravitation. 
 What is called weight, is only an effect of gravity on the 
 atoms of matter. In figurative language, every atom is 
 drawn towards the earth by an invisible line or cord of 
 attraction ; and when one atom rises or falls ten inches, the 
 same quantity of attraction is drawn out from, or sent 
 back to the earth, as if ten atoms were to rise or fall only 
 one inch. 
 
 20. Thus, by a proper mode of applying the power, we 
 
 16. What of this diagram ? 
 
 17. By what names has this principle of action been called J 
 
 18. What is this law, and how stated 1 
 
 19. What of atomic gravitation ? 
 
 20. What illustration is stated ? 
 
1 1 
 
 FIRST KIND OF LF.VKR. 
 
 may cause a weight of one pound, by moving through a 
 space of ten feet, to raise another weight of ten pounds, 
 moving through a space of one foot; or (the reverse) by a 
 weight of ten pounds moving through the space of one foot, 
 we may make a single pound move through the space of 
 ten feet. But by none of the mechanical powers shall we 
 be able, by moving a weight of ten pounds through one 
 foot, to move a single pound through eleven feet ; nor, by 
 a single pound moving through a space of nine feet, shall 
 we be able to raise a weight of ten pounds through ode 
 foot. 
 
 21. Neither by the power of the lever, therefore, nor by 
 any other of the mechanical powers, can we make any abso- 
 lute increase of the power which is applied. In other 
 words, the quantity of power expended in any great and 
 instantaneous effort, is exactly the amount of the power 
 which has been previously accumulated. All that w ? e can 
 do to procure mechanical advantage, is to accommodate 
 the velocity, force, or direction of the applied power, to the 
 purposes which we may have in view. 
 
 22. To apply this principle to the lever, figure 1 or 2, a 
 small force at A is equal to double the force exerted at a 
 point half way betwixt A and the fulcrum, yet, in both 
 cases, the same amount of mechanical power is expended. 
 A slight push downwards at A, by being continued for one 
 minute, is equal te a push of double the force at a point 
 half way towards the fulcrum, continued for the same time. 
 Any amount of force, therefore, can be exerted u r ith ease 
 at the extremity of the long arm of the lever, provided we 
 choose to make the arm long enough and strong enough. 
 
 23. It may possibly be said that it would be as expedi- 
 tious to push down the extremity of the long arm of the 
 lever, as to push dowm the arm at a point nearer the ful- 
 crum. Practically, in small levers this may be the case ; 
 but when levers of considerable length have to be used, 
 and a succession of depressions and raisings are necessary, 
 it will be found that more time is spent in working with a 
 
 21. What of the increase of power, not absolute ? 
 
 22. How is this explained ? 
 
 23. What of long and short levers ? 
 
FIRST KIND OF LEVF.R. 
 
 15 
 
 long than a short lever. For when the sweep of the lever 
 is inconveniently long, the person using it has to move his 
 body quickly up and down over a larger space, and is sooner 
 fatigued. For this reason, although a boy with a long lever 
 may balance as great a weight as a man with a shorter one, 
 yet, in raising weights successively by it, the boy would be 
 sooner fatigued. 
 
 24. It is a general rule that “the force of the lever 
 increases in proportion as the distance of the power from 
 the fulcrum increases, and diminishes in proportion as the 
 distance of the weight from the fulcrum diminishes.” In 
 making calculations to ascertain the proportions to be ob- 
 served betwixt the power and the weight, regard must be 
 paid to the respective lengths of the long and short arms 
 of the lever. We must also tix what are to be the units of 
 weight and distance, and let them be the same on both 
 ends. If we state inches to be the unit of length of the 
 short arm, inches must be the unit of length of the long 
 arm; and in the same manner, if ounces be made the unit 
 of weight of the short arm, ounces must be made the unit 
 of power of the long arm. 
 
 25. Rule. — Multiply the weight by its distance from the 
 fulcrum; then multiply the power by its distance from the 
 same point, and if the products are equal, the weight and 
 the power will balance each other. 
 
 26. Example first. — Suppose a weight of 100 pounds 
 on the short arm of a lever, at the distance of 8 inches from 
 the fulcrum, then another weight or power of 8 pounds 
 would be equal to this, at the distance of 100 inches from 
 the fulcrum. Because 8 multiplied by 100 produces 800, 
 and 100 multiplied by 8 produces 800— and thus the weight 
 and the power would mutually counteract each other. 
 
 27. Example second. — Suppose we wish to calculate 
 what power should be employed at the end of the long 
 arm of a lever to balance a given weight at the end of the 
 short arm. We multiply the weight by the length of i:s 
 
 24. What general rule is stated 1 
 
 25. How are the proportions to be calculated ? 
 
 26. Give the rule, with examples. 
 
in 
 
 FIRST KIND OF T.F.VFR. 
 
 nrm. This gives us a product ; then divide that product 
 by the number of inches in the long arm, and the result or 
 quotient is the power. Thus, a weight of 10 pounds mul- 
 tiplied by 10 inches, as the length of the short arm, gives 
 a product of 100. If the length of the long arm be 20, 
 we find how many twenties are in 100, and there being 5, 
 consequently 5 pounds is the power. In this instance, the 
 mechanical advantage is two to one — that is, the power is 
 twice as small as the weight. 
 
 28. The common spade used in delving in gardens offers 
 a familiar example of simple lever power, when employed in 
 raising the earth from its place to turn it over. Figure 3 
 represents an equally familiar example, namely, a wood- 
 
 Figure 3. 
 
 sawyer or carpenter moving a log of timber from its place, 
 by means of a long pole or beam of wood. Stone masons 
 use a lever of iron of this description, called a crow-bar. 
 
 29. The ancient Egyptians were acquainted with the 
 power of the lever, and employed it to raise the large 
 blocks of stone of which the Pyramids are composed. The 
 lever used by them, however, was of a rude description, 
 and required many men to wield it. According to Hero- 
 dotus, a Greek historian, who writes of Egypt, it consisted 
 of a beam of wood, fixed by a joint or axle on an upright 
 frame, which was the fulcrum. The longer arm of this 
 lever was several times the length of the shorter arm. To 
 lift each block, it was necessary to employ two of these 
 
 27. What familiar illustrations are cited 1 
 
 28. What ancient levers are described 1 
 
FIRST KIND OF DEVER. 
 
 17 
 
 Figure 4. 
 
 levers, with ropes attached, one lever at each end of the 
 block. A number of men were employed to pull the ropes, 
 as represented in figure 4. After the block was raised 
 one step up on the exterior of the pyramid, the levers were 
 lilted up another step higher, and the block raised to their 
 level. In this clumsy and tedious manner were the Pyra- 
 mids of Egypt erected.* In modern times, the principle 
 of the lever is employed in a much more speedy and effica- 
 cious manner in raising or lowering blocks of stone for 
 masonry, or in loading and unloading bales of goods in 
 commerce, by means of a machine called a crane, hereafter 
 to be described. 
 
 30. The power of the first kind of lever is frequently 
 
 seen to. operate in machines 
 
 Figure 5. 
 
 or instruments having two 
 arms. The most common 
 examples of this nature are 
 pincers, scissors, and simi- 
 lar instruments. In a pair 
 of scissors here represent- 
 ed. the two limbs are seen 
 
 * To erect one pyramid alone, called the Great Pyramid, required 
 the work of 100,000 men for twenty years ; and although these men 
 were compelled to work without wages, like slaves, the expense 
 incurred was enormous. In the present day, the steam-engines of 
 England, by a united effort, cor lift the whole of the stones of the 
 Great Pyramid into their places in about twenty hours. 
 
 29. How would such machines be regarded now f 
 
 30. By what means would the moderns do such work I 
 
 31. Explain the second diagram. 
 
 32. What do we iear. in the note 1 
 
13 
 
 FIRST KIND OF LEVER. 
 
 to be joined with a rivet at the centre, which is the ful- 
 crum of both. 
 
 31. A common scale beam for weighing, used by shop- 
 keepers, is an example of 
 the first kind of lever 
 formed with two arms of 
 equal length, and suspend- 
 ed over the centre of gra- 
 vity, so that the two extre- 
 mities balance each other. 
 See figure G. Sis a string or 
 line suspending the beam 
 A B at a central point F, 
 
 which is the fulcrum. The point of suspension or pivot is 
 sharpened to a thin edge, so as to allow the arms to rise or 
 fall with as little friction as possible, when any thing is put 
 in the scales. 
 
 32. There is another kind of balance, called a steelyard, 
 which consists of a lever with arms of unequal length, and 
 acts upon the principle of distance from the fulcrum on 
 the long arm compensating for weight on the short arm 
 as defined in paragraphs 26 and 27. Figure 7 is a repre- 
 sentation of the steelyard balance. C is the fulcrum or 
 pivot by which the beam is suspended, and freely plays as 
 on an axis. A is the short arm, and the opposite end is 
 
 Figure 7. 
 
 Figure 6. 
 
 33. Explain the first diagram, and its action. 
 
 34. What of the second ? 
 
FIRST KIND OF LEVER. 
 
 19 
 
 the long arm. W is the scale for the reception of the article 
 to be weighed. The long arm is graduated into divisions 
 by marks, each mark denoting by a figure a certain num- 
 ber of pounds or "Dunces, P is a weight of a certain heavi- 
 ness, and being moveable by a ring, it can be slipped along 
 the bar to any required point. The same weight is always 
 used, and thus constitutes one of the principal conveniences 
 of this kind of balance. In proportion as the article to be 
 weighed in the scale W is heavy, so is the weight P slip- 
 ped along to a greater distance from the fulcrum ; and when 
 it is brought to a point where it balances the article, the 
 figure on the bar at that point indicates the amount of the 
 weight. If P be one pound, and if, when suspended from 
 the division at (5, it balance the weight at W, it is evident 
 that the weight will be six times P, or six pounds And 
 so on with all the other divisions. 
 
 33. The steelyard, though not so ancient as the common 
 balance, is of considerable antiquity. It was used by the 
 Romans, and has long been in use among the Chinese. 
 Neither the common balance nor the steelyard is suitable 
 for showing the varying weight or heaviness of an article 
 at different latitudes of the earth’s surface, because the 
 weights employed are equally affected with the attraction 
 of gravitation and centrifugal force, as the article to be 
 weighed. For this reason the difference of weight result- 
 ing from the causes mentioned, can only be demonstrated 
 by a balance formed of a spring of elastic metal. By 
 suspending the article from the spring, it pulls it out to 
 a certain extent, and so indicates the weight on a gradu- 
 ated scale on the instrument. As the spring acts the same 
 in all latitudes, it serves as a fixed or unalterable power, 
 while the article to be weighed is liable to an alteration in 
 its weight or heaviness according as it is brought near or 
 carried from the equator.* 
 
 * See explanation of variability of weight in paragraph 68, Law, 
 Matter, and Motion. 
 
 35. What objection lies against both ? 
 
 36. What of the spring balance ? 
 
20 
 
 SECOND KIND OF LEVER. 
 
 SECOND KIND OF LEVER. 
 
 FA 
 
 nw 
 
 34. In the lever of the second kind, the weight is placed 
 
 Figure 8. between the power and the ful- 
 
 2 ) crum, as in figure 8. The line 
 
 from A to B is the long aru; ; B 
 to F is the short arm. W is the 
 weight, and P is the power. The 
 object required by this lever is to 
 lift the weight W by raising the extremity of the lever at A. 
 In this as in the case of the first kind of lever, the power 
 is increased in proportion to its distance from the fulcrum. 
 
 35. Examples of this kind of lever power are common. 
 One of the most familiar is 
 that of a man pushing or lift- 
 ing forward a bale of goods, 
 as represented in figure 9, in 
 which the bale or weight W 
 presses against the lever be- 
 tween the power P and the 
 
 Figure 9. 
 
 fulcrum F. 
 
 36. Another example of the second kind of lever is that 
 of a man using a wheelbarrow, 
 as represented in figure 10. A 
 point in the wheel of the bar- 
 row where it presses on the 
 ground, is the fulcrum. The 
 body of the barrow, with us 
 load, is the weight. And the 
 two handles lifted or held up 
 by the man form the power. In 
 
 proportion as the man shortens or lengthens the handles in 
 holding them, so does he increase or diminish the weight 
 he has to sustain. 
 
 37. Two men carrying a load between them on a pole 
 is also an example of the second kind of lever. The load 
 may either rest upon or be dependent from the pole. In 
 
 Figure 10. 
 
 37. Define the second kind of lever. 
 
 38. What of each of the diagrams 1 
 
 39. What of the two diagrams ? 
 
SECOND KIND OF LEVER. 21 
 
 the case of two porters carrying a sedan chair, by means of 
 two poles, the load or weight is partly above and partly below 
 the line of the lever. In the case of porters carrying a barrel 
 
 slung from a pole, as in figure 
 11, the weight is altogether be- 
 low the lever. In both instan- 
 ces the principle is the same. 
 Each man acts as the power 
 in moving the weight, and at 
 the same time each man be- 
 comes a fulcrum in respect to 
 the other. If the weight hang 
 fairly from the centre of the pole, each man will bear just a 
 half of the burden ; but if the weight be slipped along to be 
 nearer one end of the lever than the other, then the man 
 who bears the shorter end of the pole, supports a greater 
 load than the man who is at the long end. The weight 
 increases precisely in proportion as it advances towards 
 him. Sometimes, when a man and a boy are carrying a 
 hand-barrow between them, the man, in order to ease the 
 weight as much as possible to the boy, holds by the arms 
 of the barrow near to where they join the loaded part. 
 
 38. In yoking horses to the extremities of cross bars in 
 ploughs, coaches, or other vehicles, care requires to be 
 taken to hook the cross bar to the load at its centre, other- 
 wise one horse will have, to pull more than the other. 
 
 39. An inflexible beam resting on supports or fulcra at 
 its two extremities, acts similarly as a lever of the second 
 kind. Should no weight be appended to its centre, the 
 weight of the material itself, when the extension is consid- 
 erable, will be enough to bend it down, and even to break 
 it. Extended flexible cords or chains, are from this cause 
 always bent down in the middle, no power of extension 
 being able to overcome the gravity of the materials, which 
 will give way before they can be rendered perfectly straight. 
 The bended string of a boy’s paper kite is an example of 
 this powerful influence of gravity of materials. 
 
 40. What of the weight of the material itself ? 
 
 41. What of the string of a kite ? 
 
22 
 
 SECOND KIND OF LEV TK. 
 
 40. The instrument used for cracking nuts (figure IT: 
 is an example of the second kind of lever with two arms or 
 
 Figure 12. limbs. The fulcrum is the joint which 
 connects the two limbs; the nut be- 
 tween them is the weight or resistance ; 
 and the hand which presses the limbs 
 together, in order to break the nut, is the power. As each 
 limb is a lever, a double lever action takes place in the 
 operation. 
 
 41. The oar of a boat in rowing is a lever of the 
 second kind. The hands of the sailor who pulls constitute 
 the power; the boat is the weight to be moved ; and the 
 water against which the blade of the oar pushes, is the ful- 
 crum. 
 
 42. The second kind of lever is sometimes employed as 
 an instrument of pressure. The point of the short arm is, 
 for example, pushed into a crevice or hole in a wall, the 
 fulcrum is the object to be pressed, and at the extremity of 
 the long arm a heavy weight is applied. In this rude but 
 efficacious manner are cheeses pressed in some parts of the 
 country. 
 
 Figure 13. 
 
 
 THIRD KIND OF LEVER. 
 
 43. In the lever of the third kind, the power is placed 
 between the weight and the ful- 
 crum. Figure 13. The fulcrum 
 is at the extremity of the short arm 
 at F ; the weight VV is dependent 
 from the extremity of the long arm 
 at A ; and P is the power. 
 
 44. In this kind of lever, the power acts with consider - 
 ble disadvantage, or with small effect; but this disadvantage 
 is compensated by an opposite advantage, which is frequently 
 of great importance in the operations of both nature and 
 art. The advantage consists in the velocity with which a 
 small power will cause the extreme point of the long arm 
 
 42. Explain the first diagram. 
 
 43. What of rowing a boat, and of pressing cheeses t 
 
 44. Explain the second diagram. 
 
THIRD KIND OF LEVER. 
 
 Figure 14. 
 
 of the lever to move over a great space. This lever, theio- 
 fore, whether in nature or art, is used only when a great 
 space has to be traversed quickly by the long arm ; but in 
 tins case, the power must always be greater than the weight. 
 
 45. An example of this kind of lever is found in the 
 foot-board of the turning-lathe. 
 Figure 14. The foot of the work- 
 man presses lightly on the board 
 or plank near the end which rests 
 on the ground, or fulcrum, and 
 causes the opposite extremity of 
 the board to move in a downward 
 direction over a considerable space. 
 A spring over-head, or a crank, 
 pulls the board up again by means 
 
 of a string S; the workman again presses it downward, and 
 so a constant action of the string or cord which works the 
 lathe, is easily produced. 
 
 46. A man wielding a flail with two hands, and similar 
 instances of using weapons, are also examples of the third 
 kind of lever action. A similar action is observable when 
 we use fire-tongs ; a small motion of the fingers near the 
 joint of the instrument, causes the legs, which are two 
 levers, to open or shut over a considerable space. 
 
 47. Before the peculiar advantages of this kind of lever 
 became known, or were appreciated, it was called the losing 
 lever. 
 
 48. The movements in the limbs of animals are gene- 
 rally produced by the action of this kind of lever power. 
 
 45. What is gained by this kind of lever 1 
 
 46. Explain the first diagram. 
 
 47. What erroneous name was formerly given, and why ? 
 
 48. What example is found in animal structure 1 
 
24 
 
 COMPOUND LEVERS. 
 
 OF COMPOUND AND BENT LEVERS. 
 
 COMPOUND LEVERS. 
 
 49. When several levers of the simple kinds are con- 
 nected together, and are made to operate one upon the 
 other, the machine so formed is called a Compound Lever. 
 In this machine, as each lever acts with a power equal to 
 the pressure on it of the next lever between it and the 
 power, the force is increased or diminished according to 
 the number or kind of levers employed. 
 
 50. Figure 15 represents a compound lever, consisting 
 
 of three simple levers of the first kind, placed in a line, and 
 each working on its own fulcrum. The desired object of 
 the machine is for a small force or power at P, to move or 
 balance a large weight at W. The same rule applies, in 
 calculating the action of this combined lever, which has 
 already been given for the simple lever, namely, “ multiply 
 the weight on any lever by its distance from the fulcrum; 
 then multiply the power by its distance frocn the same 
 point, and if the products are equal, the weight and the 
 power will balance each other.” Or, for the form of lever 
 in the figure, “ multiply the length of the long arm by the 
 moving power, and multiply that of the short one by the 
 weight, or resistance.” 
 
 51. It is supposed that the three levers in the figure are 
 of the same length, the long arms being six inches each, 
 
 4i). Define a compound lever. 
 
 50. Explain the second diagram. 
 
 51. By what rule is the force of this combined lever calculated t 
 
 Figure 15. 
 
 E 
 
COMPOUND I.F.VFRS. 
 
 2- r , 
 
 mid the short ones two inches each ; required — the weight 
 which a moving power of l pound at P will balance at YV. 
 In the first place, I pound at P would balance 3 pounds at 
 E ; we say 3, because the long arm being 6 inches, and 
 the power I pound, 6 multiplied by 1 is ti ; and the short 
 one being 2 inches, we find that there are 3 twos in 6, 
 therefore 3 is the weight. The long arm of the second 
 lever being also 6 inches, and moved with a power of 3 
 pounds, multiply the 3 by 6, which gives 18 ; and multiply 
 the short arm, being 2 inches, by a number which will give 
 18 ; we find that 9 will do so (9 twos are 18) ; therefore 9 
 is the weight borne at the extremity of the short arm of 
 the second lever at D. The long arm of the third lever 
 being also 6 inches, and moved with a power of 9 pounds, 
 multiply the 9 by 6, and we have 54; and multiply the short 
 arm, being 2 inches, by a number which will give 54 ; we 
 find that 27 will do so (twice 27 is 54) ; therefore 27 is the 
 weight borne at the extremity of the short arm of the third 
 lever. Thus I pound at P will balance 27 pounds at YV. 
 Or 1 ounce at P will balance 27 ounces at YV — the pro- 
 portions being always alike, whatever denomination of 
 weight we employ. 
 
 52. In this instance, the increase of power is compara- 
 tively, small, because the proportion between the long and 
 the short arms is only as 2 to 6, or 1 to 3. If we make 
 the proportions more dissimilar, as 1 to 10, or 1 to 20, the 
 increase of force becomes very great. For example, let 
 the long arms be 18 inches each, and the short ones 1 
 inch each, and 1 pound at P will balance 18 pounds at A, 
 and the second lever will be pushed up with a power of 18 
 pounds. This 18 being multiplied by the length of the 
 lever 18, gives 324 pounds as the power which would 
 press down the third lever. Lastly, multiply this 324 by 
 the length of the lever 18, and the product is 5832 pounds, 
 which would be the final weight at YV which 1 pound at P 
 would raise. 
 
 53. The following is a general rule for calculating the 
 
 52. Repeat the calculations of these three levers. 
 
 53. How may the force be increased < 
 
26 
 
 BENT LEVERS. 
 
 advantages of a compound lever consisting of anv number 
 of levers, whether equal or not : — Cali ihe arms of the de- 
 ferent levers next the power the arms of power , and the 
 other arms the arms of weight; then, if the lengths of the 
 arms of power and the power itself be successively multi- 
 plied together, the product will be equal to the continued 
 product of the arms of weight and the weight, when the 
 power and weight are in equilibrium. 
 
 54. A similar result to that of a combination of levers, 
 might be produced by only one lever, provided it were long 
 enough, but the operation would be both clumsy and incon- 
 venient. By combining levers, and making them act one 
 upon another, great weights maybe balanced within a small 
 compass, and with an exceedingly small power. On this 
 account, machines are constructed with combinations of 
 levers, for weighing loaded carts and other heavy burdens. 
 The cart is wheeled upon a sort of table placed level with 
 the ground, beneath which the levers are arranged; and a 
 small weight placed on a scale attached to the extreme 
 point of the first lever, balances the load, which rests on 
 the table above the last lever. This species of weighing 
 machine is often to be seen at toll-bars. 
 
 BENT LEVERS. * 
 
 55. In the foregoing examples of lever powers, the levers 
 or bars are supposed to be straight, and the powers and 
 weights, or forces, are supposed to act at right angles with 
 them. 
 
 56. Levers are frequently bent in their form, for purposes 
 of convenience, and the powers and weights often act 
 obliquely , or not at right angles. 
 
 57. In calculating the mechanical advantage of bent 
 levers, the chief matter for consideration is obliquity in the 
 direction of the applied power and weight. Obliquity in 
 the action of the forces, generally diminishes the mechanical 
 advantage. 
 
 54. What of the arms of power and of weight 1 
 
 55. To what uses are compound levers applied ? 
 
 56. What of bent levers and their action f 
 
LEVERS <-»!■' OBLKiUE ACTION. 
 
 27 
 
 58. Whatever be the form of the lever, or the direction 
 of the power and the weight, the mechanical advantage of 
 the power or the weight is always represented by a line 
 drawn from the. fulcrum, at right angles to the direction in 
 which the forces are respectively exerted. 
 
 Figure 16. 
 
 59. Figure 16 is a bent 
 ^lever, with the power P hang- 
 ing from A, and the weight 
 ,W hanging from B. In this 
 case, both the power and the 
 weight act at right angles to 
 an ideal line, drawn as from E 
 to G across the fulcrum, which 
 strikes the lines of direction 
 of the forces at right angles. This ideal line, therefore, 
 represents the true lever of calculation, and we proceed with 
 it according to the ordinary rule for calculating lever powers 
 In this manner, the bending goes for nothing. 
 
 Figure 17. 
 
 69. Figure 17 is a straight 
 lever with the power P acting 
 G obliquely from D to A, and the 
 * vveight W acting obliquely from 
 G to B. In order to calculate 
 the power of this kind of lever, 
 we must draw lines as represented in figure 18. First, we 
 draw a line obliquely upwards in the direction of the pulling 
 
 Figure 18. 
 
 M N 
 
 power. This line is seen dot- 
 ted from A to M. We then 
 draw a line off from it, or at 
 right angles with it, to F the 
 ulcrum. This line is seen 
 dotted and marked H. We 
 next draw a line obliquely up- 
 wards in the direction of the 
 pull of the weight, as from B to N ; and in the same manner 
 as bef ire, draw a line at right angles from it. This line 
 
 57. Explain the diagram. 
 
 58. Explain the first diagram. 
 
 59. What does the second show 7 
 
 60. How does the third differ? 
 
28 
 
 LEVERS OF OBLIQUE ACTION. 
 
 is seen doited and marked K. We have now found an 
 ideal lever, with two arms, H and K. This jdeal lever is 
 the true lever of calculation, and we proceed with it accord- 
 ing to the ordinary rule for calculating lever powers (25). 
 til. The next example, figure 19, represents the power 
 
 Figure 19. 
 
 and weight acting obliquely the same 
 as in figure 18; but in this case the 
 lever is bent. The bending of the 
 lever, however, does not affect tiie 
 rule of calculation, which is the same 
 as in figure 18. W e begin by draw- 
 ing a line obliquely upwards in the 
 direction of the pulling power. This 
 line is seen dotted from A to C. We 
 then draw a line off, from it, or at right angles with it, to F 
 the fulcrum. This line is seen dotted from C to F. We 
 next draw a line obliquely upwards, in the direction of the 
 pull of the weight; and in the same manner as before, 
 draw a line at right angles from it (as from L), to F. W e 
 have now found an ideal lever; from C to F being the long 
 arm, and F to D the short arm. This ideal lever is the 
 lever of calculation, and we proceed with it according to 
 the ordinary rule for calculating lever powers (25). 
 
 Figure 20. 62. Sometimes the lever is bent in such a 
 
 manner that the long arm rises perpendicularly 
 from the fulcrum, as in figure 20. In this 
 case, the upright long arm from F to A acts 
 precisely as if it were horizontal, because the 
 power or hand is supposed to act at right 
 B angles to the arm. If we were to draw an 
 ideal line from the t p of the arm at A directly 
 in downwards to F, it would descend straight 
 : through the arm, and hence, in this case, there 
 would be no use in drawing it. The calculation may be 
 made with the arm itself. 
 
 W< 
 
 61. What of ideal levers, and their uses ? 
 
 62. Explain each of the diagrams. 
 
LEVERS OF OBLIQUE ACTION. 
 
 29 
 
 Figure 21. 
 
 63 But if the power be made 
 to draw obliquely downward, or not 
 at right angles to the line from 
 the fulcrum, we must draw' an ideal 
 line, as represented in figure 21. 
 The line of direction of the power 
 is seen proceeding obliquely from 
 .A to the hand P. A dotted line 
 H is drawn at right angles from 
 this line to F the fulcrum ; the line 
 H therefore represents the true arm 
 
 of power of the lever. 
 
 64. Suppose the line of direction of the power in the 
 last figure, had been drawn slantingly upward instead of 
 dowmvard, then an ideal dotted line would have been to be 
 drawn obliquely downward from it, crossing the arm at A, 
 and a line drawn at right angles from it to F, would have 
 represented the arm of power. 
 
 Figure 22. 65. The adjoining figure, represent- 
 
 ing a pronged hammer in the act of 
 being employed to extract a nail, is an 
 example of a bent lever, resembling 
 those just mentioned. The hand of 
 the workman is the pow'er exerted on 
 the long arm of the lever ; the head of 
 the hammer, where it presses on the 
 flat surface beneath it, is the fulcrum ; 
 the prongs are the short arm of the 
 lever, and the resistance of the nail is the weight. 
 
 66. From the examples now given, it will be observed 
 that, whatever be the shape or bending of the lever, and 
 whatever the degree of obliquity of the applied force, the 
 pow'er of the machine may be calculated by drawing ideal 
 lines at right angles from the lines of the forces to the 
 fulcrum, and making the calculations from them. 
 
 63. How are calculations made in all cases ? 
 
33 
 
 LEVER POWERS RECAPITULATED. 
 
 RECAPITULATION OP LEVER POWERS, AND 
 ANIMAL LEVERS. 
 
 67. To avoid confusion or misapprehension, representa- 
 tions of the three kinds of levers already defined are here 
 again exhibited, along with a few brief explanatory obser- 
 vations on their character and comparative value. For the 
 sake of clearness, a hand pulling is substituted as the power. 
 The arm of the power is used to signify the long arm, and 
 the arm of the weight the short arm. 
 
 68. Each of the three kinds of levers has its own special 
 advantages, and is peculiarly adapt- 
 ed to certain situations and pur- 
 poses. In a lever of the first kind, 
 where the point of support is be- 
 tween the power and the weight, 
 either the power or the weight may 
 have the advantage. The advan- 
 tage varying thus between the 
 
 power and the weight, the lever of the first kind is held to 
 be most convenient tor an equilibrium ; of which, as has 
 been shown, the common balance affords an example. 
 
 69. In the lever of the second kind, the arm of the power 
 
 B figure 23. 
 
 A 
 
 »w 
 
 Figure 24. 
 
 B 
 
 is necessarily longer than that of the 
 weight or resistance, since the resist- 
 ance is between the power and the ful- 
 crum, whilst the power is at one ex- 
 tremily. The advantage being thus 
 SVuhvays in favour of the power, the 
 lever of the second description is al- 
 ways favourable for overcoming re- 
 sistance. 
 
 70. In the lever of the third kind, on the contrary, the 
 advantage is m favour of the weight or resistance, which 
 is placed at an extremity, while the power lies between it 
 and the point of support. But the disadvantageous position 
 
 64. What kind of lever is shown in each diagram ? 
 
 65. Name the advantages and uses of each kind. 
 
LEVER IN THE HUMAN ARM. 
 
 31 
 
 Figure 25. 
 
 of the power in this kind of lever is compensated by the 
 extent of motion which necessarily ensues from that very 
 disadvantage ; for, the closer the 
 power is to the fulcrum, and the 
 farther it is from the weight, the 
 more extensive and rapid is the mo- 
 ^ tion to which the weight can be 
 
 subjected on the slightest action of 
 
 the power. The lever of the third 
 kind, therefore, is obviously favour- 
 l able to extensive and rapid move- 
 
 ments. 
 
 ANIMAL LEVERS. 
 
 71. A short consideration of the characteristic advan- 
 tages and defects attendant on each of the three kinds of 
 levers, will suffice to convince us of the superior applica- 
 bility of the third kind of lever to the purposes of animal 
 motion. Celerity and extent of motion, it is obvious, are 
 here objects of paramount importance; and by the employ- 
 ment chiefly of this species of lever, both in the trunk and 
 the limbs, they are beautifully and effectually attained. In 
 the animal machine, the bones form the bases or arms of 
 the levers : the muscle, contractible at the command of the 
 will or fancy, represent the potcer ; the joints, th efulcrums 
 or points of support; and the weight of the body or of in- 
 dividual limbs, as it may happen, constitutes the weight or 
 resistance, increased, as in the case of the hands at times, 
 by some substance carried or held by them. The most 
 important result of the lever powers of the animal machine, 
 is locomotion, or the transmission of the whole body from 
 place to place. [In human structure, as indeed in all ani- 
 mal organization.it is wonderful to observe the mechanism 
 o the Creator’s wisdom and goodness, anticipating all the 
 boasted discoveries of science, and plainly teaching the 
 highest lesson in practical and experimental philosophy.] 
 
 72. The spinal or vertebral column, when we regard its 
 
 6n. What of the bones, muscles, and joints of animals 1 
 
32 
 
 ANIMAL LEVERS. 
 
 motions as a whole, represents a lever of the third kind, of 
 which the fulcrum is in the articulation of the last bone of 
 the column with the sacrum (the bone on which the trunk 
 rests) ; the power being in the muscles, which are inserted 
 into the vertebral column along its course, and the resist- 
 ance in the weight of the head, neck, and trunk. 
 
 73. But a much more dis- 
 
 Figure 26. 
 
 B 
 
 C w 
 
 'F 
 
 bow to the wrist, 
 w . Figure 28 
 
 tinct and intelligib'e example 
 of a lever of the third kind 
 in the animal frame, is exhib- 
 ited in the human arm. A 
 strong muscle, arising in the 
 shoulder, passes down in front 
 over the joint of the elbow, 
 and is inserted into one of 
 the two parallel bones which 
 compose the frame work of 
 1 the lore-arm, oi from the el- 
 On being contracted in the slightest 
 degree, at the impulse of the will, this 
 muscle (the power) elevates instantane- 
 ously the hand (the weight or resistance) 
 to the shoulder, bending the arm upon 
 the elbow-joint, (th e fulcrum). Figure 
 26 illustrates perfectly this mechanism 
 of the arm. F represents the elbow- 
 joint, P the power or will acting over, 
 or from ihe shoulder S, through the 
 contracting muscle M, and B the arm 
 from the hand to the elbow, while the 
 weight W, is an object supposed to be 
 laced in the hand. 
 
 74. Nothing can better illustrate the 
 characteristic advantages of levers of the 
 third kind, than this action in the hu- 
 man arm. The contraction of the muscle 
 to the extension of only one inch, raises 
 
 67. What of the spinal column ? 
 
 68 Explain the diagram mechanically. 
 69. What does this diagram show 1 
 
ANIMAL LEVERS. 
 
 33 
 
 the hand, even with a very considerable weight in it, through 
 a semicircle of twenty-one inches ; and by relaxing the mus- 
 cle only a little, the hand, as represented in figure 27, is 
 allowed to drop over a similarly wide range. No doubt, 
 other muscles in the arm assist in this action, but the prin- 
 cipal part is performed by the one described, and here in- 
 dicated by the letter M. 
 
 75. It is worthy of observation, that in the second of 
 these figures, illustrating the mechanism of the arm, the 
 lever power acts under increased disadvantage from the 
 greater inclination of the limb than in the preceding 
 figure. We can raise or sustain a much larger weight 
 with the hand when the arm is bent at right angles, than 
 when it is extended nearly in a straight line; and the 
 more the arm is stretched out, the more is the power di- 
 minished. What is gained, however, in force, is neces- 
 sarily lost in extent of motion. 
 
 76. A fine example in the animal frame of the lever of 
 the third kind, where extent of motion was not the object 
 wanted, as it is in the arm, is seen in the mechanism of 
 the lower jaw. To overcome resistance, was in this case 
 the chief end required; and, acc >rdingly, we find a strong 
 muscle constituting the power, passing perpendicularly 
 downwards from the side of the head to the lower jaw-bone, 
 and acting on it in a straight line, the fulcrum being in the 
 articulation of the jaw near the ear. The force with which 
 the power acts in this case is immense, particularly when 
 the resistance to be overcome is placed near the fulcrum, 
 or directly beneath the action of the muscle. We take 
 advantage of this circumstance in cracking nuts, by putting 
 them to a certain distance back between the jaws. 
 
 77. As in the arms, so also in the inferior extremities, 
 the principal muscles hold such a relative position to the 
 bones and joints, as to sustain the weight of the b dy, and 
 transfer it al ng the surface of the ground, with all the ad- 
 vantage of a lever power of the third kind. If the mecha- 
 nical action of the muscles and bones in animals, whether 
 in the spinal column or in the limbs, had been arranged 
 
 70. What of the muscle of the jaw ? 
 
•34 
 
 ANIMAL LEVERS. 
 
 on the principle of either of the other descriptions of levers, 
 the requisite contraction in the length of the acting muscles 
 would have been so great as to render the shape of the 
 limbs, and the- whole figure indeed, extremely clumsy, and 
 the movements very inconvenient; and hence the wisdom 
 of the existing arrangement, in regard to simplicity, beauty 
 and efficiency. 
 
 78. Examples of the first and second kinds of levers are 
 not absent in the animal machine ; and where such exam- 
 ples occur, they uniformly corroborate what has been said 
 respecting the peculiar character of each of the three kinds 
 of levers. The head, for instance, requires, for the fulfil- 
 ment of its exalted uses, and for the comfort of the being, 
 to be maintained erect, and in equilibrium. A lever of 
 the first kind, we have seen, is the one best calculated to 
 effect this object, and accordingly, such a mechanism is 
 found to exist here. The point of support of this lever is 
 in the articulation of the lateral masses of the two first 
 bones of the spinal column, whilst the power, and the re- 
 sistance or weight, occupy each an extremity of the fever, 
 represented, the one by the face, and the other by the back 
 part of the head. To understand this fully, it must be ex- 
 plained, that the point of support, or fulcrum, on which the 
 head rests, is much nearer to the back part of the skull ihan 
 to the fore part or face ; therefore, this forepart (the weight 
 of the lever) has a tendency to fall forwards, but is retained 
 in equilibrium by the strong muscles passing from the lower 
 parts of the neck to the hind part of the head (which is 
 thus rendered the site of the power of the lever.) A perfect 
 lever of the first kind is thus made the agent in maintain- 
 ing the head in equilibrium 
 
 79. In like manner.it might be shown, that, where there 
 is a considerable resistance to be overcome, the bones and 
 muscles are so arranged as to represent a lever of the kind 
 best calculated for the fulfilment of such a purpose — namely, 
 a lever of the second kind, as the first is employed when 
 an equilibrium is to be maintained, and the second when 
 rapid and extensive motion is to be produced. 
 
 71. Would either of the other kinds oflevers have been as well l 
 
 72. Wli.it example of the first kind of lever is cited ? 
 
WHEELS. 
 
 35 
 
 OF THE WHEEL AND AXLE. 
 
 80. A lever has been defined, (10) to be “ a rod or bar of 
 iron, wood, or any other material which is moveable upon 
 or about a prop or fulcrum, or about a fixed axis.” 
 
 81. The illustrations which have been given, show the 
 lever only in its character of a simple bar, which is move- 
 able in some part “ upon or about a prop or fulcrum.” It 
 is now to be shown how it acts when moveable upon or 
 about a fixed axis. 
 
 82. When a lever is moveable upon an axis, and is sus- 
 ceptible of being turned completely round, it assumes the 
 character of the diameter of a wheel. 
 
 83. In figure 28, the simple rudiments of a wheel are 
 Figure 23. represented. A and B are the two 
 
 A F arms of a bar or lever playing upon a 
 
 fixed axis at F, and which axis is the 
 fulcrum. If we push down A, we raise B, or if we push 
 d >wn B, we raise A. In this manner the situation of the 
 power and the weight is transferable from one end to the 
 other, as in the beam of a common balance, without alter- 
 ing the equilibrium. 
 
 Figure 29. 84. Figure 29 is a representation 
 
 c of awheel in a state more advanced 
 
 to completion. Here the arms AB 
 are connected with the arms DC, 
 both at the centre F, and by means 
 B of the circumference or rim of the 
 wheel. By reason of this union of 
 parts, the central axis at F becomes 
 the common fulcrum for every por- 
 tion of the wheel ; therefore, from 
 the centre to any point of the circumference is an arm of a 
 iever, although the line of that lever be not marked or seen, 
 as in the case of a distinct spoke. 
 
 85. A line through the centre from one side of the cir- 
 
 73. What of the wheel and axis 1 
 
 74. Explain the diagrams. 
 
36 
 
 WHEEL AND AXLE PERPETUAL LEVERS. 
 
 cumference of a wheel to the opposite side, is the diameter; 
 from the centre to any part of the circumference, is the 
 semi-diameter or radius. The arms or spokes are said 
 to radiate from a centre. The circumference is sometimes 
 called the periphery. 
 
 86. Besides wheels with axes in the centre, there are 
 wheels with axes not in the centre, called eccentric wheels. 
 At present, however, we are treating only of wheels having 
 i heir axes in the centre. 
 
 87. Wheels with a central axis may be rendered avail- 
 able as levers in various ways, according to the placing of 
 the weight or resistance. The plan commonly pursued 
 consists in giving to the wheel an axle, which is fixed to its 
 arms, and placing a weight near the axle or fulcrum, to 
 work against another weight at the circumference. 
 
 88. Thus, a machine is formed called the Wheel and 
 Axle, which constitutes one of the simple mechanical 
 powers, founded on the lever. 
 
 WHEEL AND AXLE. 
 
 69. The machine termed the Wheel and Axle consists 
 of a wheel fixed upon an axle or spindle, which axle turns 
 horizontally on its two ends in upright supports. See figure 
 30. The fulcrum of the ma- 
 chine is common to both the 
 wheel and the axle, and is the 
 centre of the axle. A is the 
 wheel, B is the axle, and H is a 
 handle with which the machine 
 may be turned. By turning the 
 wheel, the axle is also turned, 
 and a rope being fixed to the 
 axle, with the weight W hang- 
 ing at its extremity, the turning 
 of the wheel causes the axle to wind up the rope, and so 
 ’lift the weight. If, instead of turning the wheel with the 
 
 75. Define radius, periphery, and eccentric wheels. 
 
 76. What is a wheel and axle ? 
 
 77. Explain the first diagram. 
 
WHEEL AND AXLE. 
 
 37 
 
 hand, we wind a rope round the circumference of the 
 wheel, in a contrary direction from that in which the axle 
 rope is wound, and also hang a weight of a certain heavi- 
 ness, P, to its extremity, then the draught or pulling of the 
 wheel rope in unwinding, will turn the axle, and so wind 
 up the axle rope with its weight. In this manner, oee 
 power works against another, exactly as in the case of the 
 lever. By properly apportioning the two powers in corres- 
 pondence with the diameters of the wheel and the axle, the 
 one power or weight may be made to balance the other power 
 or weight, so as to produce an equilibrium of the machine. 
 
 99. The wheel and axle form what is called a perpetual 
 lever. Common simple levers act only for a short space, 
 or by reiterated efforts, so as to be adapted for lifting an 
 object from one place to another on the ground. The 
 perpetual lever, formed by the wheel and axle, turns round 
 without intermission, and is therefore suitable for lifting 
 weights attached to a rope, through a considerable space 
 upward from the ground without stopping. 
 
 91. Figure 31 is a representation of the machine end- 
 Figure 31. wise, and shows how the lever operates. 
 
 The line going across the machine from 
 A to B represents the line of the lever. 
 A is the situation of the power, F is the 
 centre or fulcrum, and B is the situation 
 of the wmight ; therefore, from A to F is 
 the long arm, and from F to B is the 
 short arm of the lever. In other words, 
 the long arm is half the diameter of the 
 wheel, and the short arm is half the 
 thickness or diameter of the axle. 
 
 92. By widening the wheel, and so 
 lengthening the long arm of the lever, the smaller will be 
 the power necessary to overcome the weight on the axle or 
 short arm; but what is gained by this mechanical advantage is 
 lost by the circumstance that the power must descend through 
 a proportionally greater space in order to raise the same 
 
 78. What is the use of the second ? 
 
 79. How is this shown to he a modification of the lever? 
 
33 WHEF.l. AND AXLE. 
 
 weight through tlie same space in the same time. This is in 
 agreement with the principle mentioned in paragraph 17. 
 
 93. To find what forces will balance each other, let the 
 same rules be followed as those given for the simple lever 
 in paragraph 25. Multiply the weight by its distance from 
 the fulcrum (that distance is half the diameter of the axle; ; 
 then multiply the power by its distance from the same point 
 (that is, half the diameter of the wheel), and if the products 
 be equal, the weight and the power will balance each other. 
 Thus, a power of one pound at or depending from the cir- 
 cumference of a wheel of twelve inches in diameter, will 
 balance a weight of twelve pounds at or depending from 
 the circumference of an axle one inch in diameter. 
 
 Note. No allowance is made in these calculations for the 
 overlaying of the rope in winding, which affects the length 
 of both the long and short arm ; but this is a matter of prac- 
 tical, not of theoretic import. 
 
 94. The principle of the wheel and axle, or perpetual 
 lever, is introduced into various mechanical contrivances 
 which are of great use in many of the ordinary occupations 
 of life. One of the simplest machines constructed on this 
 principle, is the common windlass for drawing water by a 
 rope and bucket from wells. Coal is lifted from the pits 
 in which it is dug, by a similar contrivance, wrought by 
 horse or steam power. 
 
 95. The capstan in general use on board of ships for 
 hauling or drawing up anchors, 
 and for other operations, is an 
 example of the wheel and axle, 
 constructed in an upright or 
 vertical, instead of a horizon- 
 tal, position. In figure 32, 
 one of these capstans is repre- 
 sented. The axle is placed 
 upright, with the rope windin 
 about it, and having a hea 
 pierced with holes for spokes 
 
 Figure 32. 
 
 80. By what rule are the forces calculated * 
 SI. What examples are cited 1 
 
 biro 
 
PULLEYS. 
 
 33 
 
 or levers, which the men push against to cause the axle to 
 turn. This is a powerful and convenient machine on ship- 
 board ; when not in use, the spokes are taken out and laid 
 aside. 
 
 An illustration of the wheel and axle, in a combined 
 form, is afterwards given in the case of the crane. 
 
 OF CORDS AND PULLEYS. 
 
 96 The pulley, or cord, is one of the primary mechani- 
 cal powers. A pulley is a wheel, with a groove in its 
 circumference, and is suspended by a central axis. In fixed 
 pulleys, a flexible cord, which is made to pass over and 
 hang from the upper part of the groove, has at one extremity 
 a certain weight to be raised, and at the other extremity a 
 power is attached for the purpose of pulling. 
 
 97. There are two kinds of pulleys, the fixed and move- 
 able. 
 
 FIXED PULLEYS. 
 
 A ^ 
 
 t 
 
 PQ 
 
 Figure 33. 98. The annexed cut, figure 33, repre- 
 
 — B "~iimsents a fixed pulley. A is the wheel ; B 
 'is a beam or roof from which the wheel is 
 suspended. P is the power hanging at one 
 end of the rope, and VV is the weight at 
 the other end. This kind of -pulley is 
 called a fixed pulley, because it does not 
 shift from its p sition. 
 
 99. The fixed pulley possesses no me- 
 chanical advantage. The wheel is merely a lever with 
 equal arms, and therefore the cord which passes over these 
 arms gains no advantage. To raise a pound weight from 
 the ground at the one end of the cord, the power of one 
 pound must be exerted at the other. 
 
 190. The object of the single fixed pulley is not to save 
 
 6 ^ 
 
 82. Define a pulley, and how many kinds. 
 
 S3. Explain the first diagram. 
 
 84. What advantage is gained by a fixed pulley > 
 
40 
 
 PULLEYS. 
 
 power, but to give convenience in pulling. For instance, 
 by pulling downwards, a weight may be raised upwards, or 
 by pulling in one direction, a load may be made to proceed 
 in another. The same object might be gained by drawing 
 a cord over a fixed post or pivot, but in this case the fric- 
 tion of the cord would chafe or injure it; the wheel or 
 pulley is therefore a simple contrivance to prevent friction, 
 for it turns round along with the cord. 
 
 MOVEABLE PULLEYS. 
 
 101. The moveable pulley is in form the same as the 
 fixed pulley, but instead of being placed in a 
 fixed position from a beam or roof, it hangs 
 in the cord which passes under it, and from 
 it the weight is suspended. In figure 04, a 
 moveable pulley is represented. A is a hook 
 in a beam to which one’ end of a cord is 
 
 p fixed. B is the moveable pulley, under 
 L which the cord passes and proceeds upwards 
 ® to C, a fixed pulley, from which it depends 
 to P, the power or the hand pulling. The 
 fixed pulley C is of no further use than to 
 change the direction of the power. W is 
 the weight hanging from B. 
 
 102. The moveable pulley possesses a mechanical ad- 
 vantage. The first point to be observed is, that the weight 
 hangs in the cord ; second, that the weight presses down 
 each side of the cord equally — that is, it draws as hard at 
 A as at C or P ; third, that the consequence of this equal 
 pressure, is the halving of the w r eight between the two ends 
 of the cord The halving of the weight is therefore 
 the mechanical advantage, given by the moveable pulley. 
 
 103 Example. — If the weight W be ten pounds, five 
 pounds is borne by A, and five pounds by P. The case 
 is precisely the same as that of two boys carrying a basket 
 between them. The basket is the weight, and each boy. 
 
 Figure 34. 
 
 85. Explain the moveable pulley and the diagram. 
 
 86. In w hat does the advantage consist ? 
 
PULLEYS. 
 
 41 
 
 with his hand upholding the handle, bears only half the 
 load, whatever it may be. If, instead of holding by the 
 handle, the boys slip a cord beneath it, and each take an 
 end of the cord, the case is the same. 
 
 104. In order to save expenditure of power in lifting 
 weights by pulleys, it is always contrived to cause some in- 
 animate object, as for instance a beam or roof, to take a 
 share of the weight, leaving only a portion to be borne by 
 the person who pulls. But in this as in all cases of me- 
 chanical advantage, the saving of power is effected only by 
 a certain loss of time, or a longer continuation of labour. 
 To lift a weight one foot Horn the ground, by the moveable 
 pulley a man must pull up the cord two feet : therefore to 
 lift a weight, it will take double the exertion to draw it up 
 a given height in a given time without the pulley, that it 
 would require with the intervention of the pulley. 
 
 105. As the power which a man 
 can exert by his hands, is able to over- 
 come a weight greater than the weight 
 ol his own person, this circumstance 
 may be taken advantage of in a very 
 peculiar manner, through the agency 
 ( f the fixed pulley. As represented 
 in figure 35, a man may seat himself 
 in a loop or seat attached to one end 
 of a cord, and passing a cord over a 
 fixed pulley above, may pull himself 
 upwards by drawing at the other end 
 of the cord. By adding a moveable 
 pulley and another fixed pulley to 
 the apparatus, the exertion of pulling 
 would be diminished one half. An 
 apparatus of this nature having two 
 fixed pulleys and one moveable pulley, is used by house 
 masons and other artizans, in making repairs on the fronts 
 of buildings. 
 
 Figure 35. 
 
 87. What illustrations are given 7 
 
 88. Explain the diagram. 
 
 89. How may the exertion be diminished 7 
 
42 
 
 PULLEYS. 
 
 PRINCIPLE OF THE PULLEY POWER. 
 
 106. The principle upon which pulleys act, is the dis- 
 tribution of weight throughout the different portions of the 
 cord, so as to lessen the power necessary to be exerted by 
 the operator. And along with this principle is the chang- 
 ing of the direction of the power for the sake of conveni- 
 ence in pulling. 
 
 107. According to ordinary language, the mechanical 
 power of which we are treating, is called the power of the 
 pulley; but, in reality, as has been just shown, the pulley 
 has no power in itself. The power of the machine is in the 
 cord. It is the equal tension of the cord through its 
 
 WHOLE LENGTH, BY WHICH THE WEIGHT IS DISTRIBUTED 
 UPON INTERVENING POINTS, THAT THE MACHINE OFFERS 
 ANY MECHANICAL ADVANTAGE. 
 
 108. In all cases in which cords are drawn tightly, so 
 as to hold objects in close contact, the same species of 
 power or mechanical advantage is exemplified. For in- 
 stance, in drawing a cord in lacing, or a thread in sewing, 
 this distribution of power is observable. If all the power 
 which is distributed throughout the sewing of a single pair 
 of strong shoes, were released and concentrated in one main 
 draught, it would, in all likelihood, be a power sufficient to 
 lift one or two tons in weight. 
 
 109. Technically, the wheel of a pulley is called a sheave; 
 for protection and convenience this sheave is ordinarily fixed 
 with pivots in a mass of wood called a block; and the ropes 
 or cords are called a tackle. The whole machine fully 
 mounted for working is termed a block and tackle. By 
 causing a wheel and axle to wind up the cord of a block 
 and tackle, the power of the lever is combined with that of 
 the pulley in the operation. 
 
 110. There is no assignable limit to the power which 
 
 90. Explain the principle of the pulley. 
 
 91. Where is its power found ? 
 
 92. Name the illustrations of this power. 
 
 93. Define sheave, block and tackle. 
 
 94. What is said of the limit of this cower? 
 
PULLEYS IN COMBINATION 
 
 43 
 
 may be exerted by means of pulleys. The machine may 
 be constructed to raise with ease any weight which the 
 strength of materials will bear, provided the combination 
 is not so complex as to exhaust the power by the friction 
 produced. 
 
 111. The power of pulleys is increased by a combination 
 of wheels or sheaves in one tackle. There are different 
 kinds of combinations or systems of pulleys. In some there 
 is only one fixed pulley, and in others there are several. 
 
 Figure 36. 
 
 COMBINATIONS OF PULLEYS. 
 
 The following are examples of different combinations of 
 pulleys : — 
 
 112. Figure 36 represents a compound 
 system of pulleys, by which the weight is 
 distributed through four folds of the same 
 cord, so as to leave only a fourth of the 
 weight, whatever it may be, to be raised 
 by the operator. In this illustration, the 
 cord number 1 bears one fourth of the 
 weight ; the cord number 2 bears a se- 
 cond fourth ; the cord number 3 bears a 
 third rourth ; and the cord number 4 bears 
 a fourth fourth. Here the mechanical 
 advantage ceases. For, although the cord 
 number 4 passes over the topmost fixed 
 pulley down to the hand of the operator, 
 no more distribution of power takes place ; 
 this topmost pulley being of use only to 
 change the direction of the power. The 
 p rson who pulls has hus only a quarter of the weight to 
 diaw. If the we ght e one hundred pounds, he has the 
 labour of pulling only twenty-five pounds. 
 
 113. Thus it is observable that the diminution of weight 
 is in proportion to the number of moveable pulleys. To 
 
 95. How may it be increased ? 
 
 96. Explain the first diagram. 
 
 97. How is the power calculated 1 
 
4 i 
 
 PULLEVS IN COMBINATION. 
 
 calculate the expenditure of power or diminution of weight, 
 therefore, we have only to multiply the number of moveable 
 pulleys bv two, and the product shows the power to be ex- 
 erted. Two moveable pulleys multiplied by two, gives 4 ; 
 therefore a fourth of the weight is the power required, and 
 so on. The addition of a single moveable pulley to any 
 system of pulleys, at once lessens the apparent weight one 
 half, or, in other words, doubles the effect of the power ; 
 but every such addition causes more time to be spent in 
 the operation, there being at every additional fold of the 
 cord more cord to draw out, and also more friction to 
 
 overcome. 
 
 Figure 37. 
 
 
 pr 
 
 
 
 1 
 
 i i 
 
 
 
 pi 
 
 1 c 
 
 2 
 
 
 
 4 
 
 
 4 
 
 114. In the annexed system of pul- 
 leys, figure 37, a series of moveable 
 pulleys, with different cords, are made 
 to act successively on one another, 
 and the effect is doubled bv each pul- 
 ley. At the extremity of the first cord 
 a power of one pound depends. This 
 cord, marked l, by being drawn bel< w 
 a moveable pulley, supports 2 pounds 
 — that is l pound on each side. The 
 next cord marked 2, in the same man 
 ner supports four pounds, or 2 pounds 
 on each side. The next cord marked 4 
 supports eight pounds, or our potindt 
 on each side. Thus 1 pound at P, supports S pounds at 
 W. If another moveable pulley were added, the 1 pound 
 at P would support Hi pounds, and so on. 
 
 115. In working pulleys, the power must be applied in 
 a line perpendicular to, or parallel with, the weight; that 
 is, straight above the weight, in order to produce the full 
 efficacy of direct force. If the power be applied obliquek 
 — do not draw fair up — there will be a loss of power in 
 proportion as the line of draught departs from the perpen- 
 dicular. 
 
 98. What of the next diagram 7 
 
 99. What of oblique action 7 
 
THE INCLINED PLANE. 
 
 45 
 
 PRACTICAL APPLICATION OF PULLEYS. 
 
 116. Pulleys are used chiefly on board of ships, where 
 blocks and tackle are in constant requisition for raising 
 and lowering the sails, masts and yards. They are like- 
 wise in considerable use by house-builders and others, in 
 connection with the wheel and axle, for raising or lowering 
 heavy irasses of stone and other articles. 
 
 117. Figure 38 is a representation of 
 a system of pulleys commonly used in 
 practical operations. Three moveable 
 pulleys are inclosed in the block A, and 
 three fixed pulleys are inclosed in the 
 block B. Suppose, therefore, that the 
 weight W in this case, is six hundred 
 pounds, the hand P pulls it upwards by 
 exerting a force of only one hundred 
 pounds. A combination of pulleys re- 
 sembling this is used in turning kitchen 
 jacks. The weight in sinking draws 
 off the cord from a spindle, by which 
 motion the jack is turned. In order 
 that a considerable weight falling slowly 
 through a comparatively small height 
 may keep the jack in motion for a long time, as many as 
 ten or twelve moveable and fixed pulleys are used. 
 
 OF THE INCLINED PLANE. 
 
 118. A horizontal plane is a plane coinciding with that 
 Figure 39. °f the horizbn, or parallel to it; 
 
 when the plane is not level or 
 horizontal, but lies in a sloping 
 direction, with one end higher than 
 the other, it is said to incline, or is 
 called an inclined plane. Figure 
 
 39 is an example. 
 
 Figure 38. 
 
 100. Name the uses of this power. 
 
 101. Explain the diagram. 
 
 102. What of an inclined plane 1 
 
46 
 
 STANDARD OP INCLINATION. 
 
 90 80 
 
 Insure 40. 
 
 STANDARDS OF COMPARISON FOR INCLINATIONS. 
 
 119. The inclination of a plane may be to any exient, 
 from that of a slight rise off the horizontal to almost an up- 
 right or perpendicular ascent. For the sake of conveni- 
 ence in language, the extent of the inclination is defined 
 by comparing it to the numbers of degrees in a quarter of 
 
 a circle. A circle being divided by ma- 
 thematicians into 360 degrees or parts, 
 the quarter of the circle includes ninety 
 degrees. Taking, then, a quarter of a 
 circle, and marking it, as in figure 40, 
 H L is the horizontal line, and P L is 
 the perpendicular line ascending from 
 
 it. Any line drawn from the centre to 
 
 H L any point on the circumference defines 
 
 the degree of inclination. Thus, a line ascending from 
 the centre to the 10th degree is called an inclination or 
 angle often degrees; a line ascending to the 45th degree 
 is called an inclination or angle of forty-five degrees ; and 
 so on with all the other degrees, to the 90th. In this man- 
 ner a standard of comparison has been established for de- 
 fining the various slopes or inclinations in planes. 
 
 120. Another standard of comparison for slopes consists 
 in referring the rise to so many feet in a certain length or 
 distance — as for instance, a rise of one foot in ten feet, a 
 rise of one foot in twenty, a rise of so many inches in a 
 mile, and so on. 
 
 121. In the case of inclinations of hills, or other eleva- 
 tions composed of loose matter, there is a certain degree 
 of sloping, which will permit the materials to remain at 
 rest, and not slide or roll down in obedience to the law of 
 gravitation. The degree of inclination at which the parti- 
 cles of matter remain at rest, just before they would slide 
 down, is termed the angle of repose. This angle is, of 
 course, different in different kinds of bodies. 
 
 103. What variety of inclined planes and how described ? 
 
 104. Explain the diagram. 
 
 105. What other standard is used ? 
 
THE INCLINED PLANE. 
 
 47 
 
 PRINCIPLE OF THE POWER OF INCLINED PLANES. 
 
 122. The inclined plane, as already stated, is a primary 
 mechanical power. The object which is accomplished by 
 it is the raising of weights to considerable elevations, or the 
 overcoming of resistances by the application of lesser 
 weights and resistances ; or, making a small power over- 
 come a greater. 
 
 123. To raise a load of a hundred pounds to an elevation 
 of fifty feet by a direct perpendicular ascent, and without 
 using any mechanical advantage, the power exerted must 
 be a hundred pounds, or equal to the weights to be over- 
 come. If, instead of raising the load directly upwards, we 
 raise it by the gradual ascent of an inclined plane, the power 
 required is less than a hundred pounds, and the diminution 
 is in proportion to the smallness of rise in the inclined 
 plane. But this saving of power, as in all other instances 
 of mechanical advantage, is accomplished only by a corres- 
 ponding loss of time. 
 
 124. In drawing a load, as, for instance, a loaded car- 
 riage, along a horizontal plane, the resistance to be over- 
 come is chiefly the friction of the load upon the plane. If 
 there were no friction or impediment from inequalities of 
 surface, and if the load were once put in motion, it would 
 go on moving with the smallest possible expenditure of 
 power. 
 
 125. In drawing a load up an inclined plane, ordinary 
 friction has to be overcome, and also the gravity of the 
 body, which gravity gives it a tendency to roll down to the 
 lowest level. In this constant impulse to descend, it is 
 not at liberty to pursue the same line of descent as bodies 
 falling freely from heights. It falls or rolls down as much 
 less speedily than a free falling body (omitting the loss by 
 friction) as the length of the inclined plane is greater than 
 its height. A freely descending body falls about 16 feet 
 
 106. What mechanical objects are thus gained ? 
 
 107. Name the illustration here cited. 
 
 108. What resistance has to be overcome ? 
 
43 
 
 THE INCLINED PLANE. 
 
 Figure 41. 
 A 
 
 HI 
 
 in the first second; and a body rolling down an inclined 
 plane, mils just as many feet the first second as the number 
 of feet of inclination is in sixteen feet. If the inclination be 
 one foot in sixteen, the body rolls down one foot, and so on. 
 
 126. Any body in being drawn up an inclined plane, by 
 a power parallel with the plane, presses at right angles with 
 the plane. The common expression is, that the reaction 
 of the plane upon the object is perpendicular to the plane. 
 
 When an object, as a ball, rests upon a 
 horizontal plane, its pressure is at right 
 D angles with the plane ; or what is the same 
 _ thing, the reaction or resistance of the 
 B c plane is at right angles with it. This is 
 seen in figure 41, in which a ball is represented lying on a 
 
 Figure 42. level plane, with the line of pressure A pass- 
 ing down to B, which line is at right angles 
 D with the plane. Suppose, then, that the end 
 of the plane at C is elevated to D, as in 
 -C figure 42, so as to form a slope ; in this case 
 the line of pressure of the ball on the plane is also moved, 
 so as still to be at right angles with the inclination.* 
 
 127. The power which is required to be sustained for 
 the purpose of overcoming friction or inequalities of surface 
 on level planes, is for the purpose of drawing the load up 
 or over the inequalities. 
 
 RULES FOR CALCULATING THE POWER OF INCLINED PLANES. 
 
 128. The amount of the power corresponding to different 
 weights and inclinations of the plane has been correctly 
 ascertained, and the following are the rules upon the sub- 
 ject : — 
 
 129. First. — The quantity of weight is great in propor- 
 tion to the inclination of the plane; consequently, so is the 
 
 * This proposition is proved by a mathematical demonstration which 
 it is thought inadvisable to introduce here. The question is one of 
 Resolution of Forces, and is treated of in works for advanced students. 
 
 109. What of the ratio of descent ? 
 
 110. Explain the diagrams. 
 
 111. How is the power of inclined planes calculated 7 
 
THE INCLINED PLANK. 
 
 49 
 
 difficulty of raising greater, and the rate of elevation or 
 motion slower. 
 
 1 :30. Second. — To overcome the weight or resistance, 
 and the slowness of movement, a corresponding increase 
 of power must be given. 
 
 131. Third. — The smaller the inclination, so is the 
 pressure of the weight on the plane the greater. 
 
 132. Fourth, or special rule of calculation. — Whatever 
 is the unit of inclination in a given length, the same is the 
 unit of weight that can be lifted, and the unit of power to 
 be exerted. 
 
 EXAMPLES. 
 
 133. If the inclination of a road be one foot in ten, one- 
 tenth is called the unit of inclination ; hence, one-tenth part 
 of the nominal weight of the load has to be lifted ; and a 
 power to draw this one-tenth part of the load has to be 
 exerted. Or, to put the case in other words : — If the road 
 rise one foot in ten, there is in the ten only one foot of 
 perpendicular height to be lifted through ; and the weight 
 at any point of the ten feet is only a tenth of what it would 
 be if it were to be lifted through a perfect perpendicular 
 ascent of ten feet. This is exemplified in figure 13, in 
 
 Figure 43. 
 
 which a loaded cart is in the act of being drawn up an 
 inclined plane of ten feet in length, having a rise of o le 
 foot throughout its extent, that is, from A to B. This rise 
 of one foot is marked at the end of the plane, from C to R. 
 Although, therefore, the cart has to be pulled a distance of 
 ten feet, it in reality is pulled upwards only one foot, and 
 
 1 12. What is the unit of inclination ? 
 
 113. Explain the diagram, and its principle. 
 
50 
 
 THE INCLINED PLANE. 
 
 the horse which draws has the advantage of pulling only 
 orie-tenth. 
 
 134. The reason is now perceived why a small power 
 overcomes a greater in the case of draughts upon inclined 
 planes. The load is, as it were, lifted by instalments. 
 Partly supported as it advances, and always supported more 
 completely the smaller the inclination, the weight of the 
 burden is apparently lessened by merely taking the rise 
 gradually and slowly. 
 
 135. If we suppose a case of two roads, the first rising 
 one foot in twenty, and the second rising one foot in fifty, 
 a loaded carriage will be found to go over the fifty feet of 
 the one with precisely the same expenditure of power that 
 would be required to make it go over the twenty feet of 
 the other — that is, always providing that friction and other 
 circumstances are alike. 
 
 136. Figure 44 represents a supposed case of two in- 
 clined planes of the same height, but different slopes, meet- 
 ing together at the top, with a weight 
 resting on each, P and Q, hanging 
 by a string, which passes over the 
 pulley M. If the length of the 
 
 A B ■ longest plane from A to M be two 
 
 feet, and that of the shorter from B to M be one foot, then 
 two pounds at Q, on the short side, will balance four pounds 
 at P,on the long side ; and so on in this proportion, whether 
 the planes be longer or shorter. 
 
 137. In this manner, weights moving on two adjoining 
 inclined planes may be adjusted so as to balance each 
 other, although the inclinations be different; and they are 
 so made to act on various sloping railways connected with 
 public works, where one wagon descending on one plane 
 is made to draw up another wagon on another plane. 
 
 138. ^n inattention on the part of our forefathers to 
 these exceedingly simple principles of mechanical science, 
 led them to form roads over steep hills, pursuing, as it was 
 
 114. How may expenditure of power be estimated 1 
 
 115. Explain the first diagram. 
 
 116. How are inclined planes used on rail ways. 
 
THE INCLINED PLANE. 
 
 61 
 
 Figure 45. 
 
 magined,the best routes, because they were the straightest 
 in a forward direction. In modern times, this error has 
 been avoided by enlight ed engineers, and roads are now 
 constructed with as few risings and fallings as possible. 
 When roads have necessarily to be carried to the summits 
 of heights, they are very properly made either to wind round 
 the ascent, or to describe a zig-zag line of direction. Figure 
 45 represents a road pursuing a winding direction round a 
 hill on which a fort is planted. 
 
 139 The drivers of carts are aware of the saving of 
 labour to their horses by causing them to wind or zig-zag 
 up steep roads instead of leading them directly forward. 
 
 140. The inclined plane is resorted to for a saving of 
 labour in many of the ordinary occupations of life. By it, 
 loaded wheel-barrows are with comparative ease wheeled to 
 considerable elevations in house building and other works 
 of art ; hogsheads are rolled out of or into wagpns, and 
 ships are launched into or drawn from the water, the in- 
 clined plane being as useful in giving facilities for letting 
 down loads as in drawing them up. 
 
 141. It is also by inclined planes that we reach the 
 higher floors of a house from the ground, or attain other 
 
 117. Explain the second diagram. 
 
 118. Name some of the practical uses of inclined planes. 
 
52 
 
 THE WEDGE. 
 
 elevations. For all such purposes, the inclined plane is 
 formed with steps to insure our safe footing. All stairs or 
 flights of steps are inclined planes. A ladder forms a steep 
 inclined plane. 
 
 Figure 46. 
 
 OF THE WEDGE. 
 
 .42. The inclined plane has been described as being 
 fixed or stationary, as, for instance, a common ascending 
 road, or a sloping plank, upon which the weights are 
 moved. It has now to be viewed as a moveable plane, in 
 which form it suits many useful purposes. 
 
 143. When an inclined plane is moveable, and the load 
 or weight which it affects is at rest, it receives the name 
 of a Wedge. The wedge is, therefore, a mechanical power, 
 founded on the principle of the inclined plane. 
 
 144. The Wedge is an instrument or simple machine, 
 consisting of a solid body of wood, iron, or some 
 other hard material, and is triangular in form. 
 See figure 46. Here the wedge is seen to taper 
 from a thick end or head at B to a thin edge or 
 
 ) point at A. This, however, is only the more 
 'common form of the wedge. It is made with 
 sides of various angularities or degrees of slope; 
 and, in some cases, it possesses a flat and a slop- 
 ing side, as in figure 47. W ? hen it slopes on both 
 sides, it consists of two inclined planes joined together; 
 Fig 4 7 and when one of its sides is flat, as in figure 47, it 
 acts as only one inclined plane. 
 
 145. The wedge is employed as an instrument for 
 cleaving solid masses asunder, to compress bodies 
 more closely together, and to move weights through 
 small spaces. Figure 48 is a front view of a wedge 
 in the act of splitting asunder a piece of timber. The 
 power employed to force the wedge forward, is either 
 repeated blows with a mallet or hammer, or the gradual 
 
 119. What of a moveable plane 1 
 
 120. Explain the diagram. 
 
 121. What of the varieties and uses of the wedge. 
 
WEDGES. 
 
 o) 
 
 Figure 48 P ressure °f a weight. Iii general, the power 
 is applied by rapid strokes, or quick applica- 
 tions of some kind of external pressure. 
 
 RULES FOR CALCULATING THE POWERS OF THE 
 WEDGE. 
 
 146. The rules for calculating the power of 
 the wedge are similar to those for the inclined 
 plane. In proportion as the inclination or 
 angularity is great, so is the resistance greater, and I he 
 power must be greater to overcome it. Thus, if the wedge 
 be of short dimensions and thick at its head, it will require 
 a greater power to move it than if it be long and thin in its 
 form. 
 
 147. The resistance offered to the wedge 
 * gure 49, of equal sides, when the pressure is equally 
 \ 7 applied, is, as in the case of the inclined 
 
 plane, at right angles with the sides. See 
 \ /'^-'figure 49, in which the oblique cross lines 
 \ / represent the direction of the pressure pas- 
 ty sing at right angles through the sides, and 
 
 meeting at the centre. 
 
 148. It is difficult to calculate the precise power of the 
 wedge, for much depends on the force or the number of 
 blows which may be given it, together with the obliquity 
 of the sides, and the power of resistance in the object to be 
 split In the splitting of timber, for instance, the divided 
 parts act as levers, and assist in opening a passage for the 
 wedge. 
 
 EXAMPLES OF WEDGE POWERS. 
 
 149. The wedge is the least used of the simple machines, 
 but the principle upon which it acts is in extensive appli- 
 cation. Needles, awls, bodkins, and driving-nails, are the 
 most common examples. Knives, swords, razors, the axe, 
 chisel, and other cutting instruments, also act on the prin- 
 
 122. By what rules are the power of wedges calculated 1 
 123 What common examples are cited 1 
 
54 
 
 THE SCREW. 
 
 ciple of the wedge; so likewise does the saw, the teeth of 
 which are small wedges, and act by being drawn along 
 while pressed against the object operated upon. 
 
 150. The principle of the inclined plane, which is the 
 basis of that of the wedge, is particularly observable in ti e 
 action of the razor and the scythe, both of which cut best 
 by being drawn along the materials against which they are 
 applied. When the edge of a scythe or razor is examined 
 with a microscope, it is seen to be a series of sm ill sh n 
 angularities of the nature of the teeth of a saw. 
 
 Figure 50 . 151. The principle of the wedge ope- 
 
 rates in the case of two glass tumblers, 
 one placed within the other, as in figure 
 50. A very gentle pressure applied to the 
 uppermost tumbler would be sufficient 
 to burst the lower. At every little advance 
 of the uppermost tumbler, it acts more 
 and more as a lever power on the rim of 
 i ;e lower, and at last overcomes the 
 resistance, and fractures the vessel. 
 
 OF THE SCREW. 
 
 152. The screw is the fifth, and usually the last-men- 
 tioned mechanical power. Like the wedge, it is founded 
 on the principle of the inclined plane. 
 
 Fig 51 153. The screw consists of a projecting ridge 
 
 winding in the form of an inclined plane, and in a 
 spiral direction, round a central cylinder or spindle, 
 similar to a spiral road winding round a precipitous 
 mountain. Figure 51 is a representation of a common 
 strong screu r used in various mechanical operations. 
 The projecting ridge on the spindle is technically 
 called the. thread. The thread is not always made 
 in this square projecting form; it is frequently sharp- 
 ened to a single thin edge, as in figure 54, but this does 
 not affect the principle of the machine. 
 
 124. What of a microscopic inspection of a razor or sc vthe ? 
 
 125. Explain the first diagram. 
 
 126. What is the principle of the screw ? 
 
 127. Explain the diagrams, and the italicised terms. 
 
THE SCREW. 
 
 55 
 
 154. One circumvolution or turn of a thread of a screw 
 is, in scientific language, termed a helix (plural helices), 
 from a Greek word signifying winding or wreathing, 'i he 
 spiral winding of the thread is called the helical line. 
 
 155. The helices of a screw do not necessarily 
 require to have a central spindle. They may form 
 a screw of themselves, and do so in the case of the 
 i common cork-screw. Figure 52. A screw of this 
 pointed or tapering form, in penetrating a substance, 
 possesses the advantage of the inclined plane in 
 three ways; first, by the gradual thickening of the 
 substance of the thread from a sharp point ; second, 
 the gradual widening, and third, the gradual ascend- 
 ing, of the thread. 
 
 POWERS OF THE SCREW. 
 
 156. The screw acts on the principle of the inclined 
 plane, and this is obvious from the consideration of the 
 Figure 53. nature of the threads. If we were to cut 
 through the turns of the threads straight from 
 top to bottom, and draw them out to their full 
 extent, each separate and retaining its own 
 inclination, we should find that they were so 
 many inclined planes. In the annexed cut, 
 a figure 53, one entire turn of the thread is thus 
 drawn out, reaching from b to a, and is seen to form an 
 inclined plane. If not drawn out, it would wind down to 
 r ; therefore, while a weight is raised by one turn of the 
 Figure 54 screw over the limits of one thread, or 
 lgui- e^— ^ f rom c to b, it has actually been carried 
 
 Lt C — i up the inclined plane from a to b. 
 
 157. The screw has no power by itself. 
 It can operate only by means of pressure 
 against the threads of another screw 
 which overlaps it and holds it. This 
 exterior screw, which is technically called 
 a box or a nut, consists of a block with a 
 
 128. Explain the first diagram. 
 
 129. What does the second prove ? 
 
 130. Explain the relation between the nut and screw. 
 
50 
 
 THE SCREW. 
 
 central tube cut out in spiral grooves so as to fit with perfect 
 exactness with the screw which has to work in it. Figure 
 54 represents both screws in combination. M is the box or 
 nut through which the screw passes. L is a lever inserted 
 into the head of the screw, for the purpose of turning it. 
 
 158. The object required by the use of the screw is to 
 apply force or pressure. To produce the intended effect, 
 either the outer or inner screw, that is, either the nut or the 
 screw, must be fixed. If the screw be fixed at one ex- 
 tremity, say at the top, to a solid body, the nut may be 
 turned round it so as to move from the bottom to the top ; 
 and if the nut be fixed, held fast by some solid body, the 
 screw in the same manner may be turned round till it reach 
 its extremity. Thus, either the point of the screw, or the 
 nut, may be forced in such a way as to squeeze or press 
 any object presented to them. 
 
 159. Practically, the screw is never used as a simple 
 machine ; the power being always applied by means of a 
 lever, passing either through the head of the screw, or 
 through the nut. The screw', therefore, acts with the com- 
 bined power of the lever and inclined plane, and in investi- 
 gating the effects, we must take into account both these 
 simple mechanical powers, so that the screw now becomes 
 really a compound machine. 
 
 160. In the inclined plane, as has been seen, the less it 
 is inclined, the more easy is the ascent, though the slower 
 is the process of rising to a certain elevation. In applying 
 the same principle to the screw, it is obvious, that the 
 greater the distance is betwixt the threads, the greater or 
 more rapid is the inclination, and, consequently, the greater 
 must be the power to turn it under a given weight. On the 
 contrary, if the thread inclines downwards but slightly, it 
 will describe a greater number of revolutions in a given 
 space, so as to diminish the distance betwixt the threads, 
 and the smaller will be the power required to turn the ma- 
 chine under a given weight. Therefore, the finer the screw, 
 or the nearer the threads to each other, the less the power 
 will require to be for a given resistance. 
 
 131. Why is the screw called a compound machine t 
 
 132. How is the power of the screw regulated ? 
 
THE SCREW, 
 
 57 
 
 161. Suppose a case of two screws, one having the 
 threads one inch apart, and the other half an inch apart; 
 then, the force which the first screw will give with the same 
 power at the lever, will be only half that given by the 
 second. The second sctew must be turned twice as many 
 times round as the first, to go through the same space. At 
 the lever of the first, two men would raise a weight to a 
 given height, by making one revolution ; while at the lever 
 of the second, one man would raise the same weight to the 
 same height, by making two revolutions. 
 
 162. It is apparent, that the length of the inclined plane 
 up which a body moves in one revolution, is the circum- 
 ference of the screw, and its height, the interval between 
 the threads. The proportion of the power would therefore 
 be — “ as the circumference of the screw is to the distance 
 between the threads, so is the weight to the power.” By 
 this rule, the power of the screw could alone be found, 
 provided the action of the machine was not affected by the 
 lever which works it. As that is the case, the circumfer- 
 ence described by the outer end of the lever employed is 
 taken instead of the circumference of the screw itself. 
 
 RULES FOR CALCULATING THE POWERS OF THE SCREW. 
 
 163. The rule by which the true force of the screw is 
 calculated, is, by multiplying the circumference which the 
 lever describes by the power. Thus — The power multi- 
 plied BY THE CIRCUMFERENCE WHICH IT DESCRIBES, IS 
 EQUAL TO THE WEIGHT OR RESISTANCE, MULTIPLIED BY THE 
 DISTANCE BETWEEN THE TWO CON TIGUOUS THREADS. Hence 
 the efficacy of the screw may be increased, by increasing 
 the length of the lever by which it is turned, or by dimin- 
 ishing the distance between the threads. If, then, we 
 know the length of the lever, the distance between the 
 threads, and the weight to be raised, we can readily calcu- 
 late the power; or, the power being given, and the distan e 
 of the threads and the length of the lever known, we can 
 estimate the weight which the screw will raise. 
 
 133. What illustration is stated ? 
 
 134. How is the power calculated ? 
 
58 
 
 THE SCREW. 
 
 164. Suppose the length of the lever to be forty inches, 
 the distance of the threads one inch, and the weight 8000 ; 
 required — the power, at the end of the lever, to raise the 
 weight. The lever being 40 inches, the diameter of the 
 circle which the lever describes fs double that, or 80 inches. 
 Reckoning the circumference at thrice the diameter (though 
 it is a little more), we multiply 80 by 3, which gives 240 
 inches for the circumference of the circle. The distance 
 of the threads is one inch, and the weight 8000 pounds. 
 To find the power, multiply the weight by the distance of 
 the threads, and divide by the circumference of the circle. 
 
 8000 weight 
 1 distance 
 
 240)8000 
 
 165. Thirty-three and a third is the product, and it 
 would require that power or number of pounds to raise the 
 weight. This, however, is only in theory. In practice, a 
 third of the amount of power would require to be added to 
 overcome the friction of the machine. 
 
 166. In the ordinary working of the screw, velocity is 
 incompatible with great power. This is a truth, however, 
 which applies only to a screw with one thread. There is 
 a way of making a screw, by which great velocity and power 
 may be combined. This is done by forming the screw 
 with two, three, or more threads. To understand ho\v this 
 is accomplished, we have only to conceive the idea of a 
 screw with one thread, very wide betwixt its turns, and 
 then imagine one or two other threads placed so as to fill 
 up the intervals ; thus composing a fine close screw. And 
 as by this means all the threads descend with equal rapidity, 
 we have a screw which will not only descend with great 
 velocity, but which will apply a very great degree of pres- 
 sure. A screw of this nature is used in the printing press, 
 
 135. Repeat the example of calculation. 
 
 136. What of the friction of the machine? 
 
 137. How is velocity and power combined in a screw? 
 
 138. What remarkable instance is given ? 
 
THE SCREW. 
 
 59 
 
 by which a pressure of a ton weight is applied instanta- 
 neously by a single pull of a lever. 
 
 EXAMPLES OF SCREW POWERS. 
 
 Figure 55. 
 
 1 
 
 s 
 
 
 1 
 
 1 
 
 1* 
 
 
 167. The most common purpose for which the screw is 
 applied in mechanical operations, is to produce great pres- 
 sure accompanied with constancy of action, or retention of 
 the pressure; arid this quality of constancy is always procu- 
 rable from the great friction which takes place in the pres- 
 sure of the threads on the nut, or on any substance, such 
 as wood, through which the screw penetrates. 
 
 168. The common standing-press 
 used by bookbinders for pressing 
 their books, affords one of the best 
 examples of the application of the 
 screw to produce great pressure. Fi- 
 gure 55. The screw A lias a thick 
 round lower extremity B, into holes 
 in which the lever is inserted. This 
 extremity B is attached by a socket 
 Joint to the pressing table C, so that 
 when the screw is turned in one direc- 
 tion, the table sinks, and when 
 turned in another, the table rises. 
 
 Jj 'The books D 1 le 
 
 S, and are thus between the table 
 and the sole. H is a cross beam 
 above, in which is the box or over- 
 lapping screw to give the necessary 
 resistance. 
 
 169. The force of the screw is 
 sometimes employed to turn a wheel 
 by acting on its teeth, by which 
 means there is a combination of 
 two mechanical powers — the screw 
 and the wheel and axle. Figure 56. The screw is upon 
 
 139. What is the most common mecha ixal use of the screw ? 
 
 140 Explain the first diagram. 
 
 141. What combination produces the e dless screw ? 
 
 Figure 56. 
 
 8 
 
 Zjp 
 
 8 
 
 K|— - 
 
 (l 
 
 0 } 
 
 % 
 
 vaN 
 
 
 w 
 
 a 
 
 
BO MECHANICAL COMBINATION AND STRUCTURE. 
 
 the horizontal spindle, and by turning it by the handle, 
 each turn of the thread receives a tooth of the wheel and 
 brings it forward, so as to produce a perpetual revolution 
 of the wheel. This is called an endless screw, because it 
 never stops in its action ; no sooner is one turn of the 
 thread disengaged than another has come into operation. 
 W represents a weight to be raised hanging from the cir- 
 cumference of the axle. 
 
 170. The screw concludes the list of simple mechanical 
 powers, according to the usual definitions of science. But, 
 to prevent misconception, it has to be noted that there are 
 other means and agents of force in nature besides those 
 comprehended in the number of simple mechanical powers 
 working by solids. These will come under observation in 
 the subsequent departments of Natural Philosophy. 
 
 MECHANICAL COMBINATION AND STRUCTURE. 
 
 171. Mechanical action, as already stated (3), is applied 
 to the action of forces that produce no change in the con- 
 stitution of bodies, and is therefore distinguished from 
 chemical or any other species of action in which change 
 of constitution is less or more effected. 
 
 172. Great changes are continually taking place in nature 
 and art by mechanical action. Mechanical action gene- 
 rally implies movement or change of place, and in most 
 cases alteration of external features and circumstances. 
 The whole of the planetary movements are mechanical ; 
 the motions of water and winds are mechanical ; and the 
 new appearances produced in art by placing different objects 
 together, are mechanical. 
 
 173. The action of forces upon solids, or mechanical 
 action, is taken advantage of by mankind for the produc- 
 tion of numerous useful results in the arts. And success 
 in attaining these results depends in a great measure upon 
 the knowledge we have of the principles of Mechanics, and 
 the skill and care we use in applying them. 
 
 142. How does mechanical action differ from chemical t 
 
 143. Give instance* of mechanical action. 
 
MECHANICAL COMBINATION AND STRUCTURE. 
 
 61 
 
 174. When skill, care, and ingenuity, are brought fully 
 into operation lor these results, very great wonders are in 
 many instances achieved. But where there is ignorance 
 or negligence, the object in view may not only be deieated, 
 but very mischievous consequences may take place. 
 
 175. Example first. — If a tall mast or beam break 
 through at two-thirds of its height, and the two fractured 
 ends be simply placed together and tied with a rope, the 
 
 _ 7 upper piece will, by the action of a small force, again 
 ° fall. It will act like the arm of power of a lever 
 against the rope, which is the weight ; and as this 
 weight is inconsiderable, the arm of power will pre- 
 ponderate. But if we take the two pieces and saw 
 each of them lengthwise, so as to make four pieces, 
 and then, as represented in figure 57, lay a short 
 piece alongside of a long piece, and another long 
 piece on the top of the first short piece, with the 
 second short piece opposite to this second long 
 piece, the whole will be effectually spliced together; 
 in such a case, with the aid of an overlapping rope, 
 the beam will in all likelihood be stronger than it was 
 before it was fractured. The cause of its being stronger, 
 at least of its remaining firm, is, that the weaker part at 
 one side is supported by a stronger part on the other side. 
 Thus, by skilfully taking advantage of certain forces acting 
 in connexion with solids, we are able to rear a structure of 
 the utmost possible strength. 
 
 176. Example second. — If a man, in making repairs 
 upon the outside of a building, project a plank from a win- 
 dow for the purpose of standing upon it, and if he proceed 
 to place himself near the outer extremity of the plank, with- 
 out having placed a sufficient counterbalancing weight at 
 its inner extremity, he will assuredly be precipitated to the 
 ground, and perhaps killed ; because the gravity of his 
 body acted like a power on the arm of a lever, while the 
 lever was without a sufficient weight to preserve the appa- 
 
 144. How are the principles of mechanics important in the arts 1 
 
 145. Explain the example and diagram. 
 
 146. What is the second example ? 
 
62 MECHANICAL COMBINATION AND STRUCTURE. 
 
 rntus in equilibrium. From such neglects of the operation 
 of forces in nature, dreadful consequences frequently ensue. 
 
 177. The study of the operation of mechanical forces, 
 along with experience, teaches that there are certain bulks, 
 positions, and forms of bodies, which produce the greatest 
 strength for purposes of art. 
 
 178. The strength of beams or masses of the same kind 
 and bulk, and fixed in the same manner, in resisting a 
 transverse force which tends to break them, is simply as 
 their breadth, as the square of their depth, and inversely as 
 their length — that is the thicker and shorter they are, they 
 are the stronger. Thus, if a beam be twice as broad as 
 another, it will also be twice as strong; for the increase of 
 breadth doubles the number of the resisting particles. By 
 making the beam double the depth, the strength is four 
 times as great; because the number of fibres is doubled, 
 and the lever by which they act is also increased. 
 
 179. But this increase of strength, by increasing bulk, 
 has a practical limit. It is found that increasing the di- 
 mensions of a body, or combination of bodies, preserving 
 all proportions the same, the weight increases more rapidly 
 than the increase of strength, or power of endurance. This 
 is one of the most important principles in mechanical sci- 
 ence, and ought to prevent undue extension in structural 
 arrangements. (39.) 
 
 180. Take a block of stone, and fix one end of it into 
 a wall, leaving its other end projecting. By this arrange- 
 ment of position, each particle of matter in the block acts 
 as a weight pulling downwards as with a lever, the fulcrum 
 of the lever being at the point of support, and the particles 
 of matter in the mass forming at once the arm of power 
 and the weight. Hence every particle we add to the length 
 of the block, adds to the length of the arm of the lever, 
 and increases the weight. If we add to the block beyond 
 a certain length (whatever may be its constitutional strength), 
 we shall certainly cause the mass to break, and fall, from 
 the effect of gravity, upon the outer extremity. 
 
 147. How is the strength of beams estimated ? 
 
 148 What of undue extension ?. 
 
 149. Cite the examples here given. 
 
MECHANICAL COMBINATION AND STRUCTURE. 
 
 f>3 
 
 18 1. A similar lever action takes effect in the case of 
 blocks or beams supported at both ends, the only difference 
 being, that, in extending them to an undue length, they 
 will break in the middle, or at the weakest point between 
 the two supports. 
 
 182. The strength of a beam supported at both ends is 
 twice as great as that of a beam of half the length, which 
 is fixed only at one end ; and the strength of the whole 
 beam is again increased, if both ends or fulcra be firmly 
 fixed, as into a wall. 
 
 183. In the case of fibrous or grained materials, as. for 
 instance, wood, the body sustains the greatest pressure when 
 the weight is applied to the grain endwise, or to the beam 
 longitudinally. The nearer that the pressure can be ap- 
 plied to any beam endwise, the better. Thus a beam sup- 
 ports most weight on its upper end, the other end being 
 fixed to the ground, and its strength is next greatest when 
 the pressure is applied to it leaning at top against another 
 beam. This is exemplified in the angular roof of houses, 
 in which two beams lean against each other like the two 
 sides of the letter A. In arranging beams to support great 
 weights, as in building bridges, each beam is made to push 
 obliquely upward with one end, while it pushes obliquely 
 downward with the other, and thus an extensive combina- 
 tion of beams is firmly supported. 
 
 184. In rearing structures consisting of beams, it is an 
 important point to convert, as far as possible, by mode of 
 erection, cross or transverse strains into longitudinal strains 
 or into forces acting on the ends of beams, in the direc- 
 tion of their length. 
 
 185. Nature appears to have designed that strength of 
 structure should be accomplished with the least expenditure 
 of material. It is obvious, that, if trees and animals were 
 made many times larger than we now find them, and of the 
 same kinds of substance, they would be borne down by 
 their own weight. Small animals endure greater compar- 
 ative violence, and perform greater feats of strength, in pro- 
 
 150. What rules are given in using fibrous materials 1 
 
 151. What is said of trees and animals ? 
 
04 MECHANICAL COMBINATION AND STRUCTURE. 
 
 portion to their size, than large ones, The largest bulk 
 which a human being can possess in his person, at the 
 same time retaining activity of motion, is not more than is 
 usually seen in well-grown men. Thus, from a simple na- 
 tural cause, men of very gigantic figure never could have 
 existed on our earth. Men must always have been about 
 the size which they are at present ; or, if they were con- 
 siderably larger, they must have been constituted of much 
 stronger materials, without a corresponding increase of 
 weight. 
 
 Iritj. The same principles relative to mechanical strength 
 apply to contrivances in the arts. As already stated, the 
 strength or power of endurance in a material does not in- 
 crease in proportion as the weight increases. Hence there 
 is a practical limitation of the magnitude of machines and 
 other structures. For example, a bridge or roof of beams 
 may be very strong when of small or moderate size, but if 
 the dimensions be extended beyond a certain limit, the struc- 
 ture will fall by not beitig able to support its own weight. 
 
 187. The strength or power of endurance of pressure 
 upon a fixed body, is greatly increased by giving the body 
 a certain form. The strongest form in nature or art is that 
 of an arch. 
 
 ARCHED STRUCTURES. 
 
 188. An arch is a skilful disposition of parts, forming a 
 convex and concave side, the convex side being that upon 
 which the pressure is applied. The arch, which takes its 
 name from arcus, a Latin word signifying a bow, may be 
 either a portion of a circle or ellipse, or entirely rounded 
 in form. Whether shaped like a bridge, a round tube, or 
 the shell of an egg, the principle which causes the power 
 of endurance of pressure is the same. 
 
 189. The principle of endurance consists in the particles 
 of the arched body bearing upon each other like a series of 
 
 152. Why is it certain that giant stories are fabulous? 
 
 153. What of the proportion between material and strength \ 
 
 154. Which is the strongest form in nature or art ? 
 
 155. Define an arch, with examples of their variety. 
 
MECHANICAL COMBINATION AND STRUCTURE. 65 
 
 wedges, thus causing a compression of particles on the 
 concave side of the circle, which enables the mass to bear 
 an enormous pressure on the convex side. Indeed, the 
 greater the pressure is (to a certain extent), perpendic- 
 ular to the convexity, so also the compression and power 
 of resistance become the greater. 
 
 190. In the case of arched objects which have to meet 
 resistance on all sides, the circular form is best. In the 
 case of objects such as arches of bridges, which are ex- 
 posed to pressure chiefly on one side, the semicircular form 
 is the strongest, or offers the greatest resistance. The more 
 that the figure of an arch departs from the true circle or 
 semicircle, the weaker it becomes. 
 
 191. In arched forms such as tubes or egg-shells, the 
 compression of particles takes place all round the inside of 
 the object, so that the arch presents a power of resistance 
 at any part of its convexity ; the power being always great- 
 est where the convexity is greatest. For example, it is 
 more difficult to break an egg by pressing against the two 
 ends than against the sides. 
 
 192. In the representation of a regular-sided wedge, 
 figure 58, to which the side pressures are applied at right 
 
 angles to the sides, it is seen that the lines 
 of direction of the two forces or pressures 
 proceed obliquely to a point within the 
 wedge. The same principle applies to the 
 particles or blocks composing arches — the 
 pressing forces meet in a point within the 
 particles or blocks, and the situation of this 
 p >int is governed by the degree of convexity of the arch, 
 that is, the degree of inclination of the respective wedges. 
 
 193. Hollow cylindrical tubes, shafts, pillars, or other 
 objects of art, are much stronger than the same objects 
 would be if solid, with the same quantity of material. 
 Plates of metal bent into grooves on the surface, are simi- 
 larly much stronger than the same plates when flat. This 
 
 Figure 58. 
 
 156. Explain the principle of its strength. 
 
 157. How illustrated by an egg. 
 
 158. Explain the diagram. 
 
66 MECHANICAL COMBINATION AND STRUCTURE. 
 
 is well exemplified in the roofing of. the large warehouses 
 and wharfs at the London Docks, which are covered with 
 sheets of iron. The sheets are thin in substance, but bent 
 into semicircular grooves and ridges, and have all the 
 strengtli of thick plates without their dangerous weight. 
 
 194. In arched forms such as bridges, in which there is 
 only part of a circle or ellipse, the two extremities of the 
 arch must rest against immoveable piers or abutments, 
 sufficiently strong to resist the horizontal thrust upon 
 them ; for it is upon these parts of the structure that the 
 pressure takes effect. 
 
 Figure 59. 
 
 195. Figure 59 
 represents the sim- 
 ple elements of two 
 arches. B is an 
 outer pier, fixed 
 firmly on the ground. F is another pier, and betwixt the 
 two there are two wedge-shaped stones, E and D, lying 
 obliquely to each other. It is obvious that the more these 
 two stones press downwards, they will more firmly sustain 
 each other. The pier F serves as a prop to the other arch, 
 which consists of G H I,' and is supported at the other ex- 
 tremity by the fixed pier K. The three stones in this arch 
 press against each other in the same manner as in that with 
 the two stones; and the same principle operates, although 
 the arch consists of fifty or a hundred stones. The central 
 stone of all arches is the stone which binds the mass toge- 
 ther, as in the case of H, in the figure, and is technically 
 called the key-stone. It is always the last inserted. 
 
 196. A. similar action of mutual pressure to preserve 
 equilibrium, occurs in all arched forms. The human .oot 
 is an arch consisting of small bones bearing on each other, 
 at once to give strength, lightness, and elasticity. 
 
 197. Anciently, bridges were built of a purely semicir- 
 cular form, giving a considerable convexity or rise in the 
 
 159. What example of grooved material is g wen ? 
 
 160. Where is the pressure in arched bridges 1 
 
 161. Explain the diagram. 
 
 162. What of the human foot ? 
 
MACHINERY. 
 
 t>7 
 
 middle. This was an inconvenient form for a bridge. 
 Architects now make bridges with elliptical or slightly 
 curved arches, so that the passage above them is, in most 
 cases, as easy as along a piece of ordinary road. Although 
 these modern slightly curved arches are notstrictly so strong 
 as a perfect semicircular arch, they are sufficiently durable 
 for ail necessary purposes.* 
 
 ELEMENTS OF PRACTICAL MACHINERY. 
 
 198. The term machine is ordinarily applied to any piece 
 of mechanism, or engine, in which different parts are com- 
 bined to produce the desired effect. In Natural Philos- 
 ophy, a machine of this composite nature is called a com- 
 plex machine (4). 
 
 199. The treatment of the principles on which complex 
 machines operate, forms the subject of the department of 
 Natural or Mechanical Philosophy termed Practical 
 Machinery. 
 
 These principles are now to be defined. 
 
 200. The simple mechanical powers compose the ele- 
 ments of all machines, however complex or extensive. Thus, 
 in all machines, levers, cords, or inclined planes, in their 
 different modifications, are found to be the elementary com- 
 ponent parts of the structure, and all combined in harmo- 
 nious union to accomplish certain results. 
 
 201. Machines are usually formed of wood, iron, steel, 
 brass, or other durable materials, with sometimes leather 
 and cordage as part of the apparatus. 
 
 202. In the construction of every machine, four objects 
 are particularly desirable — 1st, Strength or durability of 
 materials; 2d, Simplicity of arrangement of parts; 3d, Ex- 
 actness of fitting of one part to another; and 4th, Easiness 
 
 * A further consideration of the subject of strength of materials be 
 longs to Practical Mathematics. 
 
 163. What improvement is there in modern bridges ? 
 
 164. Define a complex machine. 
 
 165. What powers are combined in their structure I 
 
 166. What four objects are sought in machines 1 
 
08 
 
 M WHINF.R Y. 
 
 and correctness of motion. It is a general and well-recog- 
 nized principle in mechanics, that the fewer the ports are in 
 a machine, and the more. simple its construction, the better. 
 
 203. Machines act from the impression of a certain power 
 or force communicated to them. Whatever be the amount 
 of power they receive, that amount they expend in their 
 action. They cannot in the smallest degree increase the 
 power. They can only convey, regulate and distribute, the 
 quantity of power which has been communicated to them. 
 
 204. The power communicated to machines is derived 
 from various sources; as, human labour, the power of 
 horses or other animals, the force of wind, water, or steam, 
 or any other active agent, which may be found suitable. 
 Sources of power are technically called moving forces or 
 first movers. 
 
 205. Of the original impressed power, each moving part 
 of the machine uses a certain portion. If the whole power 
 which enters a machine be supposed to consist of 1000 
 parts, this large quantity is dispersed in various small quan- 
 tities through the mechanism; some wheels taking perhaps 
 10 parts, others 5 parts, a third kind 1 part, a fourth a frac- 
 tional part, friction another part, and so on, till the whole 
 1000 parts are expended. In some large cotton, flax, or 
 silk spinning establishments, a single water-wheel or steam- 
 engine turns several thousands of spindles; each spindle, 
 consequently, consumes a minute fraction of the originally 
 impressed power. 
 
 206. Whatever be the nature of the moving forces, it is 
 generally sufficient for all purposes that they produce in the 
 first instance rotary or circular motion, and either in a ho- 
 rizontal or vertical direction. It is, however, indispensable 
 that the power be of that magnitude which will cause each 
 part of the machine to fulfil its assigned office. If the power 
 be too small or weak, the machine will move languidly and 
 ineffectually; and if too great, it will either cause the ma- 
 
 167. What moving forces are employed 1 
 16S. How is the. power divided ? 
 
 169. What illustration is cited ? 
 
 170. What motion is desirable ? 
 
MACHINERY. 
 
 m 
 
 chine to move too rapidly, or at least power will be expend- 
 ed uselessly. In the application of moving forces, it is 
 always a matter of importance to regulate the power to the 
 precise wants of the machinery. 
 
 207. The circular motion communicated in the first in- 
 stance to a machine, is, by means of certain contrivances, 
 diffused through the whole organization, and changed into 
 every conceivable direction ; some parts being caused to 
 revolve, others to rise and fall, a third kind to move hori- 
 zontally to and fro, and so forth, in all possible ways. The 
 various parts may also be made to move with any degree 
 of velocity ; there being methods of transforming quick into 
 slow motion, or slow motion into quick. Most minute and 
 complex operations are thus performed by machines with a 
 precision which often exceeds the skill of the most expert 
 artizan, but these operations are all necessarily marked by 
 the quality of uniformity of action. As machines cannot 
 reason, or act arbitrarily in stopping, moving, or altering 
 their process, according to circumstances, they proceed in a 
 blind routine, whether right or wrong, mechanically as it is 
 called, and in every case less or more require the super- 
 intendence of reasoning beings. This apparent defect, 
 however, is really advantageous. A machine by being 
 composed of inanimate matter, destitute of feeling and 
 unsusceptible of fatigue, proceeds unswervingly in its as- 
 signed duty, and may be forced to accomplish tasks which 
 it would be both inhuman and impolitic to demand from 
 living creatures. 
 
 20S. The purpose of machinery, therefore, is to lessen 
 and aid human labour. At an inconsiderable expense, and 
 with a small degree of trouble in supervision, a machine 
 may be made to do the work of ten, fifty, or perhaps as 
 many as five hundred men ; and the work so simply effected 
 by inanimate mechanism, serves to cheapen and extend the 
 comforts and luxuries of life to the great body of the people. 
 
 The following are the chief elementary parts of machi- 
 nery ; — 
 
 171. What of conformity of action and how obtained ? 
 
 172. What is the great purpose of machinery ? 
 
WHEELS AND PINIONS. 
 
 /( 
 
 WHEELS. 
 
 239. A wheel moving on a central axis is a lever with 
 equal arms radiating from the fulcrum at the centre, and is 
 thus called a perpetual lever. 
 
 210. Wheels may be used in machines simply to trans- 
 mit power from one point to another. This is done by 
 means of toothed wheels. Projecting teeth or cogs are 
 placed all round the circumference of a wheel, and, when 
 the wheel is turned, these teeth work upon or press against 
 the teeth of another wheel, and so cause it to turn also, but 
 in an opposite direction. Figure 60 represents tw r o wheels 
 
 so working upon each other. 
 As both of these wheels are of 
 the same size, and consequent- 
 ly are levers with equal arms, 
 they do not alter the effect of 
 the power communicated to 
 them. The motion of the axle 
 in the wheel B is the same as 
 the mo'ion of the first axle in the wheel A. Thus, power 
 may be transmitted from one point to another. 
 
 211. A long and large axle, in wheel-work, is called a 
 shaft, and shafts of small dimensions are termed spindles. 
 The terminating points of axles, shafts, and spindles, where 
 they rest and turn upon supports, are called their pivots or 
 gudgeons. The sockets upon which the gudgeons bear in 
 turning, are sometimes termed bushes. 
 
 WHEELS AND PINIONS, 
 
 212. When power has to be accumulated 
 p or increased in its effect in the course of its 
 transmission, a large wheel is made to play 
 upon a small wheel, by which means there is 
 
 173. How do we obtain a perpetual lever ? 
 
 174. How is power transmitted 1 
 
 175. Explain the first diagram, and the italicised terms. 
 
 176. How is power accumulated ? 
 
 Figure 61. 
 
 Figure 60. 
 
WHEELS AND PINIONS. 
 
 71 
 
 n diversity in the lengths of the levers. Figure 61 is a repre- 
 sentation of a large wheel YV, working on a small wheel or 
 pinion P The wheel is turned by the handle C. In all 
 arrangements in which large wheels are moved by small 
 wheels, or small wheels by large, the small wheels are called 
 pinions ; and when these pinions are broad in their dimen- 
 sions, they are termed trundles. 
 
 213. In this combination of a wheel and pinion, a long 
 perpetual lever works against a short perpetual lever, by 
 which a considerable mechanical advantage is gained. The 
 wheel may be supposed to possess 48 teeth and the pinion 
 6 teeth ; hence by one revolution of the wheel, the pinion 
 turns 8 times, which gives the axle of the pinion eight 
 times the velocity of the axle of the w heel ; and if we sup- 
 pose that the diameter of the wheel is ten times the diame- 
 tc r of the pinion, the power is increased in effect ten times. 
 
 214. Any degree of velocity greater than that of the first 
 rotary motion, may be imparled to the parts of a machine, 
 by making these parts so much smaller than the primary 
 moving parts. Thus, if a large wheel, having a thousand 
 teeth in its circumference, work upon and turn a small 
 wheel having only ten teeth in its circumference, the small 
 wheel will go round one time for every ten teeth of the 
 large wheel which it touches; or, in other words, it wil 1 go 
 round one hundred times for one time of the large wheel. 
 
 The respective velocities 
 of wheels in a machine 
 are, in this manner, al- 
 ways proportionate to 
 their diameters, or size, 
 unless when specially ar- 
 ranged to be otherwise. 
 
 2 15. A combination of 
 wheels acting as perpetu- 
 al levers, is represented 
 in figure 62. Three 
 wheels are placed in a 
 
 177. What example is given ? 
 
 178. How is velocity indefinitely increased ? 
 
 179. Explain the diagram and its principles. 
 
72 
 
 WHEELS AND PINIONS. 
 
 row close to each other, and it is supposed they are fixed bv 
 three axles to some upright object. On the side of the first 
 wheel A, there is attached a small toothed pinion or wheel 
 F, which, by the pressure of its teeth on the teeth of the 
 second wheel B, causes this second wheel to turn round. 
 The power applied to produce this motion is at the circum- 
 ference of the first wheel at D. From D then, to the centre 
 of the pinion E, is the long arm of a lever, of which the 
 centre of the pinion is the fulcrum; and from the centre 
 to the ends of the teeth of the pinion is the short arm. The 
 second wheel B having received its motion, the toothed 
 pinion G, which is similarly attached to its side, presses 
 against the teeth of the third wheel C, and so causes it also 
 to turn. In this way a second lever is put in action. And the 
 third wheel, from its circumference to the point from which 
 the weight VV depends, is a third lever. As the power or 
 small weight P falls, therefore, from the circumference of 
 the first wheel, the resistance VV is raised, with the accumu- 
 lated force of three levers acting on each other. The line 
 across the figure represents the three levers in action. 
 
 216. To calculate the power or mechanical advantage to 
 be gained by such a machine, suppose the number of teeth 
 on the first wheel to be six times less than the number of 
 those on the circumference of the second wheel, then the 
 second wheel would turn round only once, while the first 
 wheel turned six times. And, in like manner, if the number 
 of teeth on the circumference of the third wheel be six 
 times greater than those on the axle of the second wheel, 
 then the third wheel would turn once, while the second 
 wheel turned six times. Thus, the first wheel will make 
 66 revolutions, while the third wheel makes only one. The 
 diameter of the first wheel being three times the diameter 
 of the axle of the third wheel, and its velocity of motion 
 being 36 to 1, three times 36 will give the weight which a 
 power of 1 pound at P will raise at \V. Three times 36 
 being 108, one pound at Pwill balance 108 pounds at W .* 
 
 * In some works, the product of the force multiplied by the arm of 
 the lever with which it acts, is technically called its moment — as “ the 
 moment of the power,” “ the moment of the weight.” 
 
 179. How is its power calculated t 
 
THE CRANE. 
 
 73 
 
 PRACTICAL EXAMPLES. 
 
 217. Figure 63 is a representation of a machine called 
 a crane, which is in very common use for lifting heavy 
 Figure 63. weights. This machine af- 
 
 fords a good practical example 
 of a combination of wheels or 
 perpetual levers, acting so as 
 to transmit and accumulate 
 power. Two levers operate 
 in the machine; the first arm 
 is from the handle to the axle 
 of the first or small wheel ; 
 the second arm is this first 
 wheel from its axle to its 
 toothed circumference; the 
 third arm is the second or 
 large wheel from its toothed 
 circumference to the centre of its axle, and the fourth arm 
 is the radius of the axle. By turning the handle, the first 
 wheel is turned, which gives motion to the large wheel, 
 which causes the axle of the large wheel to warp up the 
 chain which is seen proceeding from it. Thus, any heavy 
 weight attached to the hook at the outer extremity of the 
 chain is lifted. Here, then, the advantage of two lever 
 powers is brought into operation, or concentrated upon the 
 weight attached to the hook. The machine possesses two 
 handles working on one axle, so that two men, if necessary, 
 may work at it. But there is a way of adding power without 
 using two handles. This consists in giving the machine 
 another wheel. This additional wheel is placed between 
 the small and large wheel, so as to afford another lever 
 power. In this manner, we may go on adding wheels, till 
 at length the touch of a finger is sufficient to raise a ton 
 weight. But, as already often mentioned, this advantage 
 is procured only by a loss of time or speed. In usual cir- 
 
 180. Explain the diagram. 
 
 181. What precaution is necessary in toothed wheels ? 
 
74 
 
 TOOTHED WHEELS. 
 
 cumstances, the labour of one or two men is employed, 
 which gives sufficient speed in the operation. 
 
 218. The crane, as we have represented it, is strongly, 
 but elegantly, constructed of iron. Standing on the ground 
 upon a pivot, it may be turned about to any side, so as to 
 bring the hook over a cart, or over a vessel from a wharf, 
 with the smallest trouble. This conveniency in construc- 
 tion causes it to be extensively used in shipping operations 
 at wharfs. 
 
 Figure 64. 
 
 WOIt KING OF TOOTHED WHEELS. 
 
 219. In the working of toothed wheels one upon another, 
 or of wheels working on pinions, it is essentia] to set them 
 in opposition with such exact adjustment, that the teeth of 
 one will fall into the hollows betwixt the teeth of the other. 
 When the teeth of each do not work with this nicety, they 
 are apt to jar upon and break each other, and so damage 
 the machine. In some cases teeth are made of a round or 
 pointed form at their extremities, by 
 which a very small degree of grind- 
 ing or pressing on each other takes 
 place. Figure 64 is an example of 
 a wheel and pinion with rounded and 
 pointed teeth. From the centre of 
 the axis of the pinion L to the centre 
 of the wheel C, a dotted line is mark- 
 ed, called by mechanics the line of 
 centres. The dotted circle O O 
 round the pinion, and the dotted 
 circle P P round the wheel, indicate 
 the true point of working or contact 
 of the teeth upon each other. These two circles are seen 
 to join with exactness at A. 
 
 ALTERING THE DIRECTION OF MOTION. 
 
 220. Motion often requires to be altered in its direction 
 in the course of its transmission. For example, rotary 
 
 1S2. Explain the diagram. 
 
 183. What of altering the direction of motion ? 
 
BEVEL WHEELS AND BELTS. 
 
 75 
 
 horizontal motion requires to impart rotary vertical motion, 
 or rotary vertical motion to impart horizontal motion. By 
 means of a peculiar mode of setting the wheels, and a cor- 
 responding peculiarity in the shape of their teeth, any 
 alteration may be effected in the direction of the motion. 
 
 221. Figure 65 represents a plan of 
 ^ changing the direction of motion. A 
 is a pinion or trundle working with its 
 \J shaft horizontally on a wheel B, whose 
 16 shaft is turning vertically. As the case 
 may happen to be, the horizontal move- 
 ment is causing the vertical movement, 
 or the vertical movement is causing the horizontal move- 
 ment. 
 
 BEVEL WHEELS. 
 
 Figure 66. 
 
 222. Figure 66 represents a more 
 common plan of changing the direction 
 of motion. The wheels in this case are 
 bevelled. A bevel wheel is a wheel with 
 teeth placed in a sloping or oblique di- 
 rection on its circumference. When 
 two bevel wheels are placed at right 
 angles with each other, their respective 
 teeth work against each other, and so a 
 harmonious joint motion ensues. This 
 is exemplified in the figure, in which a 
 horizontal shaft with a bevel wheel, is 
 seen turning a smaller bevel wheel above it, placed on a 
 vertical shaft. 
 
 TRANSMISSON OF POWER BY BELTS. 
 
 223. A common plan of transmitting power from one 
 point to another, when the interval is considerable, is by a 
 flat leather band, strap, or belt, communicating from a wheel 
 at the source of power to a wheel connected with the ma- 
 chine. 
 
 135. Explain the first diagram. 
 
 186. What of bevel wheels? 
 
 187. What other mode of transmitting power T 
 
7G 
 
 TRANSMISSION OF POWER BY BELTS. 
 
 224. The wheels upon which straps work are usually 
 called pulleys. They have flat and broad rims, and these 
 rims have sometimes narrow ledges, to prevent the belt 
 from slipping off. The rims must also be rather rough on 
 their surface, so as to give the belt a sufficient friction or 
 power of pulling in performing its revolutions. 
 
 225. Figure 67 represents the transmission of power by 
 a belt. A is the first pulley, which has received the power 
 
 Figure 67. 
 
 from its source, and C is the se- 
 cond pulley, moved by a belt, 
 which passes over both pulleys. 
 In this case the motion of A is 
 transmitted by the belt to C. 
 which it causes to turn in the 
 same direction as A. If these two pulleys were of precisely 
 the same diameter, and th 1 belt did not relax or slip, the 
 second pulley would unavoidably go at the same velocity as 
 the first, because the belt has exactly the property of a 
 toothed wheel, and simply transmits the power it has ac- 
 quired. As C appears to be somewhat smaller than A, it 
 would consequently turn more frequently than A ; there- 
 fore, we have here an example of the mode of increasing 
 the velocity while transmitting power. 
 
 226. Figure 68 is a representation of two pulleys moving 
 in different directions by means of a belt. The large pul- 
 
 Figure 63. 
 
 ley is supposed to be that which has 
 received its power from its source. 
 The belt after leaving it, is crossed, 
 and, therefore, it causes the smali 
 pulley to move round in a direction 
 opposite from that of the first. Here, 
 also, the second pulley is smaller than the first, and there- 
 fore moves with an increased rotary velocity. 
 
 227. Crossing the belt serves two purposes. It changes 
 the direction of the rotary motion which is sometimes re- 
 quired in machinery, and causes the belt to move more 
 steadily. When the belt is long, it is apt to vibrate consid- 
 
 1S8. Explain the first diagram. 
 189. Explain the last diagram. 
 
SHAFTS AND PULLEYS. 
 
 77 
 
 erably in its motion, from its weight being unsupported at 
 the centre. 
 
 228. Power might be transmitted to any distance by belts 
 without loss, if their weight, vibratory motion, and tendency 
 to slacken, did not present obstacles to transmission to any 
 considerable distance. Practically, belts are not generally 
 employed to transmit power to above a distance of twenty 
 or thirty feet, and more frequently the distance is from ten 
 to fifteen feet. 
 
 229. When power requires to be carried to a distance 
 beyond that which belts can conveniently manage, the 
 transmission is effected by a long shaft; and if it be ne- 
 cessary to change and rechange the direction of the motion, 
 bevel wheels are added. Or the transmission may take 
 place by a long flat chain acting like a belt, but caused to 
 travel over small wheels or pulleys, to prevent the chain hang- 
 ing down in any part of its course. A chain of this nature 
 is called an endless chain. 
 
 230. Motion is often required to be communicated to 
 many different machines, at different points, from one source 
 of power. This is effected by means of a shaft and pulleys. 
 From tfie pulley which receives the first motion, a belt is 
 sent to a pulley fixed upon a shaft, which shaft is generally 
 hung horizontally from the roof over the machines. As the 
 shaft turns through its whole extent, it is able to turn pul- 
 
 SHAFTS AND PULLEYS. 
 
 Figure 69. 
 
 B 
 
 leys fixed at any point upon 
 it, and from these pulleys, 
 belts are sent down to pul- 
 leys at the respective ma- 
 chines. 
 
 A 231. Figure 69 represents 
 an apparatus of a sha t and 
 pulleys. A is the pulley 
 receiving motion from the 
 
 190. What are the disadvantages of belts ? 
 
 191. How are shafts and pulleys used and why ? 
 
 192. Explain the first diagram. 
 
78 
 
 CHANGING VELOCITY. 
 
 source of power, and, by means of the belt L, turns the pulley 
 on the end of the shaft S. At the same time the pulley D at 
 the opposite end of the shaft is turned. From a pulley on 
 the shaft situated close to B, a belt descends to turn C,and 
 from D another belt descends to turn E. Thus, an extended 
 axle or shaft from C will turn a machine, and an extended 
 axle or shaft from E will turn another machine. The ap- 
 paratus can turn two machines. 
 
 232. Shafts with pulleys, working on the plan now stated, 
 are to be seen at almost every considerable manufactory in 
 which machinery is employed; and the power, by means 
 of bevel wheels, and upright connecting shafis, is carried 
 upwards from story to story in a building, giving motion to 
 hundreds of wheels, spindles and other parts of the mech- 
 anism. 
 
 CHANGING VELOCITY. 
 
 233. It is sometimes necessary that a machine, or part 
 of a machine, should be propelled with a velocity which is 
 not equable, and is continually changing from fast to slow 
 and slow to fast. This happens in cotton mills, where it is 
 necessary that the speed of certain parts of the machinery 
 should continually decrease from the beginning to the end 
 of an operation. To effect this an apparatus is used, as re- 
 presented in figure 70. Two cones, or 
 conically shaped drums, are used, hav- 
 ing their larger diameters in contrary 
 directions. They are connected by a 
 belt, which is so governed by proper 
 mechanism, that it is gradually shifted 
 along from one extremity of the cones to 
 the other, thus acting upon circles of dif- 
 ferent diameter, causing a continual change of velocity in 
 the driven cone with relation to that which drives it. 1 he 
 shifting of bands from large to small wheels, and Iroin 
 small to large, has similar effects. 
 
 193. What examples of their use are stated 1 
 
 194. How is velocity changed 1 
 
SPRING AND CHAIN APPARATUS. 
 
 79 
 
 PRESERVING REGULARITY OF MOTION BY A VARIABLE FORCE. 
 
 234. In some mechanical contrivances, the force which 
 is applied vanes in its intensity, while the wheels of the 
 machinery require to be kept at a uniform speed. This is 
 generally the case when the force is communicated from a 
 
 steel spring, which, after being 
 wound up, is suffered to relax. 
 Figure 71 is a spring suited for 
 operations of this kind. It is re- 
 presented in a state of relaxation, 
 and is wound up into a compact 
 form by means of a spindle fixed 
 to i'p inner extremity. The coiling of a strip of paper round 
 the finger, and allowing it to unwind itself, is a familiar 
 illustration of the action of a spring of this description. 
 
 235. The force communicated by the relaxing of the 
 spring varies in its intensity. The force is greatest when 
 it begins to relax, and it gradually weakens till its expan- 
 sive energy is exhausted. To compensate this defect, a very 
 ingenious plan is adopted, and which is put in operation 
 in the apparatus of the common watch. 
 
 236. Figure 72 represents the apparatus of motion of a 
 
 watch, somewhat magni- 
 fied. The spring is con- 
 fined in a brass cylinder 
 or barrel B. To this 
 barrel the spring is at- 
 tached by a slit at its 
 outer extremity. The 
 
 inner extremity of the spring is fixed by a similar slit to the 
 central axis or spindle. F is a brass cone, broad at bottom 
 and narrow at top, with a path winding spirally round it as 
 an inclined plane. This cone is called the fusee, and has 
 also a central axis or spindle K, to which it is fixed. To a 
 point on the lower inclined path of the fusee, a small steel 
 chain C is attached, and the other extremity of this chain 
 
 F, ;olain the first diagram and how uniform velocity is secured. 
 
80 
 
 ECCENTRIC WHEELS. 
 
 is attached to the top part of the barrel. When the spring 
 is relaxed, the chain is almost altogether round the barrel. 
 To set the apparatus in motion, the watch-key is made 
 to turn the spindle K, by which the chain is drawn from 
 the barrel to the fusee, filling up the inclined path to the 
 summit. The chain in leaving the barrel causes it to turn, 
 and consequently to wind up the spring inside. The pro- 
 cess of unwinding or relaxing ensues, and now the ingeni- 
 ous plan for regulating the motion is to be remarked. At 
 first, when the force of the spring is greatest, the chain 
 acts upon a small round of the fusee ; in other words, it 
 pulls with a small lever — for as already explained under the 
 head Wheel and Axle, a wheel or round object on an axis 
 is simply a perpetual lever. In proportion as the intensity 
 of the force weakens, and the barrel takes off the chain 
 from the fusee, and winds it about itself, so does the chain 
 act upon a longer lever, or so does it gain a greater lever 
 advantage, by drawing at a wider part of the cone. Thus, 
 the gradual loss of force is counterbalanced by a gradual 
 increase of lever advantage. (The case resembles that of 
 a strong man working with a short lever, and a weak man 
 working with a long lever; both are equal in effect in 
 balancing any resistance.) The wheelwork of the watch 
 is moved by teeth on the lower circumference cf the cone. 
 
 ALTERNATE OR RECIPROCATING MOTION — ECCENTRIC WHEELS. 
 
 237. Alternate or reciprocating motion is applied to 
 movements which take place continually backwards and for- 
 wards in the same path. In most complex machines, both 
 rotary and reciprocating motion occur, and these motions 
 may be converted into each other by various contrivances. 
 
 238. A common contrivance for gradually raising and 
 depressing an object by machinery, is that of an eccentric 
 wheel. 
 
 239. An eccentric wheel is a wheel with an axis not in 
 its centre, but at a point nearer one side than the other. 
 
 196. Explain the mechanism of a watch. 
 
 197. How is alternate motion secured 1 
 
ECCENTRIC WHEELS. 
 
 81 
 
 Figure 73. Figure 73 represents the action of a wheel 
 of this kind. W is the wheel, and A the 
 axis upon which it is fixed. When the axis 
 turns, the wheel turns with it. As the axis 
 never moves out of its place, the wheel neces- 
 sarily describes a path of gradual rising and 
 falling in its revolutions. Suppose an object, as T, pressing 
 upon the upper edge of the w'heel, so as to accommodate 
 itself to the motion, it is obvious that, by the action of the 
 wheel, this object will be alternately raised and allowed to 
 fall. Or suppose that a rod is hung from a point of the 
 wheel near where T rests, it is similarly obvious that the 
 rod would be raised or depressed, according as the wheel 
 turned. Thus, a rising and falling motion may be effected 
 by an eccentric wheel. 
 
 240. Eccentric wheels are made of different forms. Ac- 
 cording as they may be required to act, they are circular, 
 oval, heart-shaped, or pointed at one end, and so forth — the 
 i bject in each case being to produce alternate motion, by 
 continually altering the distance of some moveable part of 
 the machine, from the axis about which they revolve. Tech- 
 nically, the projecting parts of eccentric w'heels are called 
 cambs. 
 
 241. In some cases, eccentric wheels 
 are not required to perform entire revo- 
 lutions on their axes. It is perhaps 
 sufficient for the purpose of the me- 
 chanism, if they gradually rise to the 
 height of their power, and then, without 
 turning round, gradually descend by 
 retracing their course. An example 
 of this kind of motion is given in the 
 adjoining figure. L is a lower circular 
 wheel turning on a fixed central axle, 
 which axle rests on two supports not 
 drawn in the figure. P is a bar or lever 
 by which the axle is turned. By de- 
 pressing the lever at P, the wheel turns, 
 
 198. Explain the diagram. 
 
 199. Name the variety of eccentric wheels. 
 
 200. Explain the d agrain. 
 
 Figure 74. 
 
82 
 
 ECCENTRIC WHEELS. 
 
 and by its teeth propels the semicircular eccentric wheel 
 above it. The eccentric wheel in going forward is com- 
 pelled to rise to its full height, which height it has attained 
 when its extremity at F is brought straight above E. In 
 thus ascending, it pushes upwards the beam E, which is 
 attached to it by an axle through E. The beam E con- 
 sequently pushes up the board M, and presses any material, 
 in n, against the topmost board A B. This topmost boaid 
 is fixed to supports, not drawn in the figure, and neither 
 rises nor falls. By this process of winding up the semi- 
 circular eccentric wheel, the utmost height of pressure of 
 the machine is attained. The lever is then turned by a 
 reverse motion, and the semicircular eccentric wheel conies 
 to its lowest depression when its extremity at F is brought 
 near to L. 
 
 242. The principle upon which this machine gives pres- 
 sure, is that of the lever. In working. the lower circular 
 wheel against the eccentric above, there is a combination 
 of two levers; and the power increases as the eccentric 
 ascends, because the leverage of the eccentric is at even- 
 tooth increased in its length. 
 
 243. The leverage power given by an eccentric wheel or 
 camb is one of the most convenient and ingenious applica- 
 tions of force. It is now used in small presses for stam;>- 
 ing books and other processes in which a^rm rapid pres- 
 sure requires to be given. The example in figure 74 is 
 that of a machine for pressing putty or any other soft 
 material into moulds, to produce casts of ornaments; and 
 it appears to be excellently adapted for the purpose. 
 
 244. When an alternate rising and falling is required 
 twice in a piece of machinery, by only one revolution of an 
 axle, an eccentric wheel is used of an oval form, with the 
 axle in the middle of'the oval, by which means each end 
 of the oval rises in the course of a revolution. 
 
 245. When an alternate rising and falling is required 
 thrice, by only one revolution of an axle, an eccentric wheel 
 is used having three projecting cambs on its circumference, 
 and as each camb comes round, it lifts and lets fall any 
 
 201. Upon what principle is this machine 7 
 
OBLIQUE ACTION. 
 
 83 
 
 object presented to it. An example of this apparatus is 
 Figure 75. given in Figure 75. The object 
 
 required is to work a heavy ham- 
 mer upon an anvil for beating 
 iron. W is the wheel with the 
 three cambs, and it turns by an 
 axle in upright supports. In turn- 
 ing, each camb, with its rounded 
 or convex side, presses down the 
 end of the handle of the hammer, 
 so as to raise the heavy head II at the opposite end. After 
 pressing down the handle and escaping, the head of the 
 hammer falls with a heavy blow on the anvil A. There it 
 remains till raised up and let fall by the next camb, and 
 so on. 
 
 OBLIQUE ACTION. 
 
 246. A mechanical advantage, which is frequently of a 
 very serviceable nature, is obtained by causing the points 
 of two straight bars to meet each other, but fixed loosely, 
 so as to be free to move from an oblique to a straight direc- 
 tion, and the reverse. The power consists in bringing the 
 bars to the straight, by which they force asunder or press 
 hard upon any object presented to their outer extremities. 
 
 Figure 76. In the adjoining figure, the bars are 
 
 l I "w” seen first in their oblique position, 
 
 and next when brought towards a 
 straight. Betwixt the two points a 
 small hollowed piece of metal is in- 
 serted, in which the points work, and 
 against which the power is exerted 
 to produce the action. The straight- 
 ening and bending of the apparatus 
 resembles the action of the knee- 
 joint in animals. The pressure pro- 
 duced by the forcing downwards of the outer extremity of 
 the lower bar (the upper working against a fixed beam) is 
 
 202. Explain the diagram and its object. 
 
 203. Whit of oblique action and the example. 
 
84 
 
 CRANKS AND RATCHETS. 
 
 very easily and rapidly accomplished, and is almost unlim- 
 ited; and these advantages, as well as the extreme simpli- 
 city of the mechanism, have led to the application of the 
 power to the printing-press wrought by the hand, instead 
 of screw pressure. 
 
 CRANKS. 
 
 247. The crank affords one of the simplest and most 
 useful methods of changing an alternate rising and falling 
 motion into rotary motion. 
 
 248. A crank resembles a common handle or winch for 
 turning a machine by the hand ; the chief difference being, 
 that a rod or shaft jointed to the handle, and going up and 
 down, works the machine. If the crank be made double, 
 it will turn two wheels or machines. 
 
 Figure 77. 249. Figure 77 represents a dou- 
 
 ble crank in action. S is the rod 
 or shaft ascending and descending, 
 and attached by a joint to the lower 
 w part of the crank C, which it alter- 
 nately pulls up and pushes down, 
 so as to cause the axles W W to 
 turn a wheel at each side. Take 
 away one of the sides of the crank 
 and its support, and the apparatus becomes a single crank. 
 
 250. Turning-lathes, knife-grinders’ machines, and similar 
 apparatus, are usually turned by cranks wrought by an 
 alternate pressing and raising of the foot of the operator; a 
 rod going upwards from the foot-board to the crank, caus- 
 ing the wheel or spindle to go round. The crank has been 
 hitherto indispensable in the action of the steam engine. 
 
 RATCHET WHEELS. 
 
 251. It is sometimes necessary to prevent wheels and 
 axles, bearing the strain of heavy weights, from flying in a 
 backward motion after being wound up. This purpose is 
 
 204. Define a crank and explain the diagram. 
 20y. Cite examples of its use. 
 
ACCUMULATING POWER. 
 
 85 
 
 effected by fixing a ratchet wheel to the extremity of the 
 Figure 7S. axle. This wheel has teeth all round 
 its periphery, inclining in one direction, 
 and a small catch is so placed as to 
 enter the indentations and stop the 
 wheel if it inclines to turn backwards, 
 but the catch slides over the teeth with- 
 out obstructing them, if it moves for- 
 ward. A spring pressing on the catch 
 causes it to keep in its proper place. Figure 78. 
 
 ENGAGING AND DISENGAGING MACHINERY. 
 
 252. In many cases, particularly where numerous ma- 
 chines are propelled by a common power, it is important 
 to possess the means of stopping any one of them at plea- 
 sure, and of restoring its motion, without interfering with 
 the rest. To produce this effect, various plans are pursued. 
 The most common and simplest device, used in cases of 
 motion by belts, consists in having a live and dead pulley. 
 Alongside of the pulley whose axle moves the machinery, 
 and on which the belt works, there is a pulley or wheel 
 loose on its axle, called the dead pulley, from its inopera- 
 tive character. When the machine is to be stopped, the 
 belt is shifted from the live or active pulley to this dead 
 pulley, w'hich it turns without producing any effect on the 
 machinery. Motion is restored to the machine by shifting 
 the belt back to the live pulley. A long rod with a clutch 
 at its extremity, and easily affected by the hand of the 
 workman, turns the belt off or on at a moment’s notice. 
 
 PRACTICAL MACHINERY CONTINUED— OF AC- 
 CUMULATING AND EQUALISING POWER. 
 
 ACCUMULATION. 
 
 253. Power is susceptible of accumulation — that is, of 
 increasing little by little — and of being expended eithei 
 
 206. What are ratchet wheels and their use. 
 
 207. How is machinery stopped at pleasure. 
 
 208. What of live and dead pulleys ? 
 
86 
 
 ACCUMULATING POWER. 
 
 gradually or in one or more violent efforts; the efforts 
 being entirely the concentrated amount of the previous ac- 
 cumulation. The apparently wonderful powers displaced 
 through the agency of levers and other simple machines, 
 are all a natural consequence of an accumulation of any 
 degree of force into a small space; by which, effects take 
 place that could never have been accomplished by the 
 original force. 
 
 254. In consequence of this convenient accumulation 
 of power in machines, plans have been devised for estab- 
 lishing reservoirs of power, as they may be called, in con- 
 nection with moving machinery. 
 
 255. A well-known method of accumulating power con- 
 sists in suspending a heavy body by a chain or strong rope 
 of considerable length— forming what is called by young 
 persons a swing. This body may be put in motion by a 
 very small degree of power, and will acquire a vibrating 
 motion like a pendulum. By continuing the impulse as 
 the body returns,- it will continually acquire greater and 
 greater force, the arcs through which it moves becoming 
 continually larger, until at last it might be made to over- 
 come almost any obstacle. Upon this principle, the batter- 
 ing rams, or engines i or beating down the fortifications of 
 towns in ancient times, were constructed, and the force of 
 their blows was as great as that of a cannon ball ; never- 
 theless, the power of their blows never could exceed the 
 accumulated power of the impulses given to them in order 
 to produce these blows. 
 
 256. The forcible expenditure of accumulated power in 
 the swing apparatus, resembles that which is observable in 
 the case of a person occupying several minutes in bending 
 a spring — that is, accumulating power — and then allowing 
 the spring to unbend itself by one violent effort, which 
 effort is nothing more than the giving out of the accumu- 
 lated power. 
 
 257. A boy taking a race to gain force before making a 
 leap, is another familiar example of accumulating power 
 
 209. What of reservoirs of power ? 
 
 210. What of battering rams ? 
 
 21 1. What familiar examples are cited ? 
 
ACCUMULATING POWER. 87 
 
 and expending it instantaneously. The boy is gathering 
 up power at every step he runs, and the force of his kap 
 corresponds exactly with the quantity of the power he has 
 acquired. 
 
 258. In the same manner, the lifting of a hammer, axe, 
 or other instrument, to an elevation as far as our arm can 
 reach, in order to give a blow with good effect, is a method 
 we naturally pursue to gain an accumulation of power. 
 
 259. In contrivances in the arts, power is sometimes 
 accumulated in order to be given out in the form of a rapid 
 and effective blow. This may be done by nr ans of a 
 horizontal bar or lever, poised on a central axis, and loaded 
 at each end with a heavy ball of lead or iron. After com- 
 municating to the machine a sufficient power of rotation, 
 it will proceed with an enormous accumulated energy and 
 momentum, till it expend its force either by friction in 
 turning, or upon some fixed obstacle presented to it. 
 
 260. The press used for stamping or taking impressions 
 of coins and similar articles from dies, furnishes one of the 
 
 Figure 79. best examples of the instantaneous ex- 
 L s L penditure of accumulated power. A 
 
 press of this kind is represented in figure 
 79. The apparatusis very simple. It con- 
 sists of a strong upright frame of iron, 
 with a thick screw S suspended from the 
 upper cross beam, and going through a 
 middle cross beam. In these two beams 
 the screw works freely. The screw is 
 wrought by a horizontal lever bar, poised on a central axis, 
 and loaded at each end with a heavy ball L L- The die 
 lies on the point D below, and the blank piece of metal to 
 be struck is laid upon it. If a coin with two sides is to be 
 impressed, another die is fixed upon the point of the screw. 
 The rapid and forcible pulling round of the lever causes 
 the screw to sink, and by a single rapid crush or blow 
 upon the metal against the die, or dies, the impression is 
 made. The shock of concussion causes the screw to re- 
 bound upwards, and the instant a vacancy is left below, the 
 
 212. Explain the diagram, and its use. 
 
83 EQUALISING POWER FLY VVHEEL3. 
 
 impressed me'al is taken out, and a new piece is inserted. 
 By this simple process, coins, medals, ornamented metal 
 buttons, and similar articles, are struck. 
 
 EQUALISATION FLY WHEELS. 
 
 261. In most machines, both the moving force and the 
 resistance to be overcome are liable to fluctuations of inten- 
 sity at different times, during the operation of working. 
 For instance, when a man turns a winch or handle of a 
 piece of machinery, he is apt to relax in his efforts for an 
 instant from loss of strength, or from an inability to keep 
 his attention closelv and uniformly fixed to the labour he 
 has to perforin. These relaxations cause an irregularity of 
 motion in the machinery, which are detrimental to the 
 machine and to the work performed. Other moving forces 
 are liable to similar irregularities. 
 
 2ii2. The irregularities in the motion of machinery, from 
 whatever cause they arise, are remedied by giving to each 
 machine a reservoir of power, from which force may be 
 given at all times to equalise the motion according as it 
 may be required. These reservoirs of power are usually in 
 the form of fly wheels. 
 
 263. A fly wheel is generally made 
 of iron, and consists of a heavy rim 
 or circumference, joined to a central 
 axis by cross bars or spokes. Figure 
 80. In most cases it is placed in 
 close connection with the first moving 
 force, the effect of which it equalises 
 in its passage to the machine. 
 
 264. Whatever quantity of power is 
 communicated to a fly wheel, the fly 
 
 accumulates it and gives it forth as may be required, in 
 order to overcome any small variations in the first moving 
 fijrce or in the working of the machine. 
 
 265. The power is communicated to the fly wheel at its 
 axle, and thence affects the whole fabric. The motion is 
 
 213. What is the nature and use of fly-wheels 1 
 
 214. Explain the diagram. 
 
OBSTACLES TO MOTION. 
 
 89 
 
 a' first given in a gradual manner, till it becomes steady. 
 If there were no machine to retard the speed, and the im- 
 pulsive force continued to be administered, the effects, from 
 centrifugal force, would soon be overpowering. In prac- 
 tice, the friction of the various parts of the machine checks 
 the tendency to over velocity, and when the machine lags, 
 or tends to work irregularly, the gathered momentum of the 
 fly is expended in preserving regularity. 
 
 268. The weight, size, and velocity of fly wheels, are 
 regulated bv the nature and quantity of the power applied, 
 and the nature of the machinery to be put in motion. 
 There is a certain degree of velocity at which the force 
 employed will produce the greatest effect; and it is of im- 
 portance to keep this circumstance in view, in the construc- 
 tion of machines. 
 
 PRACTICAL MACHINERY CONTINUED- 
 OBSTACLES TO MOTION. 
 
 267. Moving bodies, as machines and wheel carriages, 
 are less or more retarded in their velocity by friction, and 
 the resistance of the atmosphere, while vessels moving on 
 water are retarded by the resistance both of the atmosphere 
 and of the liquid in which they are buoyant. 
 
 FRICTION. 
 
 268. Friction is an effect of the action of rubbing of 
 bodies one upon another. 
 
 269. This effect is produced by inequalities of surface. 
 No such thing is found as perfect smoothness of surface in 
 bodies In every case there is, to a lesser or greater extent, 
 a roughness or unevenness of the parts of the surface, 
 arising from peculiar texture, porosity, and other causes; 
 and, therefore, when two surfaces come together, the promi- 
 nent parts of the one fall into the hollow parts of the other. 
 This tends to prevent or retard motion. In dragging the 
 
 215. What particulars are important? 
 
 216. Name the various obstacles to motion. 
 
 217. What is the source and influence of friction ? 
 
DO 
 
 FRICTION. 
 
 one body over the other, an exertion must be used to ft 
 the prominences over the parts which oppose them, and 
 this exertion is similar to that of lifting or drawing of bodies 
 up inclined planes or over upright protuberances. The 
 effect so caused is called friction. 
 
 270. Friction acts as a retarding influence in the action 
 of all mechanical contrivances, and a due allowance must 
 in every case be made for it. In many instances it destroys 
 more than a half of the power employed, and seldom de- 
 stroys less than a third. However small it may be, it sooner 
 or later causes the wearing down and destruction of me- 
 chanism, and therefore forms an insurmountable obstacle to 
 the lasting duration of bodies and the perpetuity of motion. 
 
 271. The action in overcoming friction being of the 
 nature of lifting or drawing of bodies up inclined planes, 
 gravity is permitted to have an effect in the drawing of 
 bodies upon horizontal planes not perfectly smooth. Thus, 
 weight forms an important element in calculating the pro- 
 bable amount of friction of a body. 
 
 272. Friction is found to depend on the following circum- 
 stances : — 1st, The degree of roughness of the suriaces. 2d, 
 The weight of the body to be moved. 3d, The extent of 
 surfaces in certain bodies presented to the action of rubbing. 
 4th, The nature of the bodies. 5th, The degree of velocity 
 of the motion. 6th, The manner of (he motion. 
 
 273. Roughness . — It is of the utmost importance to 
 smooth the surfaces. An apparently insignificant piece of 
 matter, or even particles of dust, will greatly retard the 
 motion of a body. But there is a limit beyond which it 
 would be imprudent to smooth the surfaces of bodies 
 having a close texture. If the surfaces be highly polished 
 and levelled, the bodies will adhere by the effect of attraction 
 of cohesion, even when the atmospheric air is not entirely 
 expelled from between them, and more forcibly when the 
 air is completely expelled. Practically, roads, railways, and 
 similar bodies, cannot be made too smooth. 
 
 274. Weight . — Friction from w'eight differs in different 
 
 218. What circumstances affect friction 1 
 
 219. What of roughness, and weight 1 
 
FRICTION. 
 
 91 
 
 bodies, and depends on concurring circumstances, as nature 
 of surface, and so forth. Friction always increases in exact 
 proportion as the weight increases, when all other circum- 
 stances remain the same. Any moving part of machinery, 
 therefore, should be made as light as possible, consistent 
 with strength and durability. 
 
 275. Extent of surfaces . — Rough bodies are more easily 
 drawn along when their surface of contact is narrow than 
 w hen they are broad. For example, it is easier to draw 
 two narrow brushes across each other, than two broad ones 
 of the same weight. Friction may, therefore, be diminished 
 in rough bodies by lessening the extent of surfaces in con- 
 tact. But there is a limit to this diminution. If the moving 
 surface be very thin, and the other soft, the thin surface 
 w'ill plough a groove in the soft one, and thus the friction 
 w'ill be increased, and the machine injured. In the case 
 of smooth hard bodies, extent of surface makes no differ- 
 ence in the friction. 
 
 270. Nature of Bodies . — It is a remarkable truth that 
 two bodies which are of the same nature, or homogeneous, 
 produce greater friction in movement, than bodies which 
 are different in their nature, or heterogeneous. Thus, iron 
 working against iron, steel against steel, or brass against 
 brass, causes in each case greater friction and wearing of 
 parts, than when iron or steel is made to work against 
 brass. This circumstance is always attended to in the 
 construction of machinery. Frequently, a small piece of 
 leather is adjusted round an axle, to prevent the metals 
 from coming in contact. 
 
 277. Degree of Velocity . — Friction is a uniformly retard- 
 ing force, except in the case of small velocities, when it is 
 greater in proportion. The reason for it being greater in 
 small velocities, is, that in these cases, time is allowed lor 
 the prominences of the moving body to sink deeply into the 
 hollows of the surface on which it is moving, which has a 
 retarding effect. 
 
 278. Manner of the Motion . — The least advantageous 
 
 220. How is extent of surface to be modified 1 
 
 221. What of the nature of bodies, and of velocity 1 
 
92 
 
 FRICTION. 
 
 manner in winch one body can be moved upon another, is 
 to cause it to slide or drag. The most advantageous man- 
 ner, is to cause it to roll or turn. The causing of a body 
 to roll instead of to slide, is one of the chief means of 
 diminishing friction. The opposition presented bv inequa- 
 lities of surf-ice to a rolling wheel, is overcome with ease, 
 in proportion to the extent of diameter of the wheel On a 
 perfectly horizontal plane, the Irictiou of wheels on the 
 plane is very inconsiderable ; the chief seat of friction in 
 such cases, being in the axles working in their sockets. 
 
 279. Various plans have been tried to modify the friction 
 of wheels in their sockets. One remedy consists in con- 
 stantly keeping up a lresh lubrication from small reservoirs 
 of oil placed in the axles or gudgeons, and which supply 
 the deficiency as it occurs. A more effectual plan consists 
 in surrounding the inner sides of the gudgeons with small 
 wheels, upon the rims of which wheels the axle works in 
 turning. These friction wheels, as they are called, save 
 the axle from rubbing on the inner sur ace of the gudgeons, 
 and transfer the friction to their own small axles. 
 
 280. Friction is greatly diminished by lubricating the 
 rubbing surfaces with an oily or greasy substance, which 
 substance forms a medium of small soft particles betwixt 
 the bodies, and so prevents the tendency to grind or wear 
 down the surfaces. Water or any similar fluid will also act 
 as a medium to prevent friction, but the effects are only tem- 
 porary, and would frequently be injurious, as the substance 
 speedily evaporates, and would corrode metals. Practically, 
 fine pure oil is found to be the best unguent for machinery. 
 
 281. One of the first considerations on the part of con- 
 trivers of mechanism, should be how to provide for and 
 diminish the effects of friction in their machines. For 
 want of forethought on thi important point, thousands of 
 ingenious schemes, which seemed perfect in the form of 
 models and drawings on paper, have been completely 
 frustrated when attempted to be brought into use. 
 
 222. What of rolling and sliding motion ! 
 
 223. How is friction modified in wheels ? 
 
Csr.S OF FRICTION. 
 
 93 
 
 USES OF FRICTION. 
 
 282. Whatever may be the retarding and frequently 
 inconvenient effects of friction, in reference to the action 
 of mechanism, it is certain that friction is indispensable in 
 the economy of both nature and art, and serves as an essen- 
 tial auxiliary to gravitation. It is a property which is 
 frequently necessary, in order to allow one kind of matter 
 to possess a hold upon another, without actual cohesion. 
 We walk and maintain our erect posture by means of gravi- 
 tation and action arid reaction — in other words, we are 
 held to the earth by gravitation, and our pressure with our 
 feet exemplifies action and reaction — but if there was no 
 such property as friction, we should either stick to the 
 earth by attraction of cohesion, or slide along it as upon 
 the smoothest ice. In order to keep our feet from sliding 
 when on ice, if we received any impulse, we either tie 
 rough substances on our shoes, or scatter ashes in our 
 path; and thus we receive the benefit of friction. It is by 
 friction that rains wear down hills, and that rivers wear 
 away their banks, by which ceaseless process the external 
 configuration of the globe is constantly undergoing a change. 
 The operations in art, of washing, cleaning, scouring, sharp- 
 ening, polishing, cutting, bruising, beating, and so forth, 
 are all effected less or more by friction. The hold which one 
 fibrous substance has on another, or mutual friction, permits 
 the operations of weaving cloth, twisting ropes and threads, 
 and the tying of one body to another. Thus, friction is of 
 universal service; and the only known instances in nature 
 in which it is not required, and therefore not present, are 
 the movements of the heavenly bodies, which revolve in a 
 vacuum, and are consequently riot impeded in their motions, 
 
 RESISTANCE OF AIR AND WATER. 
 
 283. Atmospheric air and water are fluids of different 
 densities, and both present an obstacle to the motion of 
 solid bodies through them. 
 
 225. Illustrate the uses of friction. 
 228. What of the heavenly bodies ? 
 
91 
 
 RESISTANCE OF AIR AND WATER 
 
 284. There is a rule in respect to the resistance pre- 
 sented in moderate velocities, which applies both to air and 
 water. It is, that the resistance is proportional to thf. 
 square of the velocity. For example, a velocity of 
 twenty miles an hour causes a resistance four times greater 
 than a velocity of ten miles an hour, for the square of 
 twenty (which is 20 times 20, or 400) is four times the 
 square of ten (which is 10 times 19, or 100). Thus, by 
 increasing the velocity of bodies through the air or water, 
 we must increase the power in a greater proportion, in 
 order to compensate the loss caused by resistance. 
 
 285. Although the above rule is nearly correct for mode- 
 rate velocities, it deviates considerably from what is obser- 
 vable in the case of great velocities, such as that of a cannon 
 ball. When the velocity is upwards of 1009 feet per second 
 through the air, the quick, passage of the body is believed 
 to cause a partial vacuum behind it, which causes a retarda- 
 tion of its motion. 
 
 286. Resistance to motion in fluids is greatly modified, 
 also, by the form of the moving body. The form that gives 
 least resistance is nearly that of a parabola, or a form some- 
 what resembling the breast of a duck, the head of a fish^or 
 the rounded bow of a vessel, sharpened to cleave the fluid 
 through which the body passes. 
 
 PRACTICAL MACHINERY CONCLUDED— MOVING 
 FORCES. 
 
 287. The sources of power for moving machinery are 
 various, and are employed according to circumstances. 
 Men and animals, water, wind, and steam, are the principal 
 sources, or, as they are called, agents of force. Men and 
 animals operate by muscular energy; water acts by its 
 momentum and gravity; wind by its pressure when in a 
 state of motion ; and steam, by the expansive energy of 
 heat. There are also other agents of power in nature ; 
 such as magnetism, galvanism, electricity, and capillary 
 
 227. What is the rule of resistance by air and water ? 
 
 228. How with a cannon ball 1 
 
 229. How does form effect motion in fluids ^ 
 
 230. Name the agents of force, and their mode of action. 
 
moving forces. 
 
 95 
 
 attraction; but these have hitherto produced motion only 
 on a Jirm ed scale. 
 
 HUMAN LABOUR. 
 
 288. The muscular energy of men forms the most insuf- 
 ficient, or the weakest, of all the prime moving forces. 
 Human labour is very limited in its compass, and is the 
 least to be depended on for regularity. The power exerted 
 by one man is comparatively small, and it is both inconve- 
 nient and expensive to cause a large number of individuals 
 to unite their powers in a continued or concerted effort. 
 
 289. The power of a man to produce motion in a ma- 
 chine, weight, or resisting body, varies according to the 
 mode in which he applies his force, and the number of 
 muscles which are brought into action. In the operation 
 of turning a winch or handle of a wheel, as for example 
 that of the crane, figure 63, a man’s power changes in 
 every part of the circle which the handle describes. His 
 power is greatest when he pulls the handle upward from 
 the height of his knees, next greatest when he pushes it 
 down on the opposite side, though here the power cannot 
 exceed the weight of his body, and is therefore less than 
 can be exerted in pulling upward. His power is weakest 
 when at the top and bottom of the circle, where the handle 
 is pushed or drawn almost horizontally. 
 
 290. A man can exert the greatest active strength when 
 he is at rest in his person (that is, not walking), and when 
 he pulls or lifts a body upwards from his feet, because the 
 strong muscles of his back, as well as those of his arms 
 and legs, are then brought advantageously into action, and 
 the bones are favourably situated, by the fulcra of the levers 
 being near to the resistance. Hence, the action of rowing, 
 or pulling oars, is one of the most advantageous modes of 
 muscular exertion. In that operation, the whole frame 
 exerts itself in the most favourable manner ; and no method 
 which has been devised for propelling boats by the labour 
 of men, has hitherto superseded it. 
 
 231. What of muscular power 7 
 
 232. How does this vary as in turning a crank 7 
 
 233. How may the greatest strength be exerted 7 
 
HUMAN LABOUR. 
 
 9f> 
 
 291. It is usual, in estimating the amount of power which 
 can be exerted by animals, to reckon it by the weight 
 which the animal can lift in a given length of time to a 
 given height. By this standard, it is computed that a man 
 of ordinary strength ran raise a weight of 10 pounds to the 
 height of 10 feet once in a second, and continue this labour 
 for 10 hours in the day. This is supposing him to use his 
 force under common mechanical advantages, and without 
 any deduction from friction. 
 
 292. All such estimates as this, however, are exceedingly 
 illusive. The ability for exercising power varies in different 
 countries, and depends greatly on exercise and diet. There- 
 fore, no practically useful calculations can be made regard- 
 ing it. 
 
 293. Human strength, as has been said, can be exerted 
 with greatest effect in lifting from the ground, and pulling 
 as with an oar. But this species of action produces ex- 
 haustion; and hence the advantage is neutralized by a 
 certain disadvantage. The way in which the greatest effect 
 can be produced by human labour, with a moderate degree 
 of fatigue, is simply to allow the weight or gravity of the 
 person to work. For example, let a man walk up a ladder 
 to a certain height, and then stepping into a bucket which 
 is attached to a cord and pulley, permit himself to sink 
 with the bucket to the ground, drawing up a load at the 
 other end of the cord. Whatever be his weight, he will 
 be able to raise at each descent a load nearly as great; and 
 therefore, by such a plan, would, in the course of a day, 
 raise a great deal more weight of material to the top of a 
 house, than by the common process of carrying up a mass 
 of matter in his hands or on his shoulders. 
 
 294. In giving effect to the gravity of the person, no 
 exertion is used ; and the only source of fatigue is that of 
 walking up an inclined plane to obtain a due elevation. 
 According to the principle defined in paragraph 135, the 
 expenditure of exertion in ascending inclined planes, is not 
 according to the degree of inclination, but according to the 
 
 234. What estimate has been made of animal power t 
 
 235. What illustrations are cited 7 
 
HUMAN LABOUR. 
 
 97 
 
 elevation reached; this is agreeable to the rule of mecha- 
 nics mentioned in paragraph 17, namely, that a small force 
 exerted for a long period of time is equivalent to a great 
 force exerted lor a short period of time. Thus, nearly the 
 same degree of animal fatigue is incurred by reaching the 
 same elevation in the same time, whatever be the ineliu a- 
 tion of the ascent. 
 
 295. In walking on a perfectly horizontal plane, the 
 gravity of the person, in ordinary cases, is not felt; for the 
 fabric of the body is so nicely balanced, and the weight so 
 generally borne by the different parts that we are hardly 
 conscious of the exertion. When we try to ascend a hill, 
 we begin to feel that our gravity retards, and consequently 
 fatigues us, for we are pulling against the force of terres- 
 trial attraction. But when we commence descending a hill, 
 we feel that we are greatly assisted by our gravity — that is, 
 we are allowing attraction to pull us. We are also assisted 
 in descending, by an acquired momentum in our person. 
 
 Figure 81. 29b. The mo- 
 
 ving power given 
 to machinery by 
 the mere gravity 
 of the person, is 
 seldom used ex- 
 cept in the case 
 of involuntary la- 
 bour at the tread- 
 mill. A tread-rnill 
 is a large broad wheel with steps all round on its circumfer- 
 ence, and on which steps men are compelled to ascend, hold- 
 ing on by a fixed bar or rail in front. The weight of the 
 men turns the wheel, which, by turning an axle, gives mo 
 tion, if necessary, to certain machinery. The tread-mill 
 thus forms a revolving or endless stair. Figure 81 repre- 
 sents one of these machines in operation. A is the axle, 
 S are the steps, and P is a fixed platform in front of them. 
 
 297. It is evidently disadvantageous to employ human 
 
 236. What of ascending and descending a hill ? 
 
 237. Explain the tread mill. 
 
98 
 
 HORSES POWER DRAUGHT. 
 
 labour as a moving power, except in cases in which the 
 force required is so small as not to require further aid, or 
 where skill as well as muscular energy is necessary. The 
 human being has been designed for executing higher 
 duties than those which can be adequately performed by 
 the lower animals, and by the agency of inanimate forces. 
 
 298. The power 
 of the ass is some- 
 times employed as 
 a moving force, in 
 operations not re- 
 quiring great la- 
 bour, and on a 
 principle similar to 
 that of the tread- 
 mill. At Caris- 
 brook Castle, in 
 the Isle of Wight, 
 an ass was lately 
 employed to move a machine acting like a windlass for 
 drawing water from an exceedingly deep well. The animal 
 acted entirely by giving effect to its weight, as represented 
 in figure 82 
 
 horse’s POWER DRAUGHT. 
 
 299. Horses and oxen are used, in all countries where 
 they exist, as agents of force. Horses are more valuable 
 for this purpose than oxen, because they are generally more 
 tractable, and otherwise better suited for the labour. Oxen 
 are used only for draught. 
 
 300 A horse employs two forces in drawing — the force 
 of his muscular energy exerted against the resistance of his 
 hind legs and feet, and the force of his weight or gravity. 
 Power of draught is estimated according to the constitu- 
 tional strength, height of breast from the hind feet, and 
 weight of the animal. 
 
 301. The force of a horse diminishes as his speed 
 
 233". What does the last diagram show ? 
 
 239. VVliat of oxen and horses and their forces ? 
 
horse’s POWER — DRAUGHT. 
 
 99 
 
 increases beyond a certain limit. If the load that he can 
 pull, when moving at the rate of two miles in an hour, is 
 represented by 109, that at three miles in an hour will be 
 81 — at f>ur miles in an hour, G4 — at five miles in an hour, 
 49 — and at six miles in an hour, 36.* In this way the 
 draught of a horse continues to diminish, till he attains his 
 greatest speed, when he can barely carry his own weight. 
 
 302. A horse exerts his power most advantageously, when 
 walking at the rate of about four miles in an hour. This 
 advantageous rate of speed, however, does not apply in the 
 case of short efforts. In these, a rapid motion, to get at 
 once over the difficulty, is most advantageous for the mus- 
 cular energy. 
 
 303. There are various estimates of a horse’s power, but 
 that of James Watt is generally adopted as the standard. 
 The measure of a horse’s power, according to Mr. Watt, is, 
 that he can raise a weight of 33,090 pounds (for instance, 
 drawing it over a pulley) to a height of one foot in a minute. 
 
 394. In comparing the strength of horses with that of 
 men, it is estimated that the force of one horse is equal to 
 that of five men. But this estimate is liable to certain im- 
 portant exceptions. Much depends on the manner in which 
 the exertion takes place. 
 
 305. Any body moving forward on a smooth horizontal 
 plane, can be drawn with the least possible force, when the 
 line of draught is straight in a horizontal line from the power 
 to the point of resistance. But a horse, in drawing, can use his 
 weight and muscular energy with greatest advantage when 
 the line of draught inclines from the load upward to his 
 breast. Thus, the convenience of the horse must always 
 be consulted in practical operations. 
 
 396. A horse, also, can pull a wheeled carriage with 
 greater advantage when the wheels are large than when 
 they are small, because large wheels get most easily over 
 
 * These proportions are given by Professor Leslie, and are confirmed 
 by the observations of other experimental mechanics. 
 
 240. How is the force of a horse calculated ? 
 
 241. Mr. Watt’s estimate. 
 
 242. How does it compare with the power of man 1 
 
 243. How should the line of draught be regulated ? 
 
100 
 
 horse’s POWER DRAUGHT. 
 
 Figure 83. 
 
 obstacles lying before them. This is an evident truth, but 
 it can be proved by an appeal to the principle of the lever. 
 
 307. The operation of drawing a wheeled vehicle, pre- 
 sents an example of lever action of a peculiar kind. The 
 load of the vehicle, or the weight , presses on the nave or 
 axle of the wheel, and the direction of its action thence 
 passes down in a straight line to the plane on which the 
 vehicle rests. The direction of the power is a line from 
 the moving agent to the axle. If the plane be perfectly 
 smooth, the fulcrum is identified with the point on which 
 the weight presses on the ground. If any obstacle be 
 placed before the wheel, then, that obstacle, at the instant 
 of contact, becomes the fulcrum 
 
 308. Figure 83 represents a wheel, with an obstacle, 
 which we may suppose to be a 
 stone, lying before it. The line 
 of draught P A is the direction 
 of the power. A horse may be 
 
 ■P supposed to be pulling at P. The 
 line A W is the direction of the 
 weight. F is the obstacle, or 
 fulcrum, upon which the power 
 has to act. A line from A to F may represent the lever, 
 having the fulcrum F at one extremity, and the power and 
 weight applied to the other extremity A. The apparatus 
 is thus a lever of oblique action with a single arm. Accord- 
 ing to the rules laid down for estimating the power of bent 
 levers, the arm of power is an ideal line drawn at right 
 angles from the line A P to F, and the arm of weight an 
 ideal line drawn at right angles from the line A W to F. 
 The mechanical advantage is calculated from these two 
 ideal lines. By increasing the diameter of the wheel, 
 these ideal lines increase, but that of the power increases 
 in the greatest proportion, and hence the advantage of 
 increasing the diameter of wheels. 
 
 309. It is customary to place small wheels before large 
 ones in four-wheeled carriages. This is done only for 
 the sake of convenience in turning the vehicle ; if the front 
 
 244. What of wheels and their motion J 
 
 245. Explain the diagram. 
 
HORSu’s POWER DRAUGHT. 
 
 JOi 
 
 wheels were made as large as the hind ones, the carriage 
 would be more easily drawn. 
 
 310. In yoking several horses, one before the other, to 
 ploughs or wheeled carnages, it is of importance to cause 
 the line of draught of all the horses to proceed in a straight 
 linetothepointof resistance, or as nearly so as is convenient. 
 The resistance of the plough is in the sock or cutting part 
 in the earth, and the resistance of the load in wheeled car- 
 riages, is at the axles. The distance of the animals from 
 the machine they are drawing, is of little consequence, 
 provided each horse is able to exert his force directly in a 
 line to the resistance. 
 
 311. Horses draw with best effect when they aie yoked 
 singly or abreast. In yoking them one before the other, a 
 portion of their force is generally expended uselessly, if not 
 mischievously, in hampering each other. When a horse 
 draws a four-wheeled carriage, the line of his draught should 
 go to a point between the two axles, and come over the 
 front axle. The same rule holds with two or more horses 
 in four-wheeled vehicles. 
 
 312. Wheels have least friction where they are narrow in 
 the rim, but this is supposing the road to be hard and 
 smooth. In cases of great weights, and when the roads are 
 not very smooth or hard, broad wheels are the best for both 
 safety and draught. Wheels which are perfectly straight 
 or upright are pulled with less exertion than wheels which 
 are of a dished form — that is, with the spokes sloping to 
 the rim ; but the dished form is of use in widening the 
 base and preventing overturning; it is also particularly 
 useful where the road is inclined to one side, as the spokes 
 of the lower wheel, which then support more than half the 
 weight, are more nearly in a vertical direction, and there- 
 fore resist the pressure with the greatest effect ; so that 
 when the load is thus increased upon them, their resisting 
 power is at the same time increased. 
 
 313. When the load is suspended on springs, the shocks 
 
 246. Why the difference in the wheels of carriages ? 
 
 247. What of the point of resistance in draught ? 
 
 248. What of more horses than one 1 
 
 249. What of a variety in wheels t 
 
102 
 
 DRAUGHT OF WHEELED CARRIAGES: 
 
 caused by friction in movement are lessened — that is, the 
 force of the concussions is spent upon the elasticity of the 
 spring, a circumstance of great convenience to passengers 
 in carriages. The elasticity, also, preserves equability of 
 weight to the horse. At every jolt over a protuberance, 
 without springs, the load receives a momentum in descend- 
 ing, which on being checked gives a shock to the animal 
 in the shafts; whereas, in using springs, the weight has 
 always a comparatively equal pressure. 
 
 314. Horses communicate moving power to machinery, 
 by being yoked to a horizontally turning beam or wheel, 
 and walking in a circle. The motion of the beam or wheel, 
 by acting on a pinion and shaft, moves the machinery. Many 
 mills are turned in this manner. To give full advantage to 
 the capacity of the horse, the circle should not be less than 
 from thirty to forty feet in diameter. 
 
 Figure 84. 
 
 315. Figure 84 represents the action of horse power upon 
 a mill. U is an upright axle working on pivots, from which 
 axle a beam B B is projected, and into which two horses 
 H H are yoked. W is a horizontally moving wheel on the 
 axle, which wheel turns a trundle T fixed to the shaft S. 
 The turning of the shaft moves the machinery. 
 
 316. The same principle applies with respect to the em- 
 ployment of horses and other animals, as agents of force, as 
 
 250. Of what advantage are springs ? 
 
 251. How do horses best move in machinery 7 
 
 252. Explain the diagram. 
 
WATER POWER. 
 
 103 
 
 that which applies to human labour (paragraph 297.) An 
 animal is only employed advantageously when he is caused 
 to do work which could not be as conveniently executed 
 by inanimate forces. In all cases in which inanimate forces 
 can be conveniently substituted for animal power, the ap- 
 plication of the animal is not legitimate, because only its 
 weight and muscular energy are brought into operation, 
 and its sagacity, which is frequently a valuable part of it, 
 lies unemployed. 
 
 WATER POWER. 
 
 317. Water acts as a first mover by the force of its gravity 
 or weight ; and also in some cases by its momentum or im- 
 pulsive power It is applied by causing it to fall or flow 
 upon the outer part of a wheel, which turns with the force. 
 
 318. Water power, if to be had in a sufficient quantity, 
 is preferred to all other powers, in consequence of its sim- 
 plicity of action, extraordinary cheapness, and steadiness. 
 
 319. The mode of applying water power to a wheel de- 
 pends on the extent of the fall, or the height of the stream 
 at the point where it can be properly applied. It is of 
 importance to have as great an extent of fall as possible ; 
 but at the same time, a certain declivity must be left below 
 the mill, in order to allow the w r ater to flow freely away, 
 and not obstruct the w r heel in its motion. 
 
 320. Two chief kinds of water-wheels are used according 
 to the extent of the fall, and the nature of the stream. 
 When the water cannot be made to approach the wheel, 
 higher than a point opposite the middle of the wheel, a 
 breast wheel is used. The w ater is brought by an artificial 
 channel and permitted to flow or fall into buckets fixed in 
 the outer circumference of the wheel. The weight of the 
 w'ater in the buckets, presses down the wheel and causes it 
 to turn. When the buckets come to the bottom in revolving, 
 they let the water flow from them, and go up empty on the 
 other side, ready to be again filled. 
 
 253. What is said of animal agency in machinery ? 
 
 254. What of water power and its advantages ? 
 
 255. How is it best applied ? 
 
 256. Describe both kinds of water-wheels. 
 
104 
 
 WATER POWER. 
 
 321. Figure 85 represents the action of a breast water- 
 
 koned the height of the fall. The axle of the wheel in this 
 case turns the machinery ; but sometimes the wheel has 
 teeth round its circumference, which, working on a pinion, 
 turns the machinery. 
 
 322. When the fall is considerable, or when the water can 
 be made to approach by a channel on a level with the top of 
 the wheel, an overshot wheel is used. The water is allowed 
 to fall into the buckets at the top, so as to act much 
 more advantageously than if it fell at a lower level. It is 
 seldom that streams can be conveniently brought to operate 
 in this advantageous manner. 
 
 323. Water power, acting either by breast or overshot 
 wheels, is a much more effective and steady agent of mov- 
 ing force than wind. Windmills are used only in cases in 
 which perfect regularity and constancy of motion are not re- 
 quired, and where water cannot be obtained at a sufficient 
 height to form a fall. 
 
 STEAM POWER. 
 
 324. Water boils at 212 degrees of Fahrenheit’s ther- 
 mometer, under the common atmospheric pressure; and the 
 application of fire, after it reaches the boiling point, causes 
 it to fl v off in the form of vapour or steam.* 
 
 325. A cubic inch of water produces almost exactly a 
 cubic foot of steam, or 1728 cubic inches. In its expan- 
 sion therefore it exerts enormous force, and this circum- 
 stance has rendered it valuable as a source of pow'er. 
 
 * See Laws of Matter and Motion, in which the subject of heat 
 in application to water is fully treated of. 
 
 Figure 85. 
 
 wheel. W is the water 
 flowing from a channel L 
 into the buckets B B, 
 which are supposed to be 
 seen through the sides of 
 the rim ; these buckets 
 are emptied on coming 
 down to F, and the water 
 flow's aw'ay in the channel 
 C. F rom W, to F is rec- 
 
 257. Explain the diagram. 
 
 258. What of wind as au agent of force ? 
 
STEAM POWER. 
 
 105 
 
 326. Steam is applied to machinery by means of a boiler 
 and an apparatus called the steam-engine. Steam-engines 
 are of different constructions, and improvements and simpli- 
 fications are continually taking place in their character and 
 mode of working. The power exerted by steam-engines, 
 is estimated according to the horse powers to which they 
 are equal, and which there are certain rules for calculating. 
 
 327. There are two distinct kinds of engines, namely, 
 high-pressure or non-condensing, and low-pressure or con- 
 densing. The high-pressure engine is the most simple 
 in its construction. The steam, generated in a boiler, 
 rushes through a tube to the cylinder, which is a close 
 round vessel like a barrel. It enters the cylinder at two 
 openings, one at the bottom and the other at the top. 
 The steam which enters at the lower opening drives up a 
 round object or plug, fitting nicely to the cylinder, and 
 called the piston, to the top, whence it is driven down 
 again to the bottom by the steam which enters at the 
 upper opening ; the steam used in both cases being with- 
 drawn to allow the action. An external rod from the pis- 
 ton, thus driven up and down, passes out of the cylinder 
 at a small orifice at the top, and affects the beam, which, 
 turning a crank, moves the machinery. In this kind of 
 engine, the steam, on performing its office of depressing and 
 raising the piston, is allowed to escape into the atmosphere; 
 and the engine is called high-pressure, because, steam of a 
 high degree of pressure has to be employed to counteract 
 the pressure of the atmosphere on the escaping steam. 
 
 328. The low-pressure or condensing engine is supplied 
 with steam in much the same manner, but the mode of 
 withdrawing and destroying the used steam from the cylin- 
 der is totally different, As soon as the steam, which rushes 
 in at the lower opening of the cylinder, has driven the pis- 
 ton upwards, it is instantaneously abstracted or withdrawn 
 into a separate vessel below, called the condenser, where it. 
 is condensed by a squirt of cold water, and runs off into a 
 cistern ; from which cistern the water in a warm state is 
 
 259. What is said of steam ? 
 
 260. What principle of steam is the source of power 7 
 
 261. By whnt means is it applied, and how calculated 7 
 
 262. Describe a high-preseure engine, and why so named ? 
 
106 
 
 STEAM POWER. 
 
 pumped into the boiler to make new steam. The same 
 process takes place with the steam which drives the piston 
 downwards. The abstraction of the steam into the con- 
 denser is effected by an air-pump (wrought by the engine), 
 which, at the proper instant of time, pumps out the water 
 produced by the condensed steam, and that of the condens- 
 ing jet, and also any air that may collect, and forms a par- 
 tial vacuum in the condenser. As this vacuum presents 
 no obstacle to the action of the piston, in other words, as 
 the steam is not opposed by the atmosphere in making its 
 escape from the cylinder, the steam requires to be of com- 
 paratively small force — much smaller than if the pressure 
 of the atmosphere had to be overcome ; it is therefore called 
 a low-pressure engine. 
 
 329. The low-pressure or condensing engine, just no- 
 ticed, is also called a double-acting engine, because Us 
 piston is driven both up and down by steam. There are 
 low-pressure engines called single-acting engines. These 
 have the piston acted upon by steam only in the down 
 stroke, the up stroke or return of the piston, being pro- 
 duced by the action of a counterweight on the farther 
 extremity of the beam. 
 
 330. Figure 86 represents a rudimental outline of the 
 
 Figure 86. 
 
STEAM POWER. 
 
 107 
 
 action of steam power, whether in high or low-pressure en- 
 gines. A is the pipe by which the steam is conducted 
 from the boiler to the cylinder E E, by means of the pipe 
 B into the cylinder E E at the upper opening C and the 
 lower opening D. F is the piston with a rod G going up to 
 the end of the beam H. This beam moves up and down 
 on a central axis I. From the extremity of the beam at L, 
 a shaft M goes down to the crank on the pulley N, which 
 it turns. From N a belt O is carried to the pulley R, and 
 a shaft from this pulley moves the machinery. S is a fly 
 wheel working close beside the crank pulley. The pipe T 
 is the path for the escape of the steam from the cylinder 
 after performing its office. At the different openings in the 
 communication pipes, there are little doors or valves, which 
 are opened and shut as is required to admit or allow the 
 escape of the steam ; but these valves, and also many minor 
 parts of the mechanism, are for the sake of clearness not 
 marked in the figure, and the steam engine should be seen in 
 actual operation, if a perfect idea of the apparatus is desired. 
 
 33 L. Steam power, when properly organized, possesses 
 the quality of great steadiness of action, in which it almost 
 equals water power. It is therefore adapted for turning all 
 kinds of machinery, and may be employed in every imagi- 
 nable situation where fuel and water exist. The most won- 
 derful of its achievements is the propulsion of vessels at 
 sea, and vehicles on railways upon land. 
 
 332. The steam power at present employed in Great 
 Britain and Ireland, is equal to about 8,000,000 of men's 
 power, or 1,600,0110 horse power. It is calculated that a 
 horse requires eight times the quantity of soil for producing 
 food that a human being does ; if, therefore, horse power 
 were made to supersede steam power, additional food for 
 1,600,000 horses would require to be raised, which would 
 be equal to the food of 12,800,000 men. [As the amount 
 of steam power employed in America is more than ten times 
 that in Great Britain and Ireland, these calculations must all 
 be increased tenfold, if we would approximate the import- 
 ance of this agent in our country.] 
 
 333. It is in consequence of the improved mechanical 
 
 266. To what useful purposes is steam applied ? 
 
 267. What calculations are made ? 
 
108 
 
 STEAM POWER. 
 
 arrangements, and employment of inanimate forces in Great 
 Britain, that that comparatively small country is enabled 
 to manufacture goods cheaper, and with greater profit, than 
 can be done by the largest and most populous countries 
 in which mechanism is imperfect, and labour performed 
 exclusively by living agents. 
 
 334. The profits of manufacture so produced, spread 
 their beneficial influence over the whole mass of society, 
 every one being less or more benefited. Thus, almost all 
 the luxuries and comforts of life, all the refinements of social 
 existence, may be traced to the use of tools and machinery. 
 Machinery is the result of mechanical skill, and mechanical 
 skill is the result of experience and a long course of inves- 
 tigation into the working of principles in Nature, which 
 are hidden from the inattentive observer. Much of the 
 present mechanical improvement is also owing to the pres- 
 sure of necessities, or wants, which have always a tendency 
 to stimulate the dormant powers of man. What are to 
 be the ultimate limits and advantages of mechanical dis- 
 coveries, no one can foresee. The investigation of natural 
 forces is yet far from being finished. Every day discloses 
 some new scientific truth, which is forthw ith impressed into 
 the service of mankind, and tends to diminish the sum of 
 human drudgery and suffering. In this manner, therefore, 
 are we usefully taught, that the study of .Nature forms a 
 never-failing source of intellectual enjoyment, and that 
 “ Knowledge is Power.” 
 
 The subject of the next Treatise is Hydrostatics, or 
 the Laws of Fluids. 
 
 26S. Name some of the advantages derived from it. 
 
 269. Are not still further improvements probable ? 
 
 270. To what source are we to look for their discovery 1 
 
 THE END. 
 
ELEM ENTS 
 
 OF 
 
 NATURAL PHILOSOPHY. 
 
 PART III. 
 
 HYDROSTATICS, HYDRAULICS, 
 
 AND 
 
 PNEUMATICS. 
 
 CHAMBERS’ EDUCATIONAL COURSE. 
 
INTRODUCTORY OBSERVATIONS 
 
 BT 
 
 THE AMERICAN EDITOR. 
 
 With this third book of Natural Philosophy, the teacher 
 will be able to conduct his pupils to an easy acquaintance 
 with the most intricate ar^l difficult features in the whole sci- 
 ence, the two former books having removed every obstacle in 
 the way of the learner. The laws of matter and motion, and 
 the elements of practical machinery, and moving forces with 
 reference to solids, having been made plain, the laws of fluids 
 will much more readily be understood than if previously 
 studied. 
 
 Hydrostatics, or the science of fluids at rest; Hydraulics, or 
 the science of fluids in motion; and Pneumatics, or the science 
 of air and gaseous fluids, are the successive topics of this 
 volume. Their kindred character and striking analogies ren- 
 der them appropriate subjects to be considered together, while 
 their great practical importance in domestic economy and the 
 business of life, would seem to commend them to young 
 people, as having special claims upon their attention. 
 
 The catechetical questions on every page will be found to 
 be thoroughly analytical of the entire volume, and the answer 
 should be required in the words of the text at first, and after- 
 wards expressed in other terms, and with other illustrations 
 than those found in the book. For this purpose, the teacher 
 should, in his discretion, vary the questions and call for other 
 examples. 
 
 A class thus instructed will be able to exhibit proofs of 
 
 3 
 
4 
 
 INTRODUCTORY OBSERVATIONS. 
 
 their actual knowledge in these departments, by once going 
 through this book, which at an exhibition would astonish 
 those who should witness it, without being acquainted with 
 the facilities which this volume furnishes to the learn;r by its 
 simplicity and skilful adaptation to the juvenile mind. 
 
 With such views, it is earnestly recommended to the prac- 
 tical teachers of our common schools, by 
 
 The American Editor. 
 
PREFACE. 
 
 The present Treatise, comprehending Hydrostatics and 
 Hydraulics (or, conjointly, Hydrodynamics), also Pneuma- 
 tics, forms the third department in Natural Philosophy. 
 
 The Pupil, having been made acquainted with the Laws of 
 Matter and Motion and with Mechanics, is now introduced to 
 a knowledge of the Laws of Fluids, both as respects liquid 
 and aeriform bodies. By uniting Hydrostatics, Hydraulics, 
 and Pneumatics, in one treatise, the whole subject of fluids is 
 at once brought before the mind, and is thereby calculated to 
 make a more forcible and agreeable impression, than if, as 
 according to custom, it were divided into separate books. 
 
 In this, as in the preceding treatises, very great pains have 
 been taken to 'render the language simple and intelligible, so 
 that the learner may find at least no technical difficulty in his 
 path. The sentences and paragraphs are likewise written and 
 arranged in such a manner as to form a progressive series of 
 distinct propositions, relieved from extraneous verbiage, and 
 suitable alike for the study of the Pupil, and as the subject 
 of a searching examination by the Master. 
 

 
 
 
 
 
 
 
 
 
 
 
 . t 
 
 
 
 : V : > - : 
 
 • • . > 
 
 
 
 _ 
 
 ' 
 
 ■ 
 
 
 
 ■ 
 
 
 
 
 
 
 
CONTENTS. 
 
 Page 
 
 H tdrostatics and Hydraulics 9 
 
 General Definitions 9 
 
 Hydrostatics 11 
 
 Pressure Equal in all Directions 12 
 
 Pressure in Proportion to Height 13 
 
 Equal Levelness of Surface 23 
 
 Levels 25 
 
 Specific Gravity 28 
 
 Fluid Support 30 
 
 Hydrometers 38 
 
 Hydraulics 40 
 
 Water, a Mechanical Agent 40 
 
 Aqueducts — Fountains 43 
 
 Springs 45 
 
 Friction between Fluids and Solids 46 
 
 Action of Water in Rivers 49 
 
 Waves 50 
 
 • Alteration of Temperature 51 
 
 Pneumatics 53 
 
 General Definitions 53 
 
 The Atmosphere 57 
 
 Laws of Air 58 
 
 Pressure of Air 59 
 
 The Air-pump 63 
 
 Pressure of Air on Solids and Liquids 66 
 
 7 
 
CONTEXTS. 
 
 8 
 
 Pneumatics. Page 
 
 Pressure on Mercury — the Barometer 68 
 
 Pressure on Water — Pumps 72 
 
 Syphons 74 
 
 Syphon Springs 76 
 
 Boilding Point determined by Atmospheric Influence 78 
 
 Steam 80 
 
 Latent Heat 81 
 
 Alteration of Temperature in Air 85 
 
 Air in Motion — Winds 88 
 
 Sea and Land Breezes 90 
 
 Ventilation ; 92 
 
 The Diving-bell 100 
 
 Buoyant Property of Aeriform Fluids 102 
 
 Balloons 104 
 
NATURAL PHILOSOPHY 
 
 HYDROSTATICS AND HYDRAULICS. 
 
 GENERAL DEFINITIONS. 
 
 1 . Matter exists in three principal forms — solid, liquid, 
 and gaseous or aeriform. These forms respectively, and the 
 various modifications of them, are the immediate result of 
 certain principles of attraction and repulsion operating on 
 the atoms or particles of which matter is composed.* 
 
 2. The solid, liquid, and aeriform varieties of matter, 
 assume a position on our globe corresponding to their 
 heaviness or density in a given volume — the solid sinks 
 lowest, and composes the chief mass of the earth ; above 
 the solid lies the liquid variety, in the form of the ocean, 
 rivers, and lakes ; and above all is the atmosphere, con- 
 sisting of an expanse of aeriform matter, which wraps the 
 whole earth round to an elevation of from forty-five to 
 fifty miles above the highest mountains. In this great 
 ocean of air, loaded less or more with particles of mois- 
 ture from the liquids beneath, we live, breathe, and move, 
 and plants grow and receive an appropriate nourishment. 
 
 3. Though differing both in substance and appearance, 
 the liquid and aeriform varieties of matter resemble each 
 
 * The principles of attraction and repulsion are explained in the 
 Laws of Matter and Motion, from paragraph 34 to i24, and must 
 be already familiar to the pupil. As forming the basis of physical 
 science, they ought to be thoroughly understood. 
 
 1 In how many forms does matter exist? 
 
 2. How are they arranged in the globe ? 
 
 9 
 
 V 
 
10 
 
 GENERAL DEFINITIONS. 
 
 other in many of their properties and tendencies, and con- 
 stitute the class of bodies termed fluids. 
 
 4. Fluids signify bodies which will flow, or whose com- 
 ponent particles are easily moved among each other. 
 
 5. Some fluids are so thick and viscous, or sticky, that 
 they can scarcely flow, as tar, honey, and some metais in 
 a state of fusion ; others flow with ease, as water and dis- 
 tilled spirits ; while others are so light and volatile, as to 
 be impalpable to the touch and invisible to the eye, as pure 
 atmospheric air and various gases. 
 
 6. It is common to divide fluids into two kinds — non- 
 elastic fluids and elastic fluids ; that is, fluids which can- 
 not be compressed into a smaller bulk, and those which 
 are susceptible of compression. The non-elastic fluids are 
 Water and all other varieties of liquid bodies ; but recent 
 experiments prove that the term is not strictly applicable 
 to them. It has been found that water may be compressed 
 in a confined vessel, to a small extent, by means of a very 
 great pressure, and it is certain that water at a considera- 
 ble depth in the ocean is more dense or compressed than 
 at the surface ; water, consequently, is an elastic substance ; 
 but as it can be compressed only with very great difficulty, 
 the term non-elastic fluid is not altogether inappropriate. 
 
 7. Atmospheric air and all gases are elastic. They 
 can, with little difficulty, be compressed into a much small- 
 er volume than they ordinarily ’possess ; and when the 
 pressure is removed, they return to their original bulk. 
 Some gases may be compressed to such an extent as to as- 
 sume the form of liquids and solids; in other words, from 
 the condition of being perfectly invisible to the eye, they 
 can be made to appear as a piece of solid matter, which 
 may be touched and handled. 
 
 8. In treating the subject of fluids, it is convenient to 
 refer in the first place to those which are of the liquid 
 form, and afterwards to those which are elastic or aeri- 
 form. 
 
 3. Define fluids, and their variety. 
 
 4. How are fluids divided ? and what of compressibility ? 
 
 5. Name the peculiarities of elastic fluids. 
 
HYDROSTATICS. 1 1 
 
 9. Pure water, at an ordinary temperature, furnishes the 
 most suitable example of liquid bodies. 
 
 10. Water also gives the name of the department of 
 science which includes the laws of liquids. Thus, Hy- 
 drostatics, from two Greek words signifying ivater and 
 to s add , treats of the weight, pressure, and equilibrium of 
 liquids in a state of rest; and Hydraulics, from two 
 Greek words signifying ira'er and a pipe, treats of liquids 
 in motion, and the artificial means of conducting liquids in 
 pipes, or raising them by pumps. 
 
 HYDROSTATICS. 
 
 11. In ancient times water was believed to be an ele- 
 ment or simple substance in nature. It is now ascertained 
 by experiment that water is not an elementary body, but 
 is a substance composed chiefly of two gases in a state of 
 chemical union, and into these gases it can be resolved by 
 an artificial process. The investigation of this subject be- 
 longs to Chemistry. 
 
 12. As a liquid, water consists of exceedingly small 
 particles or atoms of matter in mechanical combination. 
 
 Id. The exact nature and form of the atoms compos- 
 ing water are not satisfactorily known, in consequence of 
 their exceeding smallness. They may be compared to 
 very small particles of sand, cohering slightly, and easily 
 slipping or sliding over each oth r. Whatever may be 
 the nature and form of these exquisitely fine atoms, it is 
 certain that they can adhere firmly together so as to as- 
 sume the form of a solid, as in the case of ice ; and be 
 made to separate from each other, and disperse through 
 the thinner fluid of the atmosphere, in the forms of steam, 
 clouds, or mist. 
 
 14. Thus, IMPERFECT COHESION OF ATOMS OR PARTICLES 
 is a property common to all fluids. 
 
 6. Define Hydrostatics and Hydraulics. 
 
 7. What of the composition of water? 
 
 8. What of the atoms of water and their changes of form f 
 
12 
 
 HYDROSTATICS. 
 
 15. The atoms composing water, being in closer union 
 than those of air, are observable as a mass, and palpable to 
 the touch. When the hand is dipped into them, and then 
 withdrawn, a certain quantity of the atoms is brought 
 away on the surface of the skin ; and this adhesion of the 
 particles of water (caused by attraction of cohesion) is 
 what we in ordinary language call wetness. Certain sub- 
 stances, as is well known, absorb water to a great extent ; 
 in such cases, the minute particles of the water merely pene- 
 trate and fill up the crevices in the substance. 
 
 PRESSURE EQUAL IN ALL DIRECTIONS. 
 
 15. Solid bodies, as a stone, or piece of metal, or wood, 
 have a natural tendency to press only in one direction, that 
 is downwards, or in the direction of the earth’s centre, in 
 obedience to the law of terrestrial attraction. 
 
 17. Water has a similar natural tendency to press down- 
 wards, and from the same cause ; as for example, when a 
 jug of water is spilled, the water is seen to fall in a stream 
 to the ground. 
 
 18. Water, however, is governed by a law of pressure, 
 independently of this general law of gravitation. This 
 peculiar or independent law consists of the tendency in 
 the particles of any mass of water to press equally in all 
 directions. 
 
 19. Pressure equally in all directions may be con- 
 sidered as the first or great leading law in reference to 
 water, and generally all fluids, liquid and gaseous. 
 
 20. The pressure equally in all directions is a result of 
 the exceeding smallness of the individual particles, and of 
 the perfect ease with which they glide over or amongst 
 each other. 
 
 , 21. l'o t exemplify equal pressure, fill a leathern bag 
 
 witk ’ 1 water/' ani then s£& miY’thb rfibhrth of the bag so 
 
 .abiiifr ii;; a, nomn.oo 
 
 . Give an example of their cohesion, ; 
 10. How is gravitaiion,y\o,cfi^pd|jp ) w^tej l 
 
 , is g r a v a a. .orL 6 p , wa,te f ? . H , rl 
 
 H. What is ihe law.ojgjr^s^^p^Il fJuids.f , . ,-rj - 
 
 jVgfim l ,m . a 
 
 13. Explain the example cited. 
 
PRESSURE IN PROPORTION TO HEIGHT. 13 
 
 closely that none of the water can escape. Now, squeeze 
 or press upon the bag so as almost to make it burst. The 
 pressure so applied does not merely act upon the water 
 immediately under the point of pressure, but acts equally 
 upon every particle of water in the mass — the particles at 
 the centre being as much pressed upon as those at the out- 
 side ; and it will be observed that the water will squirt out 
 with equal impetuosity at whatever part you make a hole 
 in the surface. 
 
 23. In this, as in all similar cases, there is a transmis- 
 sion of pressure throughout the mass. Each particle 
 presses on those next it ; and so, by the force communicat- 
 ing from particle to particle, the whole are equally affected. 
 
 23. In the case of water lying at repose in an open ves- 
 sel, the tendency to press equally in all directions is not 
 observed to act upward, because the gravity of the mass 
 k eps the water down ; but on pressing upon the surface 
 of the liquid, we observe that it rises against the compres- 
 sion, or tries to escape in any way it can. To take another 
 example — if we plunge our hand into a vessel of water, 
 we displace so much liquid, and cause it to rise higher up 
 the sides of the vessel. In this case, the water is observed 
 to rise without any reluctance ; it as readily presses up- 
 ward as downward. 
 
 PRESSURE IN PROPORTION TO HEIGHT. 
 
 24. Although it is a property in fluids to press equally 
 in all directions, the degree of intensity of pressure in any 
 mass of fluid is estimated by the vertical height of the 
 mass, and its area at the base. 
 
 25. Pressure of water in proportion to its verti- 
 cal height and its area at the base, is therefore a 
 second leading feature in the laws of water. 
 
 2(3. In other words, the pressure of a column of water 
 does not depend on the width or thickness of the column, 
 but on its height and extent of its base or lower part. 
 
 14. Whai other illustrations are given ? 
 
 15. H.av is tiie degree ol p-eesure estimated? 
 
14 
 
 HYDROSTATICS. 
 
 27. The whole of any fluid mass may be imagined to 
 consist of a number of columns of an inconsiderable thick- 
 ness, which stand perpendicularly on the horizontal base of 
 the containing vessel, and press the base of the vessel with 
 their respective weights. The pressure, then, if the 
 height of the fluid be the same throughout, is as the num- 
 ber of columns, and this number is according to the area 
 of the base. Consequently, in vessels whose bases differ 
 as to area, and which contain fluids of the same density, 
 but different heights, the pressure will be in the compound 
 ratio of the bases and heights. 
 
 28. If the columns of which a fluid mass was supposed 
 to consist, were formed of particles lying in perpendicular 
 lines, the pressure of the fluid would be exerted on the 
 bottom of the vessel only ; but as they are situated in 
 every irregular position, there must of consequence be a 
 pressure exerted in every direction ; which pressure must 
 be equal at equal depths. For if any part of the whole mass 
 were not equally pressed on all sides, it would not move 
 
 towards the side on which the pressure 
 was least, and would not become qui- 
 escent till such equal pressure was ob- 
 tained. The quiescence of the parts 
 of fluids is therefore a proof that they 
 are equally pressed on all sides.* 
 
 29. Several interesting experiments 
 maybe made to prove that the pressure 
 of water is in proportion to its height 
 and width of base. 
 
 30. Figure 1 represents two vessels 
 of equal height, the same width of base, 
 but of different shapes otherwise. One, 
 AB, is of equal thickness from bottom 
 to top ; the other, CD. is a tall narrow 
 tube connected with a broad base. If 
 
 * These definitions, in paragraphs 27 and 28, are given by Nichol- 
 son, in his Introduction to Natural Philosophy. 
 
 ill -D 
 
 Fig. 1. 
 
 16. What method of calculation is named ? 
 
 17. What does the quiescence of fluids prove ? 
 
PRESSURE IN PROPORTION TO HEIGHT. 
 
 15 
 
 Doth be filled with water to the same height, the pressure 
 upon any part of the sides of either will be alike power- 
 ful. The pressure against the inside of the narrow tube 
 at C will be as great as against the inside of the much wider 
 tube at A — the mere width of column making no differ- 
 ence in the degree of pressure. 
 
 31. Another example. — Fi- 
 gure 2 represents a vessel with 
 a broad top EE, tapering to a 
 narrow base CD. The dotted 
 enclosure ABCD represents an 
 ideal column of water the width 
 of the base. The vessel is sup- 
 posed to be filled with water to 
 the surface EE. Yet the base 
 or bottom sustains no more pres- 
 sure than that described by the ideal colujnn ABCD; for 
 the other parts of the contained fluid can only press the 
 column ABCD, and also the sloping sides laterally, and 
 therefore do not contribute to the increase of the weight 
 or {Pressure on the bottom CD. 
 
 32. If we take a vessel of the 
 same capacity, but with a broad 
 base, as in Figure 3, the pres- 
 sure on the bottom is very dif- 
 ferent. In this case the base 
 EF sustains a pressure equal to 
 the weight of a column whose 
 base is EF, and height equal to 
 AC ; for the water in the central 
 column ABCD presses laterally 
 or sidewise, with the same force as it does on the part on 
 which it stands, and thus an uniformity of pressure is es- 
 tablished over every part of the bottom. 
 
 33. From these two cases combined, the reason is evi- 
 dent why fluids contained in the several parts of vessels 
 remain everywhere at the same height ; for the low- 
 
 A B 
 
 18. Explain the diagrams, and the principle of each. 
 
 19. What of the first diagram ? 
 
16 
 
 HYDROSTATICS. 
 
 est part where they communicate may be regarded as the 
 common base ; and the fluids which rest thereon are in 
 equilibrio then only, when their heights are equal, how- 
 ever their quantities may vary. 
 
 34. We may prove the truth of these propositions in 
 various ways. Let ABCD, Figure 4, re- 
 present a cylindrical vessel, to the inside 
 of which is fitted the cover G, which, by 
 means of leather at the edge, will easily 
 slide up and down in the internal cavity, 
 without permitting any water to pass be- 
 tween it and the surface of the cylinder. 
 In the cover is inserted the small tube EF, 
 open at top. and communicating with the in- 
 side of the cylinder below the cover of G. 
 The cylinder is filled with water, and the 
 cover put on. Then, if the cover be load- 
 ed with the weight, suppose of a pound, it 
 will be depressed, the water will rise in the 
 tube to E, and the weight will be sustained. 
 In other words, a very small quantity of 
 water in this narrow tube will press with 
 
 a force as great as if the vessel were of the dimensions 
 KLCD, instead of ABCD. By filling the tube to F, a 
 force will be gained sufficient to balance additional pound 
 weights on the cover G, and as great as could be conferred 
 by a vessel of equal breadth all the way up to F. 
 
 35. Water, in its pressure equally in all directions, 
 presses upwards as well as downwards. This is seen in 
 the above experiments. Take Figure 4 as an example. 
 The water in the vessel ABCD, when the tube is filled, 
 presses, as has been said, with a force equal to that of a 
 column of water of equal breadth all the way up to F. 
 This can only be in consequence of the water in the ves- 
 sel ABCD pressing violently upwards against the cover 
 G, which violence causes a corresponding reaction on the 
 bottom of the vessel. This reaction, then, is equivalent to 
 
 E 
 
 
 Fig. 4. 
 
 20. How is the equilibrium of fluids explained ? 
 
 21. Explain the next diagram, and its use. 
 
PRESSURE IN PROPORTION TO HEIGHT. 
 
 17 
 
 v> rtical height. To use a figure of speech, the water in 
 the vessel is in the condition of a man pressing equally up- 
 wards with his shoulders and downwards with his feet at 
 the same time ; and the more he is acted upon by weight 
 above, the more powerfully does he exert his pressure in 
 both directions. 
 
 36. The great force which may be exerted by a small 
 but high column of water, is further exempli- 
 fied by a tube of from twenty to thirty feet in 
 length- fitted into the end of a cask, as in 
 Figure 5. One pouring in water sufficient to 
 fill the cask, and also the tube to its summit, 
 so great a strain will be made on the hoops 
 of the vessel, that it will in all likelihood burst ; 
 in effect, the pressure on the sides of the cask 
 will be equal to that of a column as wide as 
 the cask and as high as the tube ; and for this 
 degree of pressure, casks are not usually pre- 
 pared. If we suppose that the area of the 
 tube be no more than the twentieth of an inc , 
 and the tube altogether contain only a pound 
 of water, the pressure caused by this incon- 
 ' »• siderable quantity of liquid will be equal to a 
 pound on every twentieth of an inch in the cask ; and for 
 this enormous degree of pressure, no 
 cask is prepared. 
 
 37. An instrument called the hy- 
 drostatic bellows has been constructed 
 to exemplify the effect produced by the 
 pressure of a small column of water. 
 As represented in Figure 6, it consists 
 of two circular stout boards connected 
 together with leather, in the form of a 
 pair of strong bellows. A tube A 
 communicates with the interior between 
 the boards. Supposing the instrument 
 to be strong enough, a person standing 
 Fig. e. on the upper board may raise himself 
 
 22. How is the upward pressure of water shown ? 
 
 23 How may the force of a small column of water be exemp ified I 
 
18 
 
 HYDROSTATICS. 
 
 by pouring water into the tube, and filling it along with 
 the bellows. It is usual to estimate the pressure by 
 means of weights, W. If the tube hold an ounce of water, 
 and has an area equal to a thousandth part of the area of 
 the top of the bellows, one ounce of water in the tube 
 will balance a thousand ounces placed in the bellows. 
 
 38. This remarkable property in liquids, which is called 
 the Hydrostatic paradox, is analogous in principle to that 
 which in mechanics is called the Law of Virtual Veloci- 
 ties.* According to this fundamental rule — a small weight 
 descending a long way, in any given length of time, is 
 equal in effect to a great weight descending a proportion- 
 ally shorter way in the same space of time. The rule, as 
 applied to liquids, may be stated thus : — A small quantity 
 of water descending in a long column is equal in effect to 
 a proportionately great pressure exerted by a large volume 
 of water in a short column. 
 
 39. The law of pressure in proportion to height of 
 column is shown in the annexed re- 
 presentation, Figure 7, of a vessel 
 with an uniformly level base and full 
 of water. Dividing the depth into 
 10 equal sections, to represent feet, 
 as marked from 1 to 10, it is found, 
 that, at the depth of 1, there is a pres- 
 sure of one foot of water, at 2, two feet, and so on to 10 
 at the bottom, where there is a pressure of ten vertical 
 feet of water. The average pressure of the whole is at 
 the middle, at 5. These degrees of intensity of pressure 
 have no reference to the horizontal breadth or length of 
 the mass. The same pressure is sustained, whether the 
 vessel be a foot or a mile in breadth. 
 
 40. As in this example, whatever deficiency of pres- 
 sure there is upon the perpendicular sides of a vessel of 
 water above the middle or point of average pressure, is 
 
 * See Mechanics, paragraph 16 to 27. 
 
 24. Describe the hydrostatic bellows, and its results. 
 
 25. Dofine the hydrostatic paradox. 
 
 26. Explain the diagram. 
 
PRESSURE IN PROPORTION TO HEIGHT. 10 
 
 compensated by a corresponding excess of pressure be- 
 neath the middle ; consequently, the entire pressure dif- 
 fused over the sides is equal to that at the middle or point 
 of average pressure. A perpendicular side of a cubical 
 vessel, according to this statement, sustains a lateral pres- 
 sure precisely equal to the half of that which is endured by 
 the bottom. 
 
 41. We may calculate the degree of lateral pressure in 
 vessels having perpendicular sides and flat horizontal bot- 
 toms, by fir-t finding the number of square feet in the sides 
 below the surface of the liquid ; then multiplying that by the 
 number of feet in half the depth of the liquid; by which 
 calculation, the product will express the number of solid 
 feet of the liquid, whose weight is equal to the lateral pres- 
 sure. We may find the number of square feet in the sides, 
 by multiplying the number of feet in the circumference of 
 the bottom by the number of feet in the depth of the liquid. 
 
 42. Example. — To find the degree of pressure on the 
 perpendicular sides of a vat 24 feet deep from the surface 
 of the liquid, and 40 feet in circumference — Multiply the 
 24 by 40, and the product 96 ) gives the area of the sides ; 
 then multiply the 960 by half the height, that is 12, and 
 the product is 11,520 cubic feet of water, or the volume 
 of liquid whose weight is equal to the pressure on the sides. 
 We next find the weight per cubic foot, which is reckoned 
 to be 1000 ounces ; then 11,520 multiplied by 1000, gives 
 11,520,000 ounces, which is the pressure of the water on 
 the sides. 
 
 43. In consequence of the pressure of liquids being as 
 the vertical height and area of the base, it may happen 
 that the lateral pressure on the sides of a containing vessel 
 is greater than the whole weight of the liquid ; this will 
 be the case when the surface of the sides in contact with 
 the liquid exceeds the ratio of double the magnitude of the 
 bottom — at double the magnitude, both lateral and perpen- 
 dicular pressures are alike, and each is equal to the 
 weight of the liquid. 
 
 27. What of the lateral pressure ? 
 
 28. How may it be calculated ? 
 
 29 State the example and its result. 
 
20 
 
 HYDROSTATICS. 
 
 44. The circumstance of pressure increasing in propor- 
 tion to depth, suggests the valuable practical lesson of 
 greatly increasing the breadth of embankments for dams 
 and canals from the top downwards, so as to give much 
 greater strength to the base than the summit ; also of 
 increasing the strength of the lower hoops of large vats to 
 prevent their bursting. It likewise demonstrates the pro- 
 priety of making dams, ponds, canals, and vessels for 
 liquids generally, as shallow as is consistent with con- 
 venience or their required purpose. In each case it is 
 important to recollect that the degree of pressure on the 
 sides is irrespective of shape or size of the contents, and 
 depends exclusively on the height of the liquid from its 
 upper surface to its base. 
 
 45. That pressure in water is not according to the volume, 
 but the height above the point of pressure, is obvious from 
 many facts both in nature and art. Whether we plunge 
 an object a foot deep in the ocean or in a jar of water, the 
 pressure upon it is the same. The mere extent of the 
 volume of liquid is of no consequence. Therefore, a pre- 
 cipitous shore press d upon by the sea to the height of 
 any given number of feet, suffers no more pressure (sup- 
 posing the sea to be at rest) than the side of a canal of the 
 same number of feet in height. 
 
 46. If the law of pressure of fluids were otherwise than 
 that now stated, no species of embankment, no strength of 
 shore, could withstand the pressure of the ocean, particu- 
 larly in a high state of the tide. In consequence of the 
 law of pressure being simply as the vertical height, we 
 are enabled by artificial means to stem the volume of a 
 far-spreading ocean, and to secure the dry land from its 
 invasion. A knowledge of this important law might 
 induce the attempt to secure many thousands of acres of 
 land which are now covered by the tide. 
 
 47. If a vessel, as for instance a barrel, be filled with 
 water, and three apertures be made in its side at different 
 
 30. How may the lateral pressure exceed the whole weight ? 
 
 31. What practical uses of this principle are named ? 
 
 32. What facts in nature are reierred to in prooft 
 
PRESSURE IN PROPORTION TO HEIGHT. 21 
 
 heights, as in Figure 8, the liquid will pour out with an 
 impetuosity corresponding to the depth of the aperture 
 
 from the top. The jet A 
 nearest the top of the bar- 
 rel, having little pressure 
 above it, will be projected 
 but a short way ; the jet 
 B, having a greater pres- 
 sure, will perhaps go to 
 double the distance ; and 
 the jet C, having the great- 
 est pressure of all, will go 
 to a greater distance still. 
 Jets of this kind obey the laws which govern solid projec- 
 tiles in their flight;* they describe a curvilinear motion, 
 the width of curve being proportioned to the impressed 
 force. 
 
 48. Practically, the discharge of liquids from apertures 
 is partly affected by the shape and width of the aperture ; 
 for water is retarded by friction, and by its own impetu- 
 osity or cross currents in a small channel. 
 
 49. It is reckoned that the pressure of water on any 
 body plunged into it, or on the bottom or sides of the 
 containing vessel, is about one pound on the square inch 
 for every two feet of the depth. 
 
 50. Pieces of wood sunk to great depths in the ocean 
 become so saturated with water by the pressure of the 
 superincumbent mass, that they lose their buoyancy, and 
 remain at rest at the bottom. The depth to which divers 
 can descend is limited by the increased pressure they 
 experience in their descent. If a bottle be firmly corked 
 and sealed, and sunk to a great depth in the ocean, the 
 cork will either be forced in or the bottle broken by the 
 pressure. An air-bell rising from a depth, expands as it 
 
 * See Laws of Projectiles, paragraph 237, &c., Laws of Matter 
 and Motion. 
 
 33. Explain the diagram and the laws it exhibits. 
 
 34. How is water retarded, and what the ratio of pressure ? 
 
 35. What examples of pressure are named ? 
 
22 
 
 HYDROSTATICS. 
 
 approaches the surface. At the depth of a thousand 
 fathoms, water is estimated to be about a twentieth part 
 more dense in the hulk than at the surface. 
 
 51. The great effects that may take place by the action 
 of a small but high column of water, are sometimes exem- 
 plified in the rending of mountains. In Figure 9, a 
 mountain or high rocky knoll is represented, with a small 
 vertical crevice A reaching from the summit to an inter- 
 nal reservoir of water near the base. If there be no 
 means of outlet to the liquid, and if rain continue to keep 
 the crevice and its terminating reservoir full, the lateral 
 
 force exerted by the upright column will be very consi- 
 derable. Supposing the crevice to be an inch in diameter, 
 and two hundred feet deep, the pressure would be equal 
 to nearly a half a ton on every square inch ; such a force 
 continually acting on the sides of the mountain (laying 
 out of view the great additional force given by expansion 
 of the liquid in freezing during winter) would probably 
 in time overcome the cohesiveness of the mass, and burst 
 the whole asunder. In this property in water, therefore, 
 we see one of the many provisions of nature for producing 
 changes on the surface of the earth. 
 
 52. Effects of a similar character, but on a less scale, 
 are observable in the bursting of walls behind which earth 
 
 36. Explain the diagram and its design. 
 
 37. What phenomena are thus explained? 
 
 38. What results from the mobility of the atoms of ater ? 
 
EQUAL LEVELNESS OF SURFACE. 
 
 23 
 
 has been piled, and in which no proper outlets for water 
 have been provided ; as also in the bursting upwards 
 of drains upon a declivity, when they become choked. 
 
 HYDROSTATICS CONTINUED. 
 
 EQUAL LEVELNESS OF SURFACE. 
 
 53. On account of the perfect ease with which particles 
 of water move over or among each other, a quantity or 
 mass of them can have no solidity, firmness, or tenacity ; 
 accordingly, any such mass readily accommodates itself 
 to the shape of any vessel or natural hollow in which it 
 may be placed ; the mass takes the form of the vessel or 
 hollow, whatever it may be. 
 
 54. While the easy motion of the particles among each 
 other causes them to accommodate themselves to the 
 shape of any vessel, the force of gravity causes them at 
 the same time, to seek the lowest level for repose. Each 
 particle tries to get as low as it can. The result of this 
 general tendency throughout the mass is a perfect level- 
 ness of surface ; the top of the water is smooth. 
 
 55. An uniform levelness of surface takes place in 
 every connected mass of water, whatever be its magnitude 
 or its shape. This forms the third leading feature in the 
 laws of water, and is the cause of many of the phenomena 
 m nature. 
 
 56. One of the most familiar exam- 
 ples of the equal height and levelness 
 of surface of water is that observable 
 in a common teapot. In the represen- 
 tation of a teapot, Figure 10, the sur- 
 face of the liquid in the pot is seen to 
 be at A, and also at the very same 
 height at B in the spout. A straight 
 dotted line is drawn from one to the 
 other, to show that both surfaces are 
 of the same level. It is customary to say that the small 
 
 Fig. 111. 
 
 39. What is the third law of water and its result ? 
 40 Explain the diagrams, Figs. 10 and 11. 
 
24 
 
 HYDROSTATICS. 
 
 column of water in the spout balances the large mass of 
 water in the pot; but, in reality, there is no balancing in 
 the case. The water necessarily possesses the same sur- 
 face level in all its parts ; one portion cannot stand higher 
 than another ; all portions, great and small, are only dis- 
 tributed parts of a single mass. 
 
 57. Figure 11 presents a similar 
 example of the same phenomenon. 
 V. is a vessel filled with water to' the 
 height of A. T is a tube proceeding 
 first downward and then upward from 
 the bottom of the vessel. In this tube, 
 accordingly, the water stands at the 
 same height or level at B as it does 
 at A. There is nothing surprising 
 in this, because it is only the same 
 piece of water throughout. 
 
 58. Figure 12 represents a vessel formed of six differ- 
 ent compartments, but all communicating with eac'h other, 
 and containing a body of water. As in the preceding 
 instance, the water stands at a uniform level throughout, 
 marked from A to B, notwithstanding the difference of 
 shape of the compartments. Thus, it is of no consequence 
 how we bend or twist the vessel into various shapes, for 
 in every connected mass of water there must necessarily 
 be but one uniform level. 
 
 Fig. 12. 
 
 59. The tendency which water has to stand at the same 
 surface level in all parts of its mass, is usually referred to 
 by the phrase “ water finding its level.” 
 
 41. What does Fig. 12 illustrate ? 
 
LEVELS. 
 
 60. It is this inherent tendency in water to find its level 
 that produces the various phenomena of the trickling down 
 of rain and moisture into the ground, the flowing of all 
 kinds of streams, from the small brook to the mighty river, 
 and the shooting of rapids and cataracts over precipices. 
 In each case, the water, in obedience to the natural law 
 or tendency which governs it, is only trying to find its 
 level. In pursuit of this object, the water, by the rubbing 
 force which it exercises, wears down all the solid objects 
 which pres nt an obstacle to it in its course. Thus, the 
 substances of which hills and plains are composed, are 
 carried away by streams into the ocean — the ground of con- 
 tinents and islands diminishes in bulk — new land rises in 
 the sea: and so, by the effects of a simple natural cause, 
 great alterations are produced in the external features of 
 the globe. 
 
 LEVELS. 
 
 1. There are two kinds of levels — the true level and 
 the natural level. 11 ’ 
 
 62. The true level is a perfectly horizontal plane, as for 
 
 instance an even line, thus , or a 
 
 perfectly even surface of a floor. 
 
 63. The natural level is a surface, every point of which 
 is at the same distance from the centre of the earth. The 
 surface level of water is always the natural level. 
 
 64. The character of a natural level is understood by a 
 reference to the spherical shape of the earth and the pres- 
 sure of gravitation. The globe is a ball, and any piece 
 of water which lies upon it, lies in the form of a plaster 
 round the ball. Water, therefore, cannot possibly have a 
 true surface level ; its level partakes of the sphericity of 
 the ball. Every piece of water, in a state of entire or par- 
 tial repose, is in this manner convex in its surface. 
 
 65. The degree of convexity of the earth is, as nearly 
 
 * In mathematics, the term apparent level is used instead of true 
 level, and the term dead level instead of natural level. 
 
 42. What natural phenomena are thus explained? 
 
 43. How many kinds of levels are named ? 
 
 44. Is the natural level of water convex, and why T 
 
26 
 
 HYDROSTATICS. 
 
 as it can be stated in figures, 7 inches and 9-10ths of an 
 inch, or nearly 8 inches in each mile. The convexity, 
 however, is somewhat less toward the north and south 
 poles, because the earth is a spheroid, or a sphere flattened 
 at the ends. 
 
 66. Figure 13 represents a segment of the earth’s sur- 
 
 p face, with the appear- 
 
 ance of a true and 
 natural level marked 
 upon it. The curve 
 ES is the earth’s sur- 
 face. PC is a per- 
 pendicular line point- 
 ing to the centre of 
 the earth. At right 
 angles from this line, 
 a line TL is drawn, 
 representing the true 
 level. Supposing that 
 the line TL is a mile in length, if we draw a line from L 
 to the centre at C, it will cut across the surface of the earth 
 at a point a mile distant from the line at T. which point 
 will be 7 inches and 9-IOths depressed below the part at L. 
 
 67. The convexity of the earth’s surface is not observ- 
 able in small quantities of water. The surface of a glass 
 of water is not a true level, but the degree of convexity is 
 so small that it cannot be practically estimated or measured. 
 It is only when a sheet of water is stretched out to an ex- 
 tent of several miles, that the convexity becomes conspi- 
 cuous. It is very perceptible on the ocean when a ship 
 is seen approaching on the horizon ; first the mast and 
 sails of the ship are seen, and lastly the hull. In order 
 to catch the first glimpse of vessels at sea, the point of out- 
 look for them is placed high above the water. By this 
 means, the person who looks is able to see over a part of 
 the convexity, and give information of the approach of 
 vessels to those placed below. 
 
 45. What is the degree of convexity of the globe ? 
 
 46. Explain the diagram. 
 
 4 t. How is the spherical level of the ocean seen ? 
 
LEVELS THE THEODOLITE. 
 
 68. The convexity of the land is not so conspicuous, in 
 consequence of the many risings and failings in the sur- 
 face. It is only in some extensive alluvial plains in 
 different parts of the world that the convexity can be per- 
 ceived, in the same manner as at sea. 
 
 69. In forming roads, railways, and canals, it is neces- 
 sary to make allowance for the convexity of the earth’s 
 surface. The first thing done in such cases is to survey 
 the land by means of an instrument called a theodolite. 
 One of the varieties of the theodolite is a small telescope fixed 
 on a stand, and must, when looked through, be placed per- 
 fectly horizontal, or in a true level. To find a true level, 
 an instrument is fixed below it, called a spirit level, and 
 by that it is regulated. 
 
 70. A spirit level is in universal request in works of 
 art requiring levelness of foundation or surface. It con- 
 
 a b c sists of a cylindrical glass tube, 
 
 ■- quantity of spirits of wine suffi- 
 
 14 cient to fill it, except a small part, 
 
 in which the air is left. The tube 
 being completely closed or sealed, the small vacancy where 
 the air is le/t shows an air-bubble at whatever part of the 
 tube is uppermost. The tube being set in a small wooden 
 case with a level bottom, this case is laid upon the block 
 of stone, wood, or other object to be levelled, and when 
 the air-bubble is seen to rest in the middle of the upper 
 side, it signifies that the object on which the instrument 
 lies is a true level. In the accompanying figure, the air- 
 bubble is seen at the middle at b ; the slightest unevenness 
 would cause the bubble to proceed to a at one end, or c at 
 the other. 
 
 71. A true level being found for the theodolite, the sur- 
 veyor looks through the glass or telescope towards a pole, 
 the lower end of which rests on the ground, and is held 
 in a perpendicular position by a man at (we shall suppose) 
 the distance of a mile, previously measured. The pole 
 having figures marked upon it, a certain figure on a level 
 
 48. By what instrument is the convexity of the land measured I 
 
 49. Explain the diagram, and the use of the spirit level. 
 
28 
 
 HYDROSTATICS. 
 
 with the eye is ascertained ; 7 inches and 9-10ths are then 
 reckoned down the pole from the figure, and at that depth 
 we have the natural level from which the surveyor makes 
 his subsequent calculations. If a road were to be made 
 on the plan of preserving a true level, it would proceed 
 in its course at a tangent from the earth’s convexity like 
 the line TL in Figure 13, and, consequently, would reach 
 a point above that to which it was destined to go. It 
 would be impossible to make the water in a canal pursue 
 a true level ; in the attempt to do so, the water would not 
 remain at rest in the channel prepared for it, but would 
 rush towards the lower end. 
 
 72. As most countries are less or more irregular in sur- 
 face, canals are usually constructed with different levels, 
 so much of the length being on one 1 vel, and so much on 
 another, as the case may be. At every change of level 
 there is a lock, or portion enclosed with gateways, to keep 
 the water at the proper level, and to allow the passage of 
 vessels. The locks of a canal, therefore, are like steps of 
 a stair, one at a greater height than another, and by their 
 means vessels may be made to proceed up or down hill. 
 
 HYDROSTATICS CONTINUElf. 
 
 SPECIFIC GRAVITY. 
 
 73. The more dense in substance that a body is, it is 
 the more heavy or weighty, because it contains the more 
 particles to be operated upon by attraction of gravitation. 
 In reference to the density of bodies, the term specific 
 gravity is employed to denote the comparison which is 
 made. Thus, the weight of a lump of lead is greater than 
 an equal bulk of cork ; therefore its specific gravity is 
 greater; and so on with all other substances, when com- 
 pared together. For the sake of convenience, pure distilled 
 water, at a temperature of 62 degrees, has been established 
 as a standard by which to compare the specific gravity or 
 
 50. Describe the use of a theodolite in canalling, &c. 
 
 51. By what means is the level changed in canals 1 
 
 52. What results are thus obtained l 
 
SPECIFIC GRAVITY. 
 
 2 ? 
 
 relative weight of solid and liquid bodies. Every such 
 body is said to be of either a greater or less specific gravity 
 than water, bulk for bulk.* 
 
 74. We have an example of a difference in the specific 
 gravities of liquids, in mercury, water, oil, and spirits. 
 Mercury is considerably more dense or heavy than any of 
 the others ; the next in density is water, then oil, and lastly 
 spirits. If we put a quantity of each of these liquids into 
 a glass vessel, one after the other, in the order here men- 
 tioned, we shall observe that all keep their respective 
 places, without intermixture, the heaviest at the bottom 
 and the lightest at the top. Should they even be jumbled 
 together in the vessel, it will be noticed that they in time 
 rectify the disturbance, each assuming its own position. 
 
 75. Sea or salt water, in consequence of being loaded 
 with foreign matter, is of greater density or specific gravity 
 than pure fresh water of the same temperature. If we 
 therefore pour a quantity of salt water into a glass vessel, 
 and then gently place some fresh water above it, we shall 
 observe the same phenomenon, of each kind of liquid re- 
 
 t-iining its position, the heaviest to the bottom, and 
 the lightest to the top. After being jumbled to- 
 gether, the two liquids will, as far as possible, re- 
 turn to their former relative position. 
 
 76. If we fill a bottle with water, and dip it 
 with the open mouth downwards into a jar or 
 barrel of spirits, the water, in virtue of its density, 
 will be emptied and sink into the spirits, and the 
 spirits will immediately rush up into the empty 
 bottle and supply the place of the water. 
 
 77. The force which liquids exert in opposing 
 each other in a state of equilibrium, corresponds 
 to their specific gravities ; in other words, a small 
 quantity of a heavy liquid will balance a much 
 
 * See paragraph 127 to 131, Laws of Matter and Motion. 
 
 53. What of specific gravity, and what is the standard ? 
 
 54. What variety in specific giavity may be sho w n 7 
 
 55. What of salt and fresh water, frnngeib erii nislq/.S Sc. 
 •SSibWhffBBiJJsdnmemiivir^ltetSI-jjqa oviishn aril onu./i .86 
 
30 
 
 HYDROSTATICS. 
 
 greater quantity of a lighter liquid. For example, take 
 a bent glass tube, as in Figure 15, and pour as much 
 water into it as will extend from the bottom at E to A. 
 This quantity of water will be balanced or kept to its sum- 
 mit level at A by a quantity of mercury measuring from 
 E to B, or by a quantity of oil from E to C, or by a quan- 
 tity of spirits from E to D. Each of these experiments 
 may be performed one after the other. The pressure of 
 liquids being as the vertical height, and not as breadth, it 
 would make no difference in the result of the experiments, 
 if the limb of the tube for the mercury, oil, or spirits, were 
 increased to a foot, a mile, or any other diameter. 
 
 78. Water, at its ordinary temperature of 62 degrees, 
 has a specific gravity of 1000 ounces to the cubit foot. 
 Platinum is 22$ times heavier, or 22! times the specific 
 gravity of water ; gold is 19!, mercury 13!, copper 8f , 
 iron 8, common stone about 2!, and brick 2. Alcohol is 
 a little more than 8-10ths of the heaviness or specific 
 gravity of water, or 0-815; and oil of almonds is little 
 more than 9-10ths, or 0 913. Atmospheric air at the 
 earth’s surface is 1-S00th part, or 0-00125 ; in other 
 words, while a cubic foot of water weighs 1000 ounces, 
 a cubic foot of air weighs one ounce and a quarter. 
 
 79. Sea-water generally possesses a specific gravity 
 of 1-035 — that is, to 1090 parts of fresh water there are 
 in addition 55 parts of saline substances.* Sea-water 
 being, therefore, thirty-five parts for every 1000 of water 
 more dense than fresh water, it possesses a proportionally 
 greater power of buoying up bodies. A vessel which 
 will carry 1000 tons on fresh water, will thus carry 1035 
 tons on the sea. 
 
 FLUID SUPPORT. 
 
 80. The immersion of solid bodies in liquids developes 
 some important principles in hydrostatics. 
 
 * This is given only as a general rule. The sea is not uniformly 
 salt. 
 
 57. Explain the diagram. 
 
 58. Name the relative specific gravities of different bodies. 
 
FLUID SUPPORT. 
 
 31 
 
 81. Any body of greater specific gravity than water, 
 bulk for bulk, will sink on being thrown into water; but 
 a body will float if its specific gravity be less than that of 
 water. 
 
 82. The mode of stating the law in reference to the 
 immersion and floating of solid bodies in any kind of 
 fluids, is as follows : — 
 
 83. First . — Any solid body immersed in a fluid dis- 
 places exactly its own bulk of fluid, and the force with 
 which the body is buoyed up is pqual to the weight of the 
 fluid which is displaced ; therefore, the body will sink or 
 swim, according as its own weight is greater or less than 
 the bulk of displaced fluid. This refers to bodies of less 
 density than water. 
 
 84. Seccnd . — Any solid body of a greater density than 
 water, when wholly immersed in that fluid, loses exactly 
 as much of its weight as the weight of an equal bulk of 
 the water — that is, of the water which it displaces. 
 
 85. It is of great importance that these propositions 
 should be fully comprehended, for they explain innumerable 
 phenomena in nature, in reference to the floating or swim- 
 ming of bodies in water or in the atmosphere. 
 
 86. Water, as has been explained, consists of innume- 
 rable small particles, pressing in all directions, or upwards 
 as well as downwards. Let us fix our attention on a sup- 
 posed single particle in the mass ; while the liquid is in a 
 condition of repose, we may imagine the particle to be sus- 
 tained between contending forces — the force of a column 
 
 of particles above, and the equally strong 
 force of particles beneath, pushing to get 
 upward or away from this column. 
 
 87. Let us now substitute any solid 
 object for the supposed particle ; for ex- 
 ample, the quadrangular object AB re- 
 Fig. 16 . presented in a vessel of water, Figu re 1 ;. 
 
 This object, supposed to be of the same density as water. 
 
 59. Upon what does the floating of bodies depend ? 
 
 60. What of bodies less dense than water ? 
 
 61. And what of those of greater density than water? 
 
 62. Do these laws apply to all other fluids ? 
 
HYDROSTATICS, 
 
 >'T 
 
 which w e see is sunk in a buoyant condition in the water, 
 has displaced a mass of particles, all of which were ope- 
 rated upon in the manner of the supposed single particle. 
 This object, then, by taking the place of the mass of par- 
 ticles, has become subject to the same contending forces, 
 a id is consequently floated or sustained to the same ex- 
 tent as they were. 
 
 88. If we suppose that the weight of the object is two 
 pounds, liquid to the amount of two pounds is displaced, 
 and the object is pressed upwards with the force of two 
 pounds. Or, to vary the example, suppose that only the 
 lower half beneath the line C is the solid object, and that 
 the space occupied by the upper half is water, the object 
 is still pressed upwards with a force of two pounds; but 
 being one pound weight in itself, and having a pound of 
 water above it, it remains suspended in equilibrium. 
 
 89. These examples refer to bodies which are of the 
 same density or weight as water, bulk for bulk : we shall 
 now take an example of a body specifically lighter than 
 water, by which it will be observed that the buoyancy is 
 governed by the same principle. 
 
 90. Figure 17 represents a solid ob- 
 ject A B half immersed in a vessel of 
 water. In this, as in all cases in which 
 there is a portion of the object above the 
 water, the weight of that portion is borne 
 by, and therefore conveyed to, the por- 
 tion which is immersed. Thus, in the 
 example before us, the portion B, though less than a 
 pound weight in itself, by supporting A, becomes, we 
 shall say, a pound, and displaces a pound of water; it is 
 therefore buoyed up with the corresponding force of a 
 pound. 
 
 91. Whether a body be large or small in bulk, in pro- 
 portion to its weight, its displacement of water depends 
 exclusively on its weight, so long as it is not heavier than 
 water. A vessel of cork, wood, or any substance lighter 
 than water, weighing a thousand tons, displaces exactly 
 
 63. 'Explain the diagram and its purpose. 
 
 64. Explain the diagram and its principle 
 
FLUID SUPPORT. 
 
 33 
 
 the same weight of water, or is buoyed up with the same 
 degree of force. 
 
 92. From these circumstances, it appears that the en- 
 tire weight of any floating body may be calculated by 
 measuring the quantity of water which it displaces. 
 
 93. On immersing a stone or any other solid object in 
 water, it is found to be buoyed up in proportion as its 
 specific gravity is less than that of water. If its specific 
 gravity be greatef than water, it will sink to the bottom, 
 and if less, it will swim. As the water of the ocean be- 
 comes of greater specific gravity the greater the depth, it 
 may happen that an object, which sinks at the top of the 
 water, will remain suspended in equilibrium when it 
 descends to a point at which the specific gravity of the 
 water is equal to its own. 
 
 94. Whatever be the weight of any solid object when 
 weighed in air, its apparent weight is lessened when 
 weighed in water. Thus a stone may be moved with 
 comparative ease in water, which cannot be lifted without 
 considerable difficulty on land. The apparent diminution 
 of weight in these cases is caused by the support afforded 
 by the liquid. Attraction of gravitation, which is the 
 cause of what we call weight, is counteracted more in 
 water than in air, because the water has a tendency to 
 buoy up the object. The weight of any object in water 
 is thereby lessened to the extent of the weight of a bulk 
 of liquid equal to the size of the object. If the object 
 displace a pound of water, it will weigh a pound lighter 
 in water than in air. 
 
 95. The circumstance of any solid object displacing its 
 own bulk of liquid, and losing exactly as much of its 
 weight as the weight of that bulk of liquid which it dis- 
 places, has led to the use of the hydrostatic or water balance 
 for ascertaining the intrinsic value of gold and other precious 
 metals. For example, by knowing in the first place how 
 much water a pound of pure gold displaces, and then 
 weighing in water, as in Figure 18, an object said to be 
 a pound of gold, we should observe whether it displaced 
 
 65- How may the weight ot any floating body be measured ? 
 66. What difference between water and air, and why? 
 
HYDROSTATICS. 
 
 34 
 
 the proper quantity of water; if it displaced more than 
 was proper, then we should be certain that it contained 
 
 alloy or some inferior sub- 
 stance, being too bulky for 
 a pound of gold. Such 
 weights are used by gold- 
 smiths.* 
 
 96. Thus, if a piece of 
 gold weigh 19^ ounces 
 in air, it w r ould weigh 
 only 18s ounces in water ; 
 the ounce of weight thus 
 counteracted being just the weight of the water that the 
 gold displaces. Therefore the weight of the gold would 
 be to that of the water as 19s ounces to 1 ounce; that is, 
 the specific gravity of gold is 19^, if water is taken for the 
 standard. 
 
 97. We may cause an object, such as a light hollow 
 ball, or bladder, to displace much more water than what 
 is equal to its own weight ; but in doing so, we must press 
 the ball into the water, and that degree of pressure com- 
 pensates the deficiency of weight in the ball. Thus, 
 extraneous pressure on a floating body, and weight in the 
 body itself, are the same thing as respects buoyancy. 
 
 98. The human body in a state of health, with the 
 lungs full of air, is specifically lighter than water, and 
 more so in the sea than in fresh-water. Persons, there- 
 fore, on going or falling into water, cannot possibly sink, 
 unless they struggle so as to prevent the liquid from 
 buoying them up. The body will float with a bulk of 
 about half (he head above the surface ; and thus a person 
 who cannot swim may live and breathe, until chilled or 
 otherwise paralyzed, by simply stretching himself on his 
 back, and with his face above the water. By throwing 
 the arms out of the water, the body does not displace so 
 
 * See paragraph 132, Laws of Matter and Motion. 
 
 Fig. 18. 
 
 67. Explain the nature and use of the hydrostatic balance. 
 
 68. What of gold as compared to water ? 
 
 69. How is buoyancy affected by ex ra: eous pressure l 
 
FLUID SUPPORT. 
 
 35 
 
 much liquid; its weight is increased, and it naturally 
 sinks. Ignorance of these facts in hydrostatics, and want 
 of resolution, cause many deaths by drowning. 
 
 99. There are various kinds of apparatus for prevent- 
 ing drowning, called life-preservers. The most common 
 are those which consist of pieces of cork or other very 
 light material attached to the upper part of the body. 
 But air-tight bags are preferable, as they may be said 
 scarcely to encumber the body when empty, and, as dan- 
 ger approaches, they can be inflated with ease by being 
 blown into. Life-boats have large quantities of cork in 
 their structure, and also air-tight vessels made of thin 
 metallic plates ; so that, even when the boat is filled with 
 water, a considerable portion of it still floats above the 
 g. nera! surface. The bodies of some animals, as sea-fowl, 
 and many other species of birds, are considerably lighter 
 than water. The feathers with which they are covered 
 add very much to their buoyancy. Quadrupeds swim 
 much easier than men. because the natural motion of their 
 legs in walking or running is that which best fits them for 
 swimming. Fishes are enabled to change their specific 
 gravity by means of an air-bag with which they are pro- 
 vided. When the air-bag is distended, thpy rise to the 
 surface ; when it is contracted, they descend to the bot- 
 tom.* 
 
 100. The buoyant property of liquids is independent 
 of their depth or expanse, for if there be only enough of 
 
 * The bodies of most fishes are nearly of the specific gravily of 
 water, and, therefore, if living in it without making exertion, 
 they neiiher sink nor swim. When ihis subject was less understood, 
 many persons believed that fishes had no weight in water ; and it is 
 related as a joke at the expense of the philosophers, that a king having 
 once proposed as a task to his men of science to explain this extraor- 
 dinary fact, many profound disquisitions came forth, but not one of 
 the competitors thought of trying what really was the fact. At last, 
 a simple man [who doubted the fact] balanced a vessel of water in 
 scales, and on putting a fish into it, showed a scale preponderating, 
 just as much as if the fish had been weighed alone. — Arnott’ s Ele- 
 ments of Physics. 
 
 70. What useful lesson is given here ? 
 
 71. What of life-preservers ? 
 
 72. What animal peculiarities are named ? 
 
HYDROSTATIC^. 
 
 86 
 
 water to surround an object plunged into it, the object 
 will float as effectually as if it had been immersed in a 
 large mass of water. Thus, a few pounds of water may 
 float an object which is a ton in weight. We account for 
 these phenomena, by the law of pressure in liquids being 
 as vertical height, not as width of column, and by a body 
 being buoyed up with a force exactly in proportion to the 
 weight of water which it displaces. 
 
 101. These important truths in hydrostatics teach the 
 practical lesson that if canals be made only as deep or 
 wide as will afford water to surround the vessels placed 
 upon them, they will be sufficiently large for all purposes 
 of buoyancy and navigation. A ship floats no better on 
 the face of a sheet of water miles in width, than it would do 
 on a mill-pond, provided there be enough of water in the 
 pond to keep it off the bottom. 
 
 102. Every solid body possesses a centre of gravity, 
 which is the point upon or about which the body balances 
 itself, and remains in a state of rest, or equilibrium, in any 
 position. 
 
 103. The equilibrium of floating bodies is regulated in 
 the same manner. The floating body has a centre of 
 gravity, about which the whole mass will balance itself in 
 the liquid ; the heaviest side will sink lowest, and the 
 more light will be uppermost. 
 
 104. In reference to floating bodies, there is a point 
 called the centre of buoyancy ; this is the centre of gravity 
 of the liquid which is displaced. If the floating body be 
 of the same specific gravity as water, the centre of buoy- 
 ancy will be at the same point in the floating body as it 
 would have been in the water; but there is seldom this 
 uniformity, at least not in vessels used for purposes of 
 navigation. It is necessary that all such vessels should 
 be of a less specific gravity than water, in order that a 
 part of their weight may be composed of cargo, stores, 
 passengers, &c., and that they may be sufficiently buoyant. 
 
 105. Besides the centre of gravity and centre of buoy- 
 
 73. By what law is the buoyancy of water calculated? 
 
 74. What practical hints are thus given ? 
 
FLUID SUPPORT. 
 
 37 
 
 ancy of a floating body, there is another important point 
 called the metarentre, a word signifying beyond the centre 
 This metacentre is a point in the axis of a floating body , 
 the axis being a vertical line through the centre of gravity 
 of the mass when it is at rest. In the case of a body 
 floating at rest or perfectly stable, an ideal line uniting the 
 
 centre, of gravity 
 and buoyancy is 
 in a vertical posi- 
 tion. as from B to 
 G, Figure 19, and 
 is called the line 
 of support. W W 
 is the water line. 
 If the body is now 
 inclined a little to 
 one side, as in Figure 20. the direction of this line is no 
 longer vertical, but slanting, as a line uniting B and G, 
 (not shown in the cut.) If a line be supposed to pass 
 upwards in a vertical direction from the centre of buoy- 
 ancy B, it will meet the axis on a point marked M, which 
 is the metacentre. Should the body sway in an opposite 
 direction to the same extent, the point M will still be the 
 metacentre. For different small inclinations from the 
 position of equilibrium, the position of the metacentre is 
 nearly the same ; but for greater deviations, its position 
 varies considerably. 
 
 106. We have now to explain the practical use of a 
 knowledge of these facts. When the metacentre happens 
 to lie above the centre of gravity, as in the figure, the 
 force of buoyancy acting upwards in the direction of the 
 line B M, makes the body turn round its centre of gravity 
 G, till it arrive at its position of rest, as in figure 19, after 
 performing a few oscillations. But if the metacentre 
 happen to lie below the centre of gravity, the buoyant 
 force would turn the body in an opposite direction, and make 
 
 75 Define the centre of gravity and of nuoyancy. 
 
 76. What of vessels used in navigation ? 
 
 77. Define the meiaeentre and exp'ain the diagrams. 
 
 78. Of what practical use is this metacentre ? 
 
38 
 
 HYDROSTATICS. 
 
 it depart still farther from its position of rest, till it would 
 be upset. 
 
 107. The discovery of the centre of buoyancy and me- 
 tacentre in any floating body, is a matter of mathematical 
 investigation ; the explanations here given, however, will 
 show the nature of the calculations required in reference 
 to the laws which secure the stability of floating bodies. 
 
 108. Heavy materials, called ballast, are usually placed 
 in the bottom of the holds of vessels, to insure a low centre 
 of gravity. A ship of the largest capacity and burden, 
 with its centre of gravity properly regulated, rests in the 
 water with a stateliness and stability which cannot be de- 
 stroyed except by some extraordinary violence. 
 
 HYDROMETERS. 
 
 109. If a substance be weighed in two fluids, the 
 weights which it loses in each are as the specific gravities 
 of those fluids. Thus, a cubic inch of lead loses g53 
 grains when weighed in water, and only 209 grains when 
 weighed in rectified spirit ; therefore, a cubic inch of rec- 
 tified spirit weighs 209 grains, an equal bulk of water 
 weighing 253; and so the specific gravity of water is 
 about a fourth greater than that of the spirit. 
 
 1 10. The instrument called a hydrometer is constructed 
 upon this principle. Its name is derived from two Greek 
 words, signifying measure of water ; but it is of course 
 used fo.- ascertaining the density of all kinds of liquids. 
 There are various kinds of hydrometers. One of them 
 consists of a glass or copper ball with a stem, on which is 
 marked a scale of equal parts or degrees. When im- 
 mersed in any fluid, the stem sinks to a certain depth, 
 which is indicated by the graduated scale. The length 
 to which it sinks in the standard of comparison being 
 known, we can thus easily ascertain how much it is spe- 
 cifically heavier or lighter than the fluid. 
 
 111. Much in the same manner is constructed another 
 hydrometer of great delicacy and exactness. It consists 
 
 79. What difference between weight in waier and spirit ? 
 
 80. How is the simplest form of hydrometer made ? 
 
HYDROMETERS. 
 
 39 
 
 of a ball of glass about three inches diameter, with another 
 joined to it, and opening into it, of one inch diameter, 6c, 
 Figure 21, and a brass neck d, into which is screwed a 
 wire ae, divided into inches and tenths of an inch, about 
 ten inches long and one-fortieth of an inch in diameter. 
 The who.e weight of the instrument is 4000 grains when 
 loaded with small weights, such as shot, in 
 the lower ball c. When plunged into water 
 in the jar, this instrument is found to sink 
 an inch, if a single grain be laid upon the top 
 a ; hence a tenth of a grain sinks it a tenth 
 of an inch. So great is the delicacy ol this 
 hydrometer, that the difference in specific 
 gravity of one part in 40,009 can be de- 
 tected. Its total weight of 4000 grains is 
 convenient for comparing water; but the 
 quantity of shot in the lower ball can be 
 varied, so as to adapt the instrument to 
 measure the specific gravities of fluids light- 
 er or heavier than the standard of compari- 
 son. 
 
 112. There is another very simple hydrometer, which 
 consists of a number of glass beads of different weights, 
 but whose proportions are known, and the beads marked 
 accordingly. These are dropped into the fluid under ex- 
 amination, until one is found which neither sinks to the 
 bottom nor swims upon the surface, but remains at rest 
 wherever it is placed in the liquid ; and this bead being 
 numbered, indicates the specific gravity. 
 
 1 13. In making calculations of the strength and specific 
 gravity of spirits, by the above or any other means, atten- 
 tion must be paid to the degree of temperature of the liquid. 
 Heat expands the liquor, and renders it specifically lighter ; 
 all spirits are therefore more bulky, in proportion to their 
 weight, in summer than in winter, and also apparently 
 stronger, not really so.* 
 
 * See paragraph 131, Laws or Matter and Motion. 
 
 81. Explain the diagram. 
 
 82. How does temperature vary specific gravity t 
 
40 
 
 HYDRAULICS. 
 
 HYDRAULICS. 
 
 Having detailed the laws and properties of water in a 
 state of rest or equilibrium, we have now to mention some 
 of the more important results of these laws, and also the 
 effects which are produced upon liquids by the application 
 of forces, whether natural or artificial. 
 
 WATER A MECHANICAL AGENT. 
 
 114. Water, as already explained in the Laws of Mat- 
 ter and Motion, may be made a useful agent of power, 
 merely by allowing it to act with the force of its own 
 gravity, as in turning a mill; and in this manner it is ex- 
 tensively employed in ail civilized countries possessing 
 brooks which are sufficiently rapid in their descent. 
 
 115. But water maybe rendered otherwise useful as 
 an agent of force in the arts. Although subtile in sub- 
 stance, and eluding the grasp of those who d -sire to han- 
 dle and hold it, it can, without alteration of temperature, 
 be made to act as a mechanical ■power , as conveniently and 
 usefully as if it were a solid substance, like iron, stone, or 
 wood. The lever, the screw, the inclined plane, or any 
 of the ordinary mechanical powers, are not more remark- 
 able as instruments of force than water, a single gallon of 
 which may be made to perform what cannot be accom- 
 plished (except at enormous cost and labour) by the strong- 
 est metal. 
 
 llfj. To render water serviceable as an instrument cf 
 force, it must be confined, and an attempt then made to 
 compress it into less than its natural bulk. In making 
 this attempt, the impressed force is freely communicated 
 through the mass, and in the endeavour to avoid compres- 
 sion, the liquid will repel whatever movable object is pre- 
 sented to it. The force with which water may be squirted 
 from a boy’s syringe, gives but a feeble idea of the power 
 of liquids when subjected in a state of confinement to the 
 impression of external force. 
 
 83. Define hydraulics. 
 
 84. What of water as a mechanical agent ? 
 
 85. How is water rendered an instrument of force ? 
 
HYDRAULIC PRESS. 
 
 41 
 
 117. The mechanical force of water is exemplified by 
 the hydraulic press. This is an engine employed by paper- 
 makers, printers, and manufacturers of various kinds of 
 goods, for the purpose of giving a high degree of pressure 
 or smooth glazed finish to their respective articles. It has 
 generally superseded the screw press, on account of its 
 much greater power, with a less degree of trouble and risk 
 of injury to the mechanism. 
 
 118. Figure 22 represents the outline of a hydraulic 
 press. AB is the frame, consisting of four upright pillars 
 supporting a cross top of great strength, and against which 
 the pressure takes place in an upward direction. C, the 
 material to be pressed, is forced upward by D, a round 
 iron piston. This piston is very nicely fitted into an iron 
 case E, which has a cavity F for receiving the water : the 
 neck of the case grasps the piston so tightly that no water 
 
 86. Describe the hydraulic press and its use. 
 
 87. Explain the diagram and its principles. 
 
42 
 
 HYDRAULICS. 
 
 can escape. A small pipe G conveys water into the hollow 
 cavity from a forcing pump H, which stands in a trough of 
 water T. All that part of the apparatus below the base of 
 the pillars is sunk out of sight in the ground. The pump 
 apparatus is here represented as exceedingly simple, but in 
 real machines it is very complex and of great power. 
 
 1 19. The pump, on being wrought, forces the water into 
 the cavity. There the water, in endeavouring to escape, 
 operates upon the moveable piston, which it causes slowly 
 to rise with its burden. The pressure thus exerted by the 
 liquid almost exceeds belief; unless the case for the water 
 be of enormous strength, it will be rent in an instant as if 
 made of the weakest material. When the weight has been 
 raised to the required height, a stopcock is turned upon the 
 pipe, and the apparatus remains at rest. The opening of 
 the cock allows the water to gush out, and the weight ac- 
 cordingly sinks.* 
 
 12d. The mode of calculating the power of the hydraulic 
 press is analogous to that for calculating lever powers. 
 Thus, the proportion is estimated between the small bore of 
 the pump and the large bore of the cavity or barrel for the 
 piston. Suppose that the pump has only one thousandth 
 of the area of the barrel, and if a man by means of its lever 
 handle, press its rod down with a force of five hundred 
 pounds, the piston of the barrel will rise with a force of 
 one thousand times five hundred pounds, or more than two 
 hundred tons. A boy working the pump by a long handle, 
 and taking a sufficiency of time, will raise a pressure of 
 thousands of tons. 
 
 * The sheets of the present treatise are smoothed by being pressed 
 between glazed boards in a hydraulic press. It is made entirely of iron, 
 and wrought by two forcing pumps ; by these a man is able by a quar- 
 ter of an hour’s labour to apply from three to four hundred tons of 
 pressure. Each hydraulic press has a safety-valve to permit the escape 
 of water when a certain pressure has been attained ; unless there was 
 a provision of this kind, no strength of metal could endure the pres- 
 sure which might be applied. A good hydraulic press costs from XI 5U 
 to £ 200 . 
 
 88. How is its power calculated ? 
 
 S9. How could the forcing pump be dispensed with ? 
 
AQUEDUCTS FOUNTAINS. 
 
 43 
 
 121. In the hydtaulic press, a force-pump is employed 
 for the sake of convenience ; the same end could be 
 attained by a small column of water of a great elevation, 
 on the principle of pressure in liquids being as vertical 
 height. 
 
 AQUEDUCTS FOUNTAINS. 
 
 122. The tendency in a liquid to find its level has per- 
 mitted the construction of apparatus, consisting of pipes 
 and cisterns, for supplying towns with water. No species 
 of hydraulic machine has been of such great use to man- 
 kind as this apparatus. 
 
 123. In ancient times, the fact of water rising to an uni- 
 form level in every part of its volume, was either not per- 
 fectly understood, or there was a deficiency of materials 
 wherewith to construct the apparatus required for carrying 
 water a great distance. 
 
 124. From whatever cause, towns were in these times 
 supplied with water by means of open canals, either cut in 
 the level ground, or supported on the top of arches built 
 for the purpose. These structures, with their elevated 
 channels, were called aqueducts. In Italy, and some other 
 countries in the south of Europe, the remains of stupen- 
 dous aqueducts, miles in length, still exist. 
 
 125. By a knowledge of the laws of fluids, and by pos- 
 sessing an abundance of lead and iron, we are enabled in 
 the present day to construct apparatus for supplying towns 
 with water in a manner the most effectual and simple, 
 causing a cheap iron or leaden tube, sunk in the ground, 
 to perform the office of the most expensive and magnificent 
 aqueduct. 
 
 126. The method of supplying towns with water consists 
 in leading a pipe of sufficient diameter from a lake, river, 
 or fountain of fresh and pure water, to the place where the 
 supply is required. The iron pipes used for this purpose 
 are composed of a number of short pieces soldered together, 
 
 90. What of aqueducts and their value ? 
 
 91. How do the moderns possess superior advantages ? 
 
44 
 
 HYDRAULICS. 
 
 and extending to any length or in any direction. From 
 these main pipes smaller tubes of lead are led into the 
 
 houses requiring the supply of water ; and by means of 
 these minor tubes, the water may be carried to any point 
 which is not of a higher level than the original fountain 
 affording the supply. 
 
 127. Figure 23 is a representation of the mode of sup- 
 plying towns with water in this convenient manner. A pipe 
 is observed to proceed from a lake on the top of a hill down 
 into a valley, and thence to supply a house situate on the 
 opposite rising ground. From the pipe in its passage across 
 the valley, a small tube is carried to supply an ornamental 
 fountain or jet d’eau. The water spouts from this jet d’eau 
 with a force corresponding to the height of the lake above. 
 
 128. In towns not commanding a supply of water from 
 a sufficient height, the water is forced by an apparatus of 
 pumps to an elevated reservoir, and from that the pipes are 
 laid. When the water is impure, or loaded with muddy 
 particles, it is usual to purify it by filtration at the reser- 
 voir; it is made to filter or ooze through a mass of fine 
 sand, in which the particles of mud are deposited. 
 
 92. Explain the diagram and its purposes. 
 
 93. How is a high level artificially obtained t 
 
 94. By what means may water be purified 1 
 
SPRINGS. 
 
 45 
 
 SPRINGS. 
 
 129. Springs in the ground are natural hydraulic opera- 
 tions, and are accounted for on principles connected with 
 the laws of fluids. 
 
 130. One kind of springs is caused by capillary attraction, 
 or natural attractive force by which liquids rise in small 
 tubes, porous substances, or between flat bodies closely 
 laid towards each other.* 
 
 131. This species of power is a remarkable variety of 
 the mutual attraction of matter, and is as unaccountable as 
 the attraction of gravitation, or the attraction exercised by 
 the loadstone. 
 
 132. We may observe the action of capillary attraction 
 in the case of two plates of glass brought almost in contact 
 
 with each other, and placed 
 with their lower end in a ves- 
 sel of water. Figure 24 re- 
 presents two glass plates placed 
 in this manner in a vessel of 
 water. The plates are some- 
 what separated at one side, 
 and close at the other. We 
 perceive, therefore, that the wa- 
 ter has risen at the close side, 
 and formed a curve in its upper surface from A to D, the 
 degree of height of the liquid being in proportion to the 
 closeness of the plates. The plates being more near each 
 other at B than at C, the water stands higher accordingly 
 at B. 
 
 133. The rising of the water between these two plates 
 of glass is precisely analogous to the rising of water from 
 low situations in the earth through small fissures in rocks, or 
 through porous beds of sand or clay, and so forming springs. 
 
 134. Springs from capillary attraction are believed to be 
 less common and of smaller importance than springs which 
 
 * Laws of Matter and Motion, paragraph 41 to 45. 
 
 95. How are springs acounted for ? 
 
 96. Explain the diagram. 
 
46 
 
 HYDRAULICS. 
 
 originate from the obvious cause of water finding its level. 
 The water which falls in the form of rain sinks rnto the 
 ground in high situations, and finds an outlet at a lower 
 level, though perhaps at a considerable distance. 
 
 135. Some springs are also accounted for by a reference 
 to atmospheric action, but these will form a subject of no- 
 tice under the head Pneumatics. 
 
 HYDRAULICS CONTINUED. 
 
 FRICTION BETWEEN FLUIDS AND SOLIDS. 
 
 136. The flowing of water through pipes, or in natural 
 channels, is liable to be materially afiected by friction. W a- 
 ter flows smoothly, and with least retardation from friction, 
 when the channel is perfectly smooth and straight. Every 
 little inequality which is presented to the liquid, helps to re- 
 tard it, and so likewise does every bend or angle in its path. 
 A smooth leaden pipe will thus convey more water than a 
 wooden pipe of the same capacity. Practically, an allowance 
 is made in the magnitude of pipes for the loss of speed by 
 friction. Where the length of the tube is considerable, and 
 there are several bendings, it is not unusual to allow a third 
 of the capacity for retardation. 
 
 137. By increasing the capacity of pipes, a prodigious 
 gain is secured in the increase of water. The loss from 
 friction on a small tube of an inch diameter of bore is so 
 great, that one of twice the capacity will deliver five times 
 as much water. 
 
 138. The rate at which water flows from an orifice in a 
 reservoir, or containing vessel, is affected by the situation 
 and the shape of the orifice. 
 
 139. The most favourable situation for the orifice is at the 
 bottom of the vessel ; but the velocity of the emission is not 
 in the ratio of the height of the liquid, or of a perpendicu- 
 lar column of particles, and the water presses in all dtrec- 
 
 97. What other sources of springs are named ? 
 
 98. How is the flow of water retarded ? 
 
 99. What proportion of gain by increasing the capacity ? 
 
 100. How is the flow of water affected by the orifice t 
 
FRICTION BETWEEN FLUIDS AND SOLIDS. 47 
 
 tions alike ; there is from all parts of the vessel a general 
 rush as it were to the outlet, thus putting the whole mass 
 in motion. 
 
 140. Although the rush of water at the outlet is not as 
 the ratio of the depth, it depends upon the depth. Thus, 
 if a vessel ten feet high be penetrated at the side on a level 
 with the bottom, and the water stand at two feet and a half 
 within, it will issue outwards with a certain degree of ve- 
 locity. If the height of the water be quadrupled, that is, if 
 the vessel be filled, the velocity will be doubled. In order 
 to obtain a threefold velocity a ninefold depth is necessary, 
 for a fourfold velocity sixteen times the depth is required, 
 and so on. In fact, in whatever pr (portion the velocity of 
 efflux is increased, the. quantity of liquid discharged in a 
 given time must be also increased in the same proportion ; 
 hence the quantity of water discharged conjointly with its 
 degree oi velocity will be increased in proportion to the 
 pressure. There is here a striking coincidence between 
 the descent of water and the relation which exists between 
 the height from which a body falls, and the velocity ac- 
 quired at the end of the fall. 
 
 141. It has been ascertained that water rushes with most 
 advantage from an orifice, when the orifice is in the form 
 of a short round tube inserted into the vessel, and of a length 
 equal to twice its diameter. 
 
 142. It has also been found, that if the pipe, instead of 
 being flush or level with the bottom of the reservoir, en- 
 tered into it to some distance, it had the effect of making 
 the flow of water even less than that which issued through 
 the simple hole without any pipe. The singular fact of a 
 oipe and hole of the same diameter discharging different 
 quantities of water under different circumstances, whilst 
 the head or pressure remains the same, must be accounted 
 for by cross or opposing currents being created by the rush 
 which all fluids make to I he orifice. Currents will thus form 
 from the top and sides of the containing vessel, and by 
 
 101. How and what ratio may the velocity be varied 1 
 
 102. What of a short tube, and why the difference ? 
 
 103. What if the tube project into the interior 1 
 
48 
 
 HYDRAULICS. 
 
 their inertia they will cross each other, and thus impede 
 the descent of the perpendicular column, causing the wa- 
 ter which issues to run in a screw-like form; this, however, 
 is in a great measure obviated by the application of a short 
 tube from the aperture. That the projection of the tube too 
 far into the interior of the vessel should make the flow less 
 than if there were no pipe at all, may be thus explained : — 
 The columns which descend from near the outside of the 
 vessel, by turning up again to reach the discharging orifice, 
 come into more direct opposition to the motion of the cen- 
 tral descending columns, whilst they are at the same time 
 themselves compelled to turn suddenly in opposition to 
 their own inertia before they can enter the pipe. Thus, 
 the discharge is more effectually impeded than if it were 
 proceeding from a mere opening in the bottom of the vessel. 
 
 143. The tube for the discharge of water should not 
 only be short and round, but also trumpet-mouthed or 
 funnel-shaped, both internally and externally, that being the 
 form which admits the flow of liquid with the least possible 
 retardation. 
 
 144. The effects of friction between liquids and solids 
 are no where so conspicuous as in the flowing of rivers. 
 The natural tendency in the water to descend at a certain 
 speed, is limited by the roughness of the bottom, bends in 
 the course of the stream, and small projections on the 
 banks. From these causes, the water in a river flows with 
 different velocities at different parts in any vertical section 
 across the current. It flows at a slower rate of speed at 
 and near the bottom than at the surface, and also slower at 
 the sides than at the middle. 
 
 145. The resistance which a body moving in liquid 
 meets with, when it comes in contact with a solid, is as the 
 square of the velocity of the moving body ; in other words, 
 the resistance is not twice but four times with a double 
 rate of speed. This is easily explained : — 
 
 146. A vessel moving at the rate of one mile per houi 
 displaces a certain quantity of water, and with a certain 
 
 104. What is the best form of the tube ? 
 
 105. What of the flowing of rivers ? 
 
 106. What relation between resistance and speed 1 
 
ACTION OF WATER IN RIVERS. 
 
 49 
 
 velocity ; if it move twice as fast, it of course displaces 
 twice as many particles in the same time, and requires to 
 be moved by twice the force on that account; but it also 
 displaces every particle with a double velocity, and requires 
 another doubling of the power on this account; the power 
 thus twice doubled, becomes a power of four. When the 
 body is moved with a speed of three or four, a force of nine 
 or sixteen is wanted, and so on. Thus, the resistance in- 
 creases as the square of the speed. 
 
 147. This important law suggests practical hints of con- 
 siderable importance. For instance, in steam navigation, 
 if an engine of fifty horse power impel a vessel at the rate 
 of seven miles an hour, it would require two of the same 
 power to drive her ten miles an hour, and three such to 
 drive her twelve miles an hour. Hence the enormous 
 expense of fuel attending the gaining of a high degree of 
 velocity. 
 
 ACTION OF WATER IN RIVERS. 
 
 148. In cases where it is desirable to preserve the banks 
 of rivers from injury, either from the regular action of tfie 
 current or from floods, the water ought to be allowed a free 
 open channel with banks of a very gradual descent. The 
 utmost violence of water in a stale of motion may be ren- 
 dered comparatively harmless, by allowing the flood or 
 torrent ,to expend itself on a sloping or shelving shore. 
 Inattention to this simple fact in hydraulics frequently 
 causes much destruction to property on the banks of rivers. 
 
 149. A very small fixed obstacle, such as a stone or 
 pebble, may partially impede and turn aside a brook of a 
 slow current. The water, by striking on a stone at one 
 side, is bent aside to the opposite bank, a little farther 
 down ; there it strikes upon the bank, and is returned to 
 the side it formerly struck. Thus, proceeding in currents 
 from side to side, the banks become worn down at parti- 
 cular places, and, in time, a new and serpentine course is 
 given to the stream. In the case of rivers flowing with 
 
 107. How is this important in steam navigation 1 
 
 108. What of the action of water in rivers ? 
 
 109. What of straight and winding rivers? 
 
50 
 
 HYDRAULICS. 
 
 considerable velocity, impediments of this kind are usually 
 overcome, and the stream pursues its straight onward 
 course, dashing down all obstacles to its progress. Thus, 
 rivers are generally winding in their course in flat countries, 
 and straight in mountainous regions. 
 
 150. It sometimes happens that the water at the surface 
 of a river may be moving in one direction, while the water 
 at the bottom is flowing in an opposite direction. This is 
 an exceedingly interesting phenomenon, which is observed 
 to occur in certain rivers communicating with the sea, and 
 is caused by the action of the tides and the difference of 
 specific gravity in salt and fresh water. When the tide is 
 flowing inwards, the salt water rushes up the channel of 
 the river, but not at such a depth as to stem the current 
 of fresh water, which, being lighter, floats on the top of 
 the salt water, and pursues its downward course to the 
 ocean. In those instances in which there is no great dis- 
 turbance of the two liquids, the fresh water, by its specific 
 lightness, floats on the surface of the sea to a distance of 
 many miles from the land. 
 
 WAVES. 
 
 151. Waves are the risings and fallings of the water, 
 caused by some power, such as the blowing of the wind. 
 The power, whatever it happen to be, communicates a force 
 to the mass of liquid, and a series of undulations is the 
 consequence. 
 
 152. These undulations, or waves, exhibit the transmis- 
 sion of the communicated force. The force does not 
 advance or alter the lateral position of the water at any 
 given point; it only alters the water in its vertical position, 
 or in relation to its depth. When therefore waves advance, 
 the water does not advance with them ; the water but rises 
 and falls, and assumes the figure of undulations on its 
 surface. When the undulations approach the shore, the 
 water then acquires a progressive motion, where it is shal- 
 ,ow, and by friction on the bottom or impulsion against 
 
 110. How are under currents explained 1 
 
 111. What is peculiar in the undulations of waves ? 
 
ALTERATION OF TEMPERATURE. 
 
 51 
 
 the shore, the communicated force is exhausted. 4 lie 
 shaking of a carpet affords an exact representation of the 
 action of waves or undulations. 
 
 153. Waves are comparatively superficial ; they seldom, 
 even in the greatest storms, rise to a height of more than 
 twelve feet above the level of calm water, and make an 
 equal descent beneath, making altogether an appearance of 
 twenty-four feet ; at eight or ten feet below the hollow or 
 trough of the waves the water is tranquil. Waves “ moun- 
 tains high” is only a figure of speech. 
 
 ALTERATION OF TEMPERATURE. 
 
 154. By altering the temperature of liquid bodies, they 
 become liable to peculiar laws, and exhibit peculiar pheno- 
 mena. 
 
 155. At a temperature of 40 degrees of Fahrenheit’s 
 thermometer, water is at the point of greatest density. 
 When the temperature is reduced below this point, the 
 liquid gradually increases in volume till it reaches 32, 
 when it freezes. When the temperature is raised above 
 40, the volume increases till it reaches the boiling point, 
 at which it has extended to the extent of l-22d additional 
 to its bulk. 
 
 156. In consequence of this expansibility in heating, hot 
 or warm water is specifically lighter than cold water ; there- 
 fore, in heating any mass of water in a vessel over a fire, 
 the lighter or warmed particles rise to the top, while the 
 cold and heavy particles sink to the bottom to be heated, 
 and to rise in their turn. In this manner the process of 
 heating proceeds, until all the particles are of an uniform 
 temperature, which is at the boiling point, when the liquid 
 gradually flies off in steam. 
 
 157. If water be heated by the action of fire, or the sun’s 
 rays on its upper surface, the mass is longer in attaining 
 the vaporific point than when heated below, because water 
 is a bad conductor of heat, and therefore the heat penetrates 
 with difficulty through the upper stratum of warmed liquid to 
 
 1 12. What of the height of waves ? 
 
 113. How is the density of water in different temperatures? 
 
 114. What of gradually heating water over the fire 1 
 
52 
 
 HYDRAULICS. 
 
 reach that which is beneath ; and if the mass be very large, 
 as for instance the ocean, no intensity of heat applied above 
 can warm it throughout, or to any considerable depth. 
 
 158. In the present treatise, our only consideration is 
 the motion of the liquid while heating, or in consequence 
 of the application of heat. 
 
 15i». This motion consists in the rising of the heated 
 portion of the water to the top, where it remains till cooled, 
 when it is liable to be displaced from its position. 
 
 160. No mass of water can possibly be at rest, if of a 
 higher temperature below than above, so long as the tem- 
 perature exceeds 40 degrees. An upward and descending 
 motion continues till the uniform temperature has been 
 established, whatever be the size or shape of the containing 
 vessel. 
 
 161. In consequence of the tendency in water to assume 
 an uniform temperature in all parts of its volume, a plan 
 has been devised for heating houses by means of a hot- 
 water apparatus. A long winding iron pipe is carried 
 from the top of a house to the bottom ; there it passes 
 through a fire, and thence rises to the top of the house 
 again, where the two extremities may be made to meet in 
 a small cistern or filler. In such a tube, water may be 
 made to boil, or at least to attain a high temperature 
 throughout its whole extent. 
 
 162. Figure 25 is a rude outline of a hot-water apparatus 
 
 of this kind. P is the 
 iron pipe, with the fil- 
 er T at the top. F is 
 the fire beneath, acting 
 on the pipe. The pro- 
 jections R R give an 
 
 the pipe into rooms or 
 passages. In the appa- 
 ratus as usually erect- 
 ed, the pipes are of 
 
 1 15. How is it when heated at its upper surface ? 
 
 116. What of the motion of water by heat ? 
 
 117. Explain the diagram and its principles. 
 
AIR. 
 
 53 
 
 about an inch in diameter, and are made to wind in all 
 directions round the walls of rooms and passages, in their 
 progress from the top to the bottom of the edifice. The 
 degree of heat which is maintained in the water warms the 
 atmosphere in the apartments, and obviates the use of fires. 
 
 163. Certain currents or sets of the ocean are known to 
 be produced by the etfort to attain an equability of tempe- 
 rature throughout. The power of the sun’s rays at and 
 near the equator heats the sea in that part of its volume, to 
 the depth of two or three hundred feet. This upper stra- 
 tum of heated water flows in currents towards the north 
 and south poles, and there to a certain extent tempers the 
 severity of the cold. The waters of the northern and 
 southern tracts of ocean, displaced by these currents, neces- 
 sarily sink below them, and push on towards the equator, 
 to supply the deficiency caused by the departure of the 
 waters above. Thus, in the economy of nature we see a 
 process in constant action precisely the same in principle 
 as that upon which the artificial hot-water apparatus has 
 been established. 
 
 Having now discussed Hydrostatics and Hydraulics, we 
 come to the kindred subject of Pneumatics, for which, as 
 will be observed, we have reserved a notice of - certain 
 hydraulic machines involving pneumatical agency. 
 
 PNEUMATICS. 
 
 GENERAL DEFINITIONS. 
 
 164. Pneumatics, from the Greek word Pneuma, breath 
 or air, is the name of the department of science which 
 relates to the weight, pressure, or motion of air, or of any 
 aeriform or gaseous fluids. 
 
 165. It was anciently supposed that the air of the atmo- 
 sphere was an element or simple substance in nature. It 
 is now satisfactorily established that air is not an elemen- 
 
 118. How do the same principles act in nature? 
 
 119. Define Pneumatics. 
 
 120. Is air compounded, and of what elements ? 
 
54 
 
 PNEUMATICS. 
 
 tary body, but is composed of certain gases in intimate 
 union, and these gases can be separated from each other by 
 a process in art. The investigation of this subject belongs 
 to Chemistry.* 
 
 166. Air, in its common condition, is a thin transparent 
 fluid, so subtile that it cannot be handled, and when at rest 
 it cannot be felt. 
 
 167. That it is a body, however, is quite obvious, because 
 we feel its impression or force when agitated as wind, or 
 when we wave our hand quickly through it. In the quick 
 motion of the hand, we feel that it is partially opposed by 
 something; and in inhaling breath into the lungs, we feel 
 t hat we are drawing something through the mouth — that 
 something is air. 
 
 168. Air, like every other substance, whether solid or 
 fluid, possesses a certain gravity or weight. The weight of 
 air certainly, bulk for bulk, is much less than that of water; 
 still the weight may be accurately computed. A bottle full 
 of air weighs heavier in a balance than a bottle of the same 
 capacity from which the air has been extracted. 
 
 169. A cubic foot of water, as has been mentioned (78), 
 
 * Pure air consists almost entirely of nitrogen and oxygen gases, 
 with a very small portion of carbonic acid gas. Of 100 parts of air, 
 reckoning by weight, 75.55 parts are nitrogen, 23.32 oxygen, and 1.13 
 carbonic acid and watery vapour. Both as respects weight and bulk, 
 nitrogen forms the chief ingredient of the atmosphere. Air is rendered 
 impure by fetid odours and other exhalations, which it has the power 
 of holding to a certain extent. Animal respiration chemically changes 
 the constitution of air ; oxygen is destroyed or deposited in the blood, 
 and carbonic acid is given out in its stead. Thus, we inhale pure air, 
 and exhale that which is foul. As every full-grown person inhales 
 about 400 cubic inches of air per minute, the tendency of respiration 
 (not to speak of loss by combustion) to deteriorate the atmosphere may 
 be easily conceived. Nature, however, abounds in provisions for pre- 
 serving atmospheric purity. We need here only notice the beneficial 
 effects of winds, the vast extent of ocean over whose surface is an 
 inexhaustible reservoir of pure air, the purification by electric agency, 
 and the influence of light or the solar rays. By whatever means effected, 
 it is certain, from experiment, that the air now consists of the same 
 ingredients, and in the same proportion, as it did fifty years ago. 
 
 121. How is the material character of air proved ? 
 
 122. How is the purification of air explained 1 (Note). 
 
 123. How is it proved that air has weight ? 
 
 121. What relation does it bear to water in gravity 1 
 
GENERAL DEFINITIONS. 
 
 ■weighs 1000 ounces. A cubic foot of air weighs only 523 
 grains, being a little more than one ounce ; water, therefore, 
 is about 840 times heavier than the air of our atmosphere. 
 
 170. Inasmuch as water is a standard for comparing the 
 gravities of liquids, air is a standard in the same respect for 
 all aerial substances. 
 
 171. The specific gravity of air being denominated 
 1000, oxygen gas is 1111 ; nitrogen gas 972; hydrogen gas 
 69; and carbonic acid gas 1529. The lightest of these 
 kinds of gas, therefore, is hydrogen, and the heaviest car- 
 bonic acid. Hence if indefinite quantities of these aeriform 
 bodies were placed in a vessel, or in an apartment, we 
 should find, that, after certain portions had gone into inti- 
 mate union, according to the laws by which they combine, 
 the surplus portions of each would assume relative positions 
 according to their respective weights — the heaviest to the 
 bottom, and the lightest to the top. Such an experiment 
 would resemble that previously noticed, of the mixture of 
 mercury, oil, water, and spirits (74). 
 
 172. Air and all kinds of gases are rendered lighter by 
 the application of heat, for then the particles in the mass 
 are repelled from each other, and occupy a greater space; 
 this process of lightening or thinning is called rarefaction. 
 Rarefied air, being specifically lightest, mounts above that 
 of a common density. The warmest air is always at the 
 top of a room, and the coldest at the bottom. 
 
 173. Air is distinguished from water not only by its 
 extreme comparative lightness, but the property of elasti- 
 city ; it is a compressible and elastic fluid. 
 
 174. When any quantity of air is compressed into a 
 smaller space than it naturally occupies, it will return to 
 its natural bulk on the pressure being withdrawn. 
 
 175. A small bladder of air may be squeezed between 
 the hands so as to be considerably reduced in size; and on 
 opening the hands again, and wilhdrawing the pressure, it 
 will instantly resume its former bulk. If a metallic tube 
 or barrel be fitted with a moveable plug or piston, which is 
 
 125. How is the specific gravity of gases computed ? 
 
 126. What effect does heat produce on air ? 
 
 127. What of the elasticity of air, with an example I 
 
5G 
 
 PNEUMATICS. 
 
 made to work in it per ectly air-tight, the air which occu- 
 pies the space between the top and the bottom of this 
 barrel when the piston enters, can be compressed to a hun- 
 dredth part, or even less, of its usual bulk. If the force, 
 however, by which the piston is pushed down, be with- 
 drawn, the air, by its elasticity, will force it up again with 
 a power equal to that by which its descent was resisted. 
 
 170. In proportion as any given volume of air is dimin- 
 ished by pressure, its elastic force is increased; in other 
 words, the elastic force or elasticity of air is proportional 
 to its density. 
 
 THE ATMOSPHERE. 
 
 177. The air, as formerly expressed, is a great ocean 
 wrapped round the earth to a depth of from forty-five to 
 fifty miles above the highest mountains, and forms a men- 
 struum which is essential to the existence of all animals 
 and plants. 
 
 178. This ocean of air penetrates into all unoccupied 
 places, in the same manner as water flows into all crevices 
 and holes beneath the level of its surface ; and it also finds 
 a place in the bodies of animals, plants, and liquid sub- 
 stances ; hardly any thing, indeed, that we see in nature or 
 art, is free from air, unless force has been employed to 
 extract it. 
 
 179. The height of the atmosphere, though usually esti- 
 mated at forty-five or fifty miles, is in reality unknown. The 
 highest point above the level of the sea, which has ever been 
 reached by any human being, is 21,000 feet, which has 
 been attained in a balloon. 
 
 180. It is only conjectured, from the refraction of the 
 sun’s rays and other circumstances, that the height of the 
 atmosphere is about fifty miles. At and near the level of 
 the ocean it is most dense, in the same manner as water at 
 the bottom of the sea is more dense than it is at the surface 
 on account of the incumbent pressure. As we ascend 
 
 128. How is the elasticity of gases computed ? 
 
 129. What of the atmosphere and its importance and universality T 
 
 130. What, of its height and density at different altitudes ? 
 
THE ATMOSPHERE. 
 
 57 
 
 mountains, or in any other way penetrate upwards into the 
 atmosphere, the air becomes gradually less dense, and so 
 thin is it at the height of three miles on the summit of 
 Mont Blanc, that breathing is there performed with some 
 difficulty. Beyond this limited height, the density of the 
 air continues to diminish, and at the elevation of about 
 fifty miles, it is believed to terminate. 
 
 181. The extreme height of the atmosphere is not ob- 
 servable from the situation in which we are placed on the 
 earth. Our eye, on being cast upwards, perceives only a 
 vast expanded vault, tinted with a deep but delicate blue 
 colour; and this in common language is called the sky. 
 The blueness so apparent to our sense of sight is the action 
 of the rays of light upon the thin fluid of the upper atmo- 
 sphere, and the brightness is in proportion to the absence 
 of clouds and other watery vapours 
 
 182. In proportion as the spectator rises above the surface 
 of the earth, and has less air above him, and that very rare, 
 the blue tint gradually disappears, and if he could attain a 
 height at which there is no air, say at above fifty miles in 
 height, the sky would appear perfectly dark or black. Tra- 
 vellers who have ascended to great heights on lofty moun- 
 tains, describe the appearance of the sky from these elevated 
 stations as dark or of a blackish hue.* 
 
 183. The atmosphere possesses the capacity for absorb- 
 ing and sustaining moisture, but only to a limited extent. 
 When saturated to a certain degree, it is relieved by the 
 falling of the moisture in the form of rain. It is calculated 
 that the whole atmosphere round the globe could not retain 
 at one time more moisture than would produce about six 
 or seven inches of rain. 
 
 184. By an elevation of temperature, the capacity of the 
 atmosphere to absorb and sustain moisture is increased, and 
 by a lowering of temperature, decreased. Cold breezes, 
 by lowering the temperature of the air, cause the aeriform 
 moisture to assume the appearance of clouds, and then to 
 
 * See Treatise on Optics. 
 
 131. What of the blueness of the sky ? 
 
 132. What of moisture and the capacity of the atmosphere ? 
 
 133. How does temperature affect, it ? 
 
58 
 
 PNEUMATICS. 
 
 fall as rain. Clouds disappear in fine weather, and again 
 appear when it is cold. When a cloud descends on the 
 side of a hill, it gradually enters a region of warmth or 
 higher temperature, and disappears; but when a cloud 
 ascends a hill, it enters a region of cold, and, consequently, 
 being condensed, it is precipitated as a shower of rain. 
 Hence the old'familiar rhyme — 
 
 When the clouds go up the hill, 
 
 They’ll send down water to turn a mill. 
 
 185. Thus, the atmosphere is the great field in which 
 the varied phenomena of clouds, rainbows, meteors, and 
 other appearances in the sky, are exhibited. As respects 
 the phenomena of light itself, the atmosphere acts a most 
 important part. Received in it, the rays of the sun are 
 harmoniously diffused in all directions through it,as through 
 a thick crystalline body, and afford light in situations which 
 otherwise would be in darkness. The atmosphere, there- 
 fore, which an ignorant person might suppose to be nothing, 
 is as invaluable a constituent of creation as land or water; 
 it is a fluid essential for the existence of animals and 
 plants ; it affords a field for all kinds of meteorological phe- 
 nomena ; it is a supporter of combustion, and an important 
 agent for the diffusion of heat and light, and also for the 
 transmission of sound. 
 
 We shall now briefly enumerate the laws of aerial fluids, 
 which it will be observed resemble those of liquid bodies. 
 
 PNEUMATICS— CONTINUED. 
 
 LAWS OF AIR. 
 
 186. First — The pressure of the air is equal in all direc- 
 tions: Second — Its degree of pressure depends on the ver- 
 tical height or depth, and at any place is proportional to its 
 density : 'fhird — Its surface is level in all parts of its 
 
 134. What phenomena are dependent on the atmosphere 1 
 
 135. Name the law's of aerial fluids. 
 
PRESSURE OF AIR. 
 
 50 
 
 volume: Fourth — It affords support, according to its den- 
 sity and to the weight of the fluid displaced. 
 
 1ST. That air presses equally in all directions, may be 
 rendered evident by filling a bladder with that fluid, and 
 then pressing upon it so as almost to make it burst. The 
 pressure is freely communicated through the mass, as in 
 the case of the bag of water (21), and it will be observed 
 that the confined air will rush out with equal impetuosity 
 at whatever part you make a hole in the surface. 
 
 188. The level of surface of air is less perfect than the 
 uniform level of water, on account of the greater elasticity 
 of the substance. In a series of strata of air of different 
 densities, one above the other, a small portion of each 
 mingles with those which immediately adjoin it — the pani- 
 cles of one commingle to a certain extent with those of 
 another. There is thus, as respects aerial bodies, a modi- 
 ficaiion of the law of uniform levelness of surface in all 
 parts of the volume of fluid. 
 
 PRESSURE OF AIR. 
 
 189. The pressure depending on the vertical height or 
 depth of air, is an important property in the atmosphere, 
 and on it depends the explanation of numerous phen imena. 
 
 190. Air being a substance possessing gravity, it must 
 of necessity press downwards in the direction ol the centre 
 of the earth; and therefore the degree of pressure on any 
 given point will be equal to the weight of the column of 
 air above the point, and proportional to the density of the 
 air at that point. 
 
 191. The idea of the atmosphere possessing the property 
 of gravity or pressure, is of comparatively modern date. No 
 such notion was entertained by the ancients, in consequence 
 of living animals being observed to move with perfect ease 
 in all directions, and because there was no other appearance 
 in nature calculated to suggest it to their minds. 
 
 192. It was, however, remarked, that, when the air w : as 
 
 • 36. What of the equal pressure of air, and its exact level? 
 137. How is atmospheric pressure computed and proved ? ' 
 
60 
 
 PNEUMATICS. 
 
 sucked out of a small glass tube, the lower end of which 
 was immersed in water, the water rushed up into the tube 
 and occupied the situation of the displaced air. In conse- 
 quence of this and similar phenomena, it was alleged as a 
 doctrine in physics, that “ nature abhors a vacuum.” 
 
 193. A vacuum is a space destitute of air or any other 
 kind of matter; and the notion was, that whenever by any 
 chance such an empty space was found, nature interposed 
 with all imaginable haste to fill it. With this very rude 
 idea, pumps were formed to raise water, the rising of the 
 water in these instruments being ascribed simply to nature’s 
 abhorrence of a vacuum. At length it was discovered that 
 water could not be drawn up by a pump above a height 
 of about thirty-two feet, and that a vacuum above that ele- 
 vation remained unfilled; whereupon the terms of the doc- 
 trine were changed, and it was said that nature abhorred a 
 vacuum only to a height of thirty-two feet, but no farther. 
 
 194. This explanation was seemingly unphilosophical, 
 and men’s minds being carefully turned to the subject, 
 various experiments were performed, and the important 
 truth became manifest, that the atmosphere possessed gra- 
 vity or pressure ; also, that that pressure w'as the sole cause 
 of the rushing of liquids into tubes exhausted of air — the 
 height of the ascending liquids being in every case limited 
 by the degree of pressure of the incumbent atmosphere. 
 Thus, the discovery of a simple truth in science at once 
 abolished the fantastic doctrine of nature’s abhorrence of a 
 vacuum, and all the laboured sophistry with which it was 
 supported.* Nature has no dislike to a vacuum ; a vacuum 
 will occur in all situations from which solids or fluids are 
 accidentally or artificially excluded. 
 
 195. The degree of pressure imposed by the atmosphere 
 on any given spot on the earth’s surface, as already noticed 
 (190), is equal to the weight of the column of air above 
 
 * This great discovery in physical science was made by Torricelli, 
 an eminent Italian mathematician, about the year 1644. It was sug- 
 gested by an ineffectual attempt to raise water from a deep well near 
 Florence, by means of a pump of a greater height than thirty-two feet. 
 
 138. What of the maxim, “ nature abhors a vacuum ?” 
 
 139. How did Torricelli discover atmospheric pressure 1 
 
PRESSURE OF AIR. 
 
 Cl 
 
 that spot, and is also proportional to the density of the air 
 at the place. The atmosphere is deepest or of greatest 
 vertical height at the level of the ocean, and there it exerts 
 the greatest pressure. The pressure of the air at the level 
 of the sea is usually reckoned to be about 15 pounds on 
 every square inch.* 
 
 19G. The pressure of 15 lbs. to the square inch refers to 
 every shape of surface at or near the sea’s level. The 
 pressure is sidewise, upward, oblique, and in every other 
 direction, as well as downward, because fluids press equally 
 in all directions. Thus, in every crevice, nook, or vessel, 
 in which air happens to be, the pressure is equally intense. 
 The human being, for example, sustains the pressure of 15 
 lbs. to the square inch all over his person, and this is a 
 load under which he could not possibly move,t unless the 
 pressure was also exerted in the interior of his body, or 
 through his whole system of muscles, viscera, and bones, 
 by which means the external pressure is counteracted, and 
 he feels no pressure whatever. 
 
 197. if, however, the air by any means 
 be withdrawn from the interior of any object 
 that object becomes immediately susceptible 
 oi the external atmospheric pressure. There 
 are many familiar examples of this pressure 
 around us. One of the most common con- 
 sists in causing a thimble to adhere to the 
 hand by sucking the air from beneath it : 
 the adhesion is the result of the pressure of 
 the atmosphere on the exhausted space on 
 the hand. Another consists in lifting a stone 
 by means of a sucker, formed of a string and 
 Figure 26. a wetted piece of leather, as in the accompa- 
 
 * The actual pressure varies from 14 lbs. to 15 lbs., according to 
 circumstances. By various authorities it is stated at 14.7 lbs. For 
 convenience, we siate it throughout in the text at 15 lbs. 
 
 t The body of a man has a surface of 2000 square inches, and there- 
 fore the pressure upon him is equal to 30,000 lbs. 
 
 140. What of the degree of this pressure and where the greatest? 
 
 141. How much to the square inch ? 
 
 142. In what directions is the pressure exerted ? 
 
 143. Why do we not feel this enormous pressure ? 
 
 144. Explain the diagram. 
 
62 
 
 PNEUMATICS. 
 
 nying figure. The wetted leather is in this case pressed 
 down upon the stone, and the string is then pulled: if air 
 were admitted under the end of the string, the sucker would 
 come off, but none being admitted, the atmosphere presses 
 on the sucker, a rigid adhesion of the sucker to the stone 
 is produced, and the stone, if not too heavy, is lifted. 
 
 08. The surgical process of cupping is upon the same 
 principle. A small glass cup is held with its mouth near 
 the part to be operated on, and the air being consumed 
 within it by a lighted taper, it is instantly applied, and ad- 
 heres with great force. The part having been previously 
 lanced, the blood, rushing to fill the vacuum, enters the cup 
 in copious small streams. The feeling endured in cupping 
 is that of considerable weight. 
 
 10‘J. The feet of fiies and some other insects are formed 
 on the principle of the sucker, by which means they are 
 enabled to walk and run with security on the ceiling of an 
 apartment, back downwards, or on an upright and smooth 
 pane of glass. At each step in advance, they procure a 
 hold by the formation of a vacuum or air-tight space beneath 
 their leet. The rapidity with which these vacuums or air- 
 tightnesses are formed and destroyed is an exceedingly 
 interesting phenomenon in the economy of the animal, and 
 cannot be rivalled by the utmost efforts of human skill. On 
 a very moderate computation, a fly, in travelling six feet in 
 the space of a minute, creates and destroys as many as 
 10,000 vacuums. When deprived of the outer extremities 
 of its legs, on which the apparatus for adhesion is situated, 
 a fly can walk without any apparent difficulty on a hori- 
 zontal surface, such as a table, but is quite incapable of 
 adhering to the roof, or of climbing any upright surface. 
 
 200. Limpets, snails, and some other crustaceous animals, 
 adhere to rocks and stones, by causing a vacuum within 
 their shells, which they accomplish by shrinking into a 
 smaller bulk ; by this simple contrivance, nature has effec- 
 tually provided for their safe adhesion to their appropriate 
 places of residence. 
 
 145. What other examples are cited ? 
 
 146. What of flies walking on the ceiling ? 
 
 147. How is a vacuum formed by certain animals 1 
 
THE AIR-PUMP. 
 
 63 
 
 THE AIR-PUMP. 
 
 201. Air may be artificially withdrawn from a containing 
 vessel by means of an apparatus called the air-pump. This 
 apparatus is usually small, lor standing on a table, and con- 
 sists chiefly of a glass jar called a receiver, placed mouth 
 downwards over a flat surface, and with a small brass pump 
 to draw the air from it. The annexed cut, Figure 27, 
 
 represents an outline section 
 of an air-pump, the working 
 of which may be described. 
 R is the glass receiver stand- 
 ing on a flat and smooth 
 plate SS,and fitting so exactly 
 that no air can penetrate be- 
 tween the edges of the recei- 
 ver and the plate. In the plate 
 SS, th; re is a channel AB 
 issuing into the barrel of a 
 pump. P is the piston of the 
 pump, with its rod C above, 
 which is moved upwards and 
 downwards bv a handle and 
 winch. The rod C works in 
 a tight collar D. At the bot- 
 Figure 27. tom Q f the pump there is a 
 
 »alve V, by which the air is to escape, and prevented from 
 again entering. On depressing the piston, a portion of the 
 contained air is expelled by the valve, and on raising the 
 piston again to its position at the top, another column ■ f 
 air is admitted from the receiver into the pump, which is 
 expelled in its turn. Thus, by a process of expulsion, the 
 air in the receiver becomes at every stroke downwards more 
 rire, till at length a vacuum sufficient for all practical pur- 
 poses is established. The valve V, which opens outwards, 
 is kept forcibly shut at every rising of the piston by external 
 pressure of the atmosphere. 
 
 148. Describe an air-pump, and its use. 
 
 149. What experiments are cited 1 
 
04 
 
 PNEUMATICS. 
 
 202. By means of the air-pump, a number of interesting 
 experiments in pneumatics may be performed. For exam- 
 ple, if a bladder, half full of air, and tightly tied at the neck, 
 be placed under the receiver, and a vacuum then produced, 
 the air in the bladder will expand by the removal of the 
 external pressure, and seem as if ready to burst. Dried 
 raisins, during a similar operation, will expand, and have 
 all the plumpness of new fruit ; and an egg, by the expan- 
 sion of its confined air, will explode. Any small animals, 
 such as mice, placed below the receiver, and deprived of 
 air, will immediately die, both from want of breath and the 
 expansion of their bodies. 
 
 203. The atmosphere serves to retard the falling of bodies 
 of a light and porous nature, and, therefore, in the exhausted 
 receiver of an air-pump, all such bodies descend with the 
 same velocity as bodies of a heavy compact nature. A piece 
 of coin and a feather let fall at the same instant of time, 
 from a hook within the top of an exhausted receiver, will 
 strike the bottom at the same moment.* 
 
 204. That atmospheric air is useful for the transmission 
 of sound, in the absence of other media, is also exemplified 
 by the air-pump. If we place a small bell in a receiver in 
 such a manner as to admit of being rung easily from the 
 outside, without admitting air into the inside, whilst the 
 receiver is full of air the sound of the bell will be distinctly 
 heard ; but after the receiver has been exhausted, and 
 although the bell be struck with the same force, the sound 
 will be inaudible, or nearly so. If a small portion of air 
 be admitted, it will be faintly heard, and it will gradually 
 increase, according to the quantity of air which is allowed 
 to enter the receiver. Thus, we are indebted to the air as 
 a medium for conveying to us the sound of each other’s 
 voices, and all the melodious notes which constitute music. 
 
 205. The act of inspiring and expiring air resembles the 
 alternating action of an air-pump. The air, on being drawn 
 in through the appropriate tubes, fills the lungs, and the 
 
 * Laws of Matter and Motion, paragraphs 173, 174, 175. 
 
 150. How is air shown to be necessary for transmitting sound l 
 
 151. What animal function resembles the air-pump? 
 
AIR-GUN'. 65 
 
 chest is expanded ; having performed its office, the air is 
 expelled in an impure condition, leaving a partial vacuum 
 within, until another inspiration causes another expansion. 
 
 206. A machine, called a condensing pump or syringe, 
 is formed tor the purpose of 
 showing experiments with air 
 more dense than that of the 
 common atmosphere. The ap- 
 paratus, which is represented 
 in Figure 28, consists of a 
 close glass jar or receiver fixed 
 in a framp. A wire and hook 
 serve to communicate with the 
 interior during the perform- 
 ance of experiments. The 
 syringe i is wrought by a piston 
 
 Figure 28. with ^g h an di e From the 
 
 bottom of the syringe there is a tube communicating with 
 the interior of the receiver. When the piston is raised, a 
 valve beneath opening inwards admits air into the cylinder 
 of the syringe, and when it is depressed, this quantity of 
 air is forced into the receiver; by the alternate raising and 
 depressing of the piston, an immense quantity of air is 
 forced into the receiver. 
 
 207. The elastic force of air so condensed is very great, 
 and is employed for the projection of balls from an instru- 
 ment called an air-gun. A certain quantity of compressed 
 air is confined in a chamber at the inner end of the barrel, 
 and when allowed to escape by touching a valve, a bullet 
 is projected with a force resembling that by gunpowder. 
 
 208. The explosive force of gunpowder itself is nothing 
 else than the sudden disengagement of air from the particles 
 of the powder. 
 
 152. Explain the diagram. 
 
 153. What of an air-gun, and of gunpowder itself? 
 
66 
 
 PNEUMATICS. 
 
 PNEUMATICS CONTINUED. 
 
 PRESSURE OF AIR ON SOLIDS AND LIQUIDS. 
 
 209. The pressure of the atmosphere affects all liquid 
 as well as solid bodies. The load of the incumbent air is 
 as sensibly exerted within any given mass of water as on 
 the surface. Thus, atmospheric pressure keeps water and 
 other liquids at the density they are usually seen to possess. 
 
 210. If a glass be filled with water, and placed under the 
 receiver of an air-pump, the abstraction of the air, by the 
 removal of the atmospheric pressure, will cause the water 
 to expand or become less dense, and it will overflow the 
 vessel in which it is contained. 
 
 211. Water in its ordinary condition contains a certain 
 quantity of particles of air mixed up with it. When the 
 atmospheric pressure is lightened, these particles o air 
 expand, and being of a less specific gravity than water, they 
 mount to the top of the liquid in the form of small globules, 
 and so fly off. The same effect is produced by expanding 
 water by means of heat ; the globules of air rise to the sur- 
 face, and escape or remain attached to the inside of the 
 vessel. Crystal bottles of, water may be observed to be 
 covered inside with small air-bells when the weather be- 
 comes suddenly light or warm. Water which has been 
 boiled is comparatively free of air, and has an insipid 
 flavour. 
 
 212. Certain gases are generated in some liquors, such 
 as in porter, beer, and champagne wine, and unless the 
 bottles in which they are contained be of sufficient strength 
 to endure the expansive tendency, they will burst. On 
 drawing the cork from a bottle of one of these liquors, the 
 confined gas or air is suffered to expand, and the contents 
 gush forth, a mixture of froth and liquid. If the liquid 
 remain in an open glass for a short time, a large portion of 
 
 154. How is air shown to exert pressure within liquids ? 
 
 155. What proofs have we that water contains air ? 
 
 156. What of gases generated in certain liquors ? 
 
PRESSURE ON SOLIDS AND LIQUIDS. 
 
 07 
 
 the long-confined gases escapes into the atmosphere, and 
 the liquor seems flat or dead. A portion of confined air, 
 however, still remains in consequence of the atmospheric 
 pressure. If we take a glass of ginger-beer which seems 
 quite dead, and place it under the exhausted receiver of an 
 air-pump, it will again froth and appear brisk. 
 
 213. Some mineral waters on springing from the ground 
 sparkle like beer. These most likely rise from great 
 depths, where the incumbent pressure is considerable, and 
 on attaining the surface of the earth they expand, and give 
 forth the air pent up in their mass. 
 
 214. If a bladder full of air be carried from a low situa- 
 tion to a great height, the contained air will expand, and 
 the bladder will burst, the same as if placed under the 
 exhausted receiver of an air-pump. 
 
 215. If a bladder be filled with air at a great height, 
 where the fluid is rare, and brought to a low situation, the 
 contained air will be compressed by the more dense fluid 
 without, and the bladder will appear as if only half or par- 
 tially filled. 
 
 216. The fluids in the animal and vegetable system are 
 similarly affected by atmospheric pressure. Our bodies, 
 for instance, would expand, and our blood-vessels probably 
 be ruptured, if placed for a short time in a vacuum. On 
 the same principle, any change in the density of the atmo- 
 sphere has an effect on the animal frame. 
 
 217. The atmospheric pressure, in ordinary conditions 
 of the air, and at the level of the sea, as already stated, is 
 equal to 15 lbs. to the square inch. If by any means, 
 such as digging into the earth, we should go below the 
 sea’s level, the weight will be found to increase. In deep 
 coal mines, for instance, the pressure of the atmosphere is 
 something more than 15 lbs. to the square inch. 
 
 218. The pressure diminishes in a similar degree as we 
 ascend into the atmosphere. At every step upwards from 
 the shore, the burden of the superincumbent mass lightens. 
 
 157. What of mineral waters 1 
 
 158. How of the experiments with a bladder ? 
 
 159. How are the fluids of the body affected ? 
 
 160. How mav the pressure be increased, or diminished f 
 
68 
 
 PNEUMATICS. 
 
 At the height of three miles, one-half of the weight is lost ; 
 or in other words, at that height the air is only half the 
 density of air at the sea’s level. 
 
 219. The breathing apparatus of animals is suited to an 
 atmospheric density and pressure such as is found at the 
 sea’s level, or at a moderate elevation above it. By ascend- 
 ing in the atmosphere, as in climbing hills, we are deprived 
 of the quantity of air to which we have been accustomed; 
 and when we reach a height of three miles, we in reality 
 inhale only one-half of the weight of air into the lungs that 
 we use at the sea’s level. Consequently, those who ascend 
 to great elevations experience difficulty in breathing, and 
 feel an expansion in their blood-vessels and muscles by the 
 removal of a portion of the ordinary pressure.* All the 
 joints in our bodies, particularly those of the knee and 
 shoulder, are in a great measure held together by the exter- 
 nal pressure of the atmosphere; and thus a principle in 
 Pneumatics compensates for a loading of muscular ligaments. 
 
 220. A consideration of the effects of atmospheric pres- 
 sure, and its variability at different elevations, also the 
 alterations in pressure caused by the expansion or lightening 
 of the air by heat, and its increased density by cold and 
 moisture, tends to explain the remarkable influence which 
 change of climate has upon the human constitution. Thus, 
 the inhabitants of countries possessing a light dry atmo- 
 sphere are usually more lively than those of countries with 
 a heavy moist climate. 
 
 PRESSURE ON MERCURY THE BAROMETER. 
 
 221. The pressure of the atmospheric column, at any 
 given point, may be weighed with considerable exactness, 
 
 * It is known that travellers, and even their practised guides, often 
 fall down suddenly as if struck by lightning, when approaching lofty 
 summits, on account chiefly of the thinness of the air which they are 
 breathing, and some minutes elapse before they recover. In the ele- 
 vated plains of South America, thednhabitants have larger chests than 
 the inhabitants of the lower regions — another admirable instance of the 
 animal frame adapting itself to the circumstances in which it is placed. 
 — ArnotVs Physics. 
 
 161. How are animals affected by atmospheric pressure ? 
 
 162. What of the effects of a change of climate ? 
 
PRESSURE ON MERCURY THE BAROMETER. 
 
 GO 
 
 by balancing it against an opposite column of mercury, 
 water, or other liquid. 
 
 222. The pressure of 15 lbs. to the square inch at the 
 ocean’s level is found by experiment to be equal to the 
 weight of a column of mercury of 30 inches in height, a 
 column of water 33 feet in height, or a column of oil 37 
 feet in height. In other words, the burden of the whole of 
 our atmosphere is equivalent to an ocean of mercury cover- 
 ing the earth to a height of 30 inches, an ocean of waier to 
 a height of 33 feet, or an ocean of oil to a height of 37 
 feet. 
 
 223. The fact of such being the degree of 
 atmospheric pressure admits of easy proof, by 
 means of a glass tube upwards of thirty-two 
 inches in length, and a cup half filled with mer- 
 cury, as represented in Figure 29. The tube is 
 close at its upper end at B, but open at its lower 
 extremity, which is immersed in the mercury 
 below the surface level C P D. The tube having 
 in the first place been filled with pure mercury, 
 a finger is placed on its open end to prevent the 
 egress of the liquid, and thus held, the lower 
 end of the tube is turned downwards, and 
 plunged into the vessel of mercury, when the 
 
 ^finger is removed from the orifice. The mercury 
 in the tube will now be observed to fall to E, 
 or the height of about thirty inches above the 
 "h surface CPD, and there it will remain. 
 
 224. The questi >n now arises, Why the mer- 
 cury in the tube does not run out altogether into the cup, 
 instead of standing to a height of thirty inches in the 
 tube? The explanation of the phenomenon is, that from 
 E to B in the tube is a vacuum, and therefore the mercury 
 at its upper extremity is entirely free of atmospheric pres- 
 sure — there is no superincumbent weight to push it out. 
 The column of mercury EP presses with nothing but its 
 
 Fig. 29. 
 
 163. How may the atmospheric pressure be weighed 1 
 
 164. What calculations are stated ? 
 
 165. Explain the diagram and its design. 
 
TO 
 
 PNEUMATICS. 
 
 own weight on the mercury of the cup. This weight of 
 thirty inches of mercury is counterbalanced by the pressure 
 of air on the surface of the mercury in the cup ; and thus 
 it is evident that the weight of the atmosphere is equivalent 
 to the weight of thirty inches of mercury. If by any means 
 we remove the atmospheric pressure from the mercury in 
 the cup, the mercury in the tube will immediately sink 
 into the cup. 
 
 225. The circumstance of the column of mercury in the 
 tube being narrow, and the surface of the mercury in the 
 cup being broad, makes no difference in the experiment, 
 because the pressure of elastic fluids is as their density, not 
 as width of volume. The same result would occur if the 
 surface of the mercury presented to the atmospheric pres- 
 sure were only the width of the tube. 
 
 226. The height at which mercury stands in a tube of 
 this kind, always bears reference to the incumbent weight 
 of the atmosphere on the open and lower extremity of the 
 column. If we increase the external pressure by artificial 
 means, or by descending below the sea’s level, the mercury 
 rises; if we decrease it by artificial means, or by ascending 
 into the atmosphere, or if the atmosphere is rarefied by heat, » 
 the mercury falls. 
 
 227. This very obvious connection between the rising 
 and falling of mercury in a tube, and the atmosphere, has 
 suggested the construction of an instrument called the 
 Barometer (a word from the Greek, signifying iceight and 
 measure ), by which the effects of atmospheric pressure may 
 be accurately known. 
 
 22S. The barometer in common use consists of a narrow 
 glass tube upwards of thirty inches in length, and bent 
 upwards at its lower extremity, as represented in Figure 
 30. The mercury is introduced into the tube with great 
 care, so that a perfect vacuum exists at the upper extre- 
 mity. The surface of the mercury in the bent part is open 
 to the action of the atmosphere, and buoys up a small 
 plummet or float F, to which a thread is attached; the 
 thread proceeds upwards to a small pulley G, over which 
 
 166. What instrument has been constructed on this principle ? 
 
PRESSURE ON MERCURY THE BAROMETER. 
 
 71 
 
 it goes, and terminates in a small ball W. The friction of 
 the thread on the pulley turns a small index 
 H, which points to figures on the surrounding 
 dial. Commonly, the whole apparatus, except 
 the dial plate, is concealed in an ornamental 
 frame. 
 
 229. Barometers of this description are ad- 
 justed in such a manner that the smallest 
 rising or falling of the mercury from atmo- 
 spheric action, affects the index on the dial, 
 and shows the degree of pressure. 
 
 239. In common circumstances, the mer- 
 cury ranges from 29 to 30 inches. It seldom 
 sinks so low as 28 or rises to 31. When it 
 falls, an indication is given of diminished 
 pressure, and as diminished pressure causes 
 the air to expand, and consequently to be 
 sensibly cooled, moisture is liable to be pre- 
 
 Figure 30. C ipitated in the form of rain (184). Hence 
 a fall in the mercury of the barometer is considered a 
 prognostic of rain or wet weather, and a rise the reverse. 
 The dial of the barometer is marked accordingly. 
 
 231. The barometer, besides being a weather-glass, is 
 used as an instrument for measuring the heights of moun- 
 tains, or heights attained in balloons, above the level of the 
 sea. 
 
 232. As the entire atmosphere sustains thirty inches of 
 mercury in the tube, it follows that at every step as we 
 ascend, the pressure will become less, and a less body of 
 mercury be sustained. It is found that at the height of 
 five hundred feet the mercury has sunk half an inch. But 
 the fall does not proceed in this ratio as we go upwards, 
 because a half of the whole atmosphere is within about 
 three miles, and the other half expanded to an altitude of 
 about fifty miles. Hence, on gaining a height of three 
 miles, the mercury is found to have sunk to fifteen inches, 
 
 167. Explain the diagram. 
 
 168. What are the indications of this instrument ? 
 
 169. To what other uses is it adapted ? 
 
 170. What of ascending to a great altitude ? 
 
72 
 
 PNEUMATICS. 
 
 or one half, and on gaining a height of four miles, to 
 ‘vvelve inches. 
 
 233. Barometers for measuring heights are constructed 
 with a determined scale, marked along the tube of mercury, 
 and by consulting it as we ascend, we learn the height of 
 any spot that we may reach. Perfect exactness, however, is 
 not to be expected in this mode of measurement, because 
 the atmospheric pressure is liable to variation from tempera- 
 ture, and the mercury is liable to contraction or expansion 
 from the same cause. To guard against error, a thermo- 
 meter, as well as a barometer, is consulted in ascending 
 heights, and the indications of both instruments according 
 to a scale established by experiment, determine the degree 
 of elevation. Thus, for a diminution of one degree of 
 temperature between 0 and 32 degrees, the mercury in the 
 barometer falls 0.0034 of an inch, and between 32 degrees 
 and 52 degrees it rises 0.0033 of an inch. 
 
 PRESSURE ON WATER PUMPS. 
 
 234. The effect of atmospheric pressure on water is 
 observable in various contrivances in the arts. 
 
 235. Fill a glass to the brim with water, and lay a piece 
 of paper over the whole surface of the liquid ; then turn the 
 glass carefully upside down, holding on the paper by the 
 hand ; the water will now remain in the glass, being upheld 
 by the pressure of the atmosphere against the paper. 
 
 236. Glass fountains of water for bird-cages, ink-holders, 
 and reservoirs of oil for lamps, are constructed on the prin- 
 ciple of the liquid being upheld by atmospheric pressure. 
 
 237. The apparatus for lifting water from wells, forming 
 the common sucking-pump, acts on the principle of remov- 
 ing the atmospheric pressure from a column of the liquid, 
 thus causing a vacuum in the pump, and allowing the 
 atmospheric pressure on the surface of the liquid in the 
 well to force up and balance the column of liquid. 
 
 238. Figure 31 represents the outline of a common 
 
 171. How may perfect exactness be attained ? 
 
 172. What examples of atmospheric pressure J 
 
PRESSURE ON WATER PUMPS. 
 
 li 
 
 Figure 31. 
 
 sucking-pump. It consists of a cylinder, furnished witli a 
 piston A made to fit air-tight. In 
 this piston there is a valve opening 
 upwards, notseen in the cut. When 
 the piston is raised, the air is rare- 
 fied more and more at each stroke m 
 that portion of thecylinder through 
 which it has moved upwards, and 
 the pressure of the air upon the 
 surface of the water on the outside 
 of the tube forces the fluid into it. 
 The valve B is at the same time 
 opened upwards, and the water 
 after several strokes rushes in above 
 it. When the upward stroke of the 
 piston is complete, it is again de- 
 pressed, the water passes through 
 the valve in the piston ; and on the next stroke, it is dis- 
 charged at the spout. It is evident, that, when the piston 
 is sunk downwards, the water cannot 
 be again forced out of the pump, 
 because the valve at the bottom is 
 pressed down, and prevents its es- 
 cape. 
 
 239. Water may in this manner 
 be lifted by a pump to any height, 
 but in each case the lower or fixed 
 valve in the pump must' be less than 
 34 feet from the surface of the water. 
 It is, however, disadvantageous to 
 lift water from great depths by this 
 means. In such cases, therefore, it 
 is usual to employ a succession of 
 pumps one above another. 
 
 Figure 32. 240. It is customary to call pumps 
 
 hydraulic machines ; properly speaking, they are both 
 
 173. Explain the first diagram. 
 
 174. Are pumps merely hydraulic machines 1 
 
 175. What of the forcing pump, and its uses ! 
 
74 
 
 PNEUMATICS. 
 
 hydraulic and pneumatic machines, for water is raised by 
 them in a great measure through the agency of atmospheric 
 pressure. 
 
 241. The form of pump used for forcing water to a 
 height above the ground, as in the case of fire-engines or 
 portable forcing-pumps for gardens, is different from the 
 common suction-pump. The object in the forcing-pump 
 is to lift water to a certain height by the formation of a 
 vacuum, and then to inject it with violence into the air. 
 
 242. The action of the forcing-pump apparatus is repre- 
 sented in Figure 32. The piston A sucks the water by its 
 upward motion; but on depressing it, the valve B is closed, 
 and the water is consequently forced through the pipe C. 
 
 243. In the case of supplying water to the boiler of a 
 steam-engine, it is necessary to employ a forcing-pump, in 
 order to overcome the pressure of steam within the boiler. 
 The force with which the water is injected overcomes the 
 tendency which the steam has to rush out. 
 
 244. Cold or moderately warm water can only be lifted 
 by a pump. If the water be above a certain temperature, 
 about 150 degrees at the utmost, the sucker cannot form a 
 perfect vacuum, because, in the attempt to do so, the water 
 yields a steam or vapour which fills the space; in other 
 words, by removing the atmospheric pressure by the piston, 
 the water begins to vaporize as if about to boil. When a 
 pump is made to operate upon hot water, it labours in vain 
 to raise the liquid. This circumstance limits the heat of 
 water injected into the boilers of steam-engines; or if the 
 water is injected at a high temperature, it must receive its 
 heat between the pump and the boiler. This is sometimes 
 done, by causing the tube from the pump to pass through 
 a vessel of waste steam. 
 
 SYPHONS. 
 
 245. Atmospheric pressure is very conspicuous in the 
 case of the syphon. 
 
 176. What is used to supply water to the boiler of a steam-engine, 
 and why ? 
 
 -7. What effect has hot water upon a pump 7 
 
SYPHONS. 
 
 246. A syphon is a tube bent in a particular manner, a id 
 is used for drawing off liquors from casks, or water from 
 
 A reservoirs. One kind of syphon is repre- 
 sented in Figure 34, and consists of a tube 
 bent into two equal limbs, each open at 
 the extremity. If such a syphon be filled 
 with water and inverted, so as to turn the 
 two orifices downwards, the liquid will 
 not run out, but remain suspended in the 
 Figure 34. tube, because the pressure of the column 
 of water within is not so great as the pressure of the air 
 without, and thus its escape outwards is prevented. If one 
 end be put into a vessel of water, the vessel will be emptied 
 down to a level with the orifice. It is evident that, when 
 one end of the syphon is inserted in water, the pressure of 
 the atmosphere upon the surface of the water impels the 
 liquid through the tube, and it could be forced upwards to 
 an elevation of above thirty feet, or the height to which 
 water rises in a vacuum. The diagram represents an in- 
 strument of this kind furnished with two cups, firmly attach- 
 ed to the ends, which, by retaining a portion of the liquid, 
 keeps the syphon always full and ready for use. 
 
 247. Syphons are more commonly made with a long and 
 B short limb, as in Figure 35. On in- 
 
 serting the short limb into a vessel 
 
 // Vv, _ of liquid, and drawing the air out of 
 
 // tU * 3e at l ^ e mout * 1 the liquid 
 
 // ifSilli VV ‘N rus h out a stream, and con- 
 // 1 llill I l ' nue fl° w i n g the vessel is emp- 
 
 // ' I |;M t] tied. The pressure upwards into the 
 
 // tube at A is the excess of the atmo- 
 
 // spheric pressure above the vertical 
 
 pressure of the column of fluid AB : 
 /|| and the similar pressure at C is the 
 
 Figure 35. excess of the atmospheric pressure 
 
 above the vertical pressure of the column of fluid BC ; but 
 
 178. Explain the syphon and its use. 
 
 179. Explain the diagram. 
 
 ISO. Explain the second diagram. 
 
76 
 
 PNEUMATICS. 
 
 the latter excess is evidently the greater, and hence the 
 liquid in the vessel is necessarily forced upwards through 
 the tube from C to B ; and thus the vessel is drained of its 
 contents. By placing a stopcock on the tube above A, the 
 stream can be checked, and permitted to flow at pleasure. 
 There are instances of towns- being supplied with water by 
 means of large syphons of this kind. In these cases the 
 syphon is brought over a rising ground from a lake or 
 fountain at some distance. 
 
 SYPHON - SPRINGS. 
 
 248. Certain kinds of springs are accounted for on the 
 princq ieof the syphon; they act from the combined effects 
 
 Figure 36. 
 
 of a vacuum and atmospheric pressure. The following are 
 examples: — Let ABC, Figure 36, represent a mountain, 
 and DEF a hollow in its centre containing water G, which 
 flows to it through several small ducts, HHHH. Let IF 
 be a natural syphon, one end of which is connected with 
 the water at a, and the other ramifies into diverse branches, 
 issuing from the mountain at bbhb. Let K be also another 
 
 181. What of syphon springs ? 
 1S2. Explain the drawing. 
 
SYPHON SPRINGS. 
 
 77 
 
 stream issuing from the hill at L, but which, for the present, 
 we shall suppose is closed at E. Now, if the hollow cavern 
 be tilled to the height M by the rivulets HHHH, it is evi- 
 dent that, on the principle of the syphon above described, 
 the hollow will be emptied to the level N ; and the water 
 thus withdrawn will emerge from the mountain in the form 
 of springs bbbb, because they are all at a lower level than 
 that to which the water rises in the syphon at I'. When 
 the whole has run off, they will then cease to flow until the 
 hollow is refilled to the level M, when it will flow again, 
 and thus the process goes on. This is what is termed an 
 intermitting spring. Some springs, called variable or reci- 
 procating , do not cease to flow, but only discharge a much 
 smaller quantity for a certain time, and then give out a 
 greater quantity. This arises from there being two hollows, 
 one above the other, in the bosom of the mountain, the 
 highest one having a runner, not of a syphon form, which 
 joins the stream of the lower one beyond the bend, or 
 inflection I'. This runner keeps the stream always supplied 
 to a certain degree, although the lower cavity be dry. But 
 when the latter is filled to M, the current is of course greatly 
 augmented, which augmentation continues until the under 
 hollow is again drained. 
 
 249. In some places there are springs which run freely 
 in summer, or in dry weather, and almost stop in winter, 
 or in wet weather. This is explained in the following 
 manner : — Suppose the passage KL to be now open at E, 
 and the water in the hollow to be very low, as it is in sum- 
 mer, or in dry weather — so low indeed that none can escape 
 through the syphon II' — then the spring at L will flow 
 constantly. If during wet weather, however, the cavern be 
 filled to the level M, the syphon will act, and drain off the 
 water; and if we suppose the mouth of the syphon to be 
 lower than the outlet at E, and to drain off as much as the 
 runners HHHH supply, it will allow none to issue from 
 the orifice at L at all, for then E would be above the surface 
 of the water. 
 
 183. What variety of springs are named ? 
 
 184. Recite the explanations given. 
 
78 
 
 PNEUMATICS. 
 
 250. The orifice at L, supposing there was no other 
 outlet from the mountain, may be taken as an instance of 
 those springs, most common, which flow continually. The 
 reservoir from which these are supplied is generally to be 
 traced to some hill or range of hills in the neighbourhood, 
 which from the quantity of rain, &c. collected by them, 
 keep the internal cavity continually full, or nearly so. 
 Springs cannot rise higher than the reservoir from which 
 they are supplied, and fountains, which are springs that 
 burst out at a level considerably lower than the water in 
 the reservoir, do not rise so high, because when they issue 
 from the orifice, they have the resistance of the air to over- 
 come, which retards their ascent. The current also branches 
 out laterally, and thus the force which impels it upwards is 
 partly expended in giving it an oblique direction. 
 
 251. In some parts, intermitting springs have afforded 
 an opportunity for designing individuals imposing upon the 
 credulous. Taking advantage of the flowing and stopping 
 of water-runs, these persons have gained credit to them- 
 selves by predicting the period when the events would happen 
 which, from a few years’ observation, would easily be learned. 
 
 PNEUMATICS CONTINUED. 
 
 BOILING POINT DETERMINED BY ATMOSPHERIC INFLUENCE. 
 
 252. The pressure of the atmosphere exerts a powerful 
 influence over the forms in which matter presents itself to 
 our senses. The force of gravity draws bodies towards 
 the earth, and the atmospheric pressure, along with the 
 property of cohesion of particles, serves to give them com- 
 pactness or firmness. By removing the atmospheric pres- 
 sure, by means of the air-pump or otherwise, some solid 
 bodies will become soft or partially liquid, and liquid 
 bodies will evaporate and assume an aeriform condition. 
 
 253. The degree of pressure exerted by the atmosphere, 
 and also the degree of general temperature, are adjusted by 
 
 1S5. What of springs and fountains as to their height ? 
 
 186. What changes result from removing the atmospheric pressure 1 
 
BOILING POINT ATMOjP H ERIC INFLUENCE. 
 
 73 
 
 nature to produce and sustain the present external properties 
 of matter. The atmospheric pressure is not so great as to 
 prevent spontaneous evaporation from liquids, but is suffi- 
 cient to moderate its action, and harmonize it with other 
 phenomena in nature. 
 
 254. Liquids spontaneously evaporate at all temperatures 
 from the freezing point upwards, though at a much slower 
 rate at a low than a high temperature. When the liquids 
 attain that temperature at which the phenomenon of boiling 
 or ebullition occurs, vaporization is in greatest activity, and 
 speedily but gradually carries off the particles of fluid into 
 the atmosphere. 
 
 255. The degree of heat at which a liquid body boils, 
 depends on the amount of atmospheric pressure, and also 
 on the nature of the body itself. The constituent particles of 
 certain liquids cohere more closely together than others, 
 and a greater heat is required to separate them. 
 
 256. Subject to the common pressure of the atmosphere, 
 ether, which is a volatile liquid used in medicine, boils at 
 a temperature of 104 degrees, alcohol or strong spirits at 
 170 degrees, water at 212 degrees, tallow at about 600 
 degrees, and mercury at 692 degrees. If we either increase 
 or diminish the incumbent pressure as given by the atmo- 
 sphere, the boiling points of these, as well as all other 
 liquids, are immediately changed. 
 
 257. By increasing the pressure on liquids beyond that 
 given by the atmosphere, a greater degree of heat is requi- 
 red to make them boil. This circumstance is taken advan- 
 tage of in the case of certain preparations, in which a higher 
 temperature than 212 degrees is required. For example, 
 to extract properly the gelatinous and oily matter from 
 bones, they must be boiled with a quantity of water in a 
 strong closed vessel; the steam consequently does not 
 escape, but presses on the water, and so keeps it from 
 boiling till a very high temperature has been attained. The 
 same end would be gained by forcing in air upon the water 
 
 187. What of evaporation and vaporization ? 
 
 1S8. Upon what does the boiling point of liquids depend 7 
 
 189. Name the boiling point of different liquids. 
 
 190. How may greater heat be attained without boiling 7 
 
80 
 
 PNEUMATICS. 
 
 to the required pressure, as for instance, to a pitch of pres- 
 sure of B'J lbs. to the square inch, or two atmospheres. 
 
 258. By endeavouring to boil water at a point below the 
 level of the sea, the same result is observable. It is found 
 that in a diving-bell sunk to a depth of sixty-eight feet in 
 the sea, water does not boil till it attain a temperature of 
 272 degrees. 
 
 25 J. When the atmospheric pressure is removed, a con- 
 trary effect is observable. At the summit of Mont Blanc 
 water boils at a temperature of 187 degrees. In certain 
 preparations in the arts, such as distilling spirits, and extracts 
 of herbs (for scents and medicines), it is important to have 
 the vaporific point at a comparatively low temperature. In 
 all such cases the preparation is effected in a vacuum 
 formed by an air-pump connected with the boiling liquid. 
 Some liquids may thus be boiled at a temperature of from 
 90 degrees to 100 degrees. Unless for this ingenious 
 arrangement, the delicate properties of some medicines 
 could not be procured by distillation, for a heat of 212 
 degrees would injure oi destroy them. 
 
 STEAM. 
 
 260. Steam produced from boiling water is a transpa- 
 rent, colourless, and invisible substance, like air. If we 
 could look into the boiler of a steam-engine, we should see 
 nothing but the water in a state of ebullition. The white 
 cloudy-looking matter which is emitted in the form of 
 vapour, is moisture produced bv the partial condensation 
 of the steam in the atmosphere — taking the form of vapour 
 is a step towards becoming liquid again. 
 
 261. A cubic inch of water produces exactly a cubic 
 foot, or 1728 cubic inches, of steam, at 212 degrees of 
 temperature ; in other words, when water is transformed 
 into steam, it occupies 1728 times its former bulk. In this 
 expanded condition steam is of a less specific gravity than 
 air. Its density is expressed by 0 625, that of air being l 
 
 191. How may they be made to boil at lower temperatures ? 
 
 192. Define steam, and vapour. 
 
 193. What of the bulk and specific gravity of steam 7 
 
LATENT HEAT. 
 
 81 
 
 ■262. The elastic force of steam in the process of heating 
 — that is, the force with which it seeks to expand — differs 
 at different temperatures. At first the force is inconsider- 
 able, but it rapidly increases as the temperature is raised. 
 At a temperature of 212 degrees, the elastic force is 15 
 lbs. on the square inch of the containing vessel, or equal 
 to the external pressure of the atmosphere ; at 250 degrees 
 it is 30 lbs., at 272 degrees it is 45 lbs., and at 290 degrees 
 it is 66 lbs. 
 
 263. As the elastic force increases, so does the density 
 of the steam; the elastic force, indeed, always corresponds 
 to the density; because the more steam which is packed 
 into a given bulk, the greater must be its expansive force. 
 
 264. In reference to steam-engines, steam of different 
 degrees of elastic force is employed. When the steam is 
 not suffered to have any communication with the atm - 
 sphere, but is condensed in a vacuum connected with the 
 engine, the steam employed is called low pressure. In most 
 instances its elastic force is not more than 15 lbs. on the 
 square inch; and as this is counteracted by an equal pres- 
 sure from the atmosphere, there is no danger of the boiler 
 exploding. When the steam is not condensed in this man- 
 ner, but is suffered to rush out in puffs into the atmosphere, 
 it must possess a force not only to move the engine, but to 
 overcome the atmosphere which presses upon it in its 
 emission. To possess the degree of force called high pres- 
 sure, the steam is raised to a temperature of from 250 
 degrees to 272 degrees, producing an elastic force of from 
 30 to 45 lbs. on the square inch of the boiler. Hence the 
 danger of explosion in working high-pressure engines. 
 
 LATENT HEAT. 
 
 265. The change of form in bodies, from solid to liquid, 
 and liquid to gaseous, or from liquid to solid, and gaseous 
 
 194. What of the elastic force and density of steam ? 
 
 195. Explain the safety of low pressure engines, and why. 
 
 196. Whence the danger of high pressure ? 
 
 197. What of a change of form in all bodies ? 
 
82 
 
 PNEUMATICS. 
 
 to liquid, is in all cases attended by a remarkable circum- 
 stance in relation to heat. 
 
 266. Heat or caloric, as already mentioned,* is an affec- 
 tion or quality pervading all things, but frequently concealed 
 or Intent, in which state it is in no respect obvious to our 
 senses, and cannot be detected by the thermometer. 
 
 267. When solids become liquids, and when liquids 
 become airs, latent heat is evolved, and combines with the 
 newly formed substances. But this heat, though elabo- 
 rated, is still latent, not perceivable by our senses or by the 
 thermometer. When, on the other hand, liquids become 
 s lids and airs become liquids, as by condensation, the 
 latent heat is instantaneously relieved from its disguise, and 
 makes itself known. 
 
 These propositions maybe exemplified as follows : — 
 
 268. YVhen a vessel of water open to the atmosphere is 
 placed on the fire, the water gradually becomes hotter till 
 it readies 212 degrees, when it boils ; afterwards its tem- 
 perature is not increased. Now, heat must be constantly 
 entering from the fire, and combining with the water ; as 
 the water, however, does not become hotter, the heat must 
 combine with that part of it which flies off in the form of 
 steam ; but the temperature of the steam is only 2 12 degrees, 
 the same as the water from which it rises, and therefore 
 this constantly adding heat does not obviously increase its 
 temperature. 
 
 269. Thus, the steam which rises from boiling water 
 becomes a receptacle for the heat which is constantly enter- 
 ing the liquid from the fire, and in this receptacle it remains 
 in a dormant or latent state, till the steam is reduced to 
 vapour or its elementary liquid, when the accumulated 
 heat is instantaneously developed. The scald given by 
 steam on its emission into the atmosphere, in the form of 
 vapour, is well known to be far more severe than that given 
 by boiling water. The deposition of the latent heat from 
 
 * Laws of Matter and Motion, paragraph 78 to SI. 
 
 19S. Explain latent heat, and when it is evolved. 
 
 199. How is the fact exemplified, and what of scalds ? 
 
LATENT HEAT. 
 
 83 
 
 the vapour is the cause of this excess in the severity of the 
 scald. 
 
 270. Dr. Black, professor of chemistry in the University 
 of Edinburgh, made the discovery of the principle of latent 
 h at, about the year 1757. The following was one of his 
 expcmnents: — He put some water at a temperature of 50 
 degrees m a tin-plate vessel upon a red-hot iron. In four 
 minutes it began to boil, and in twenty minutes it was all 
 bmled off. During the first four minutes the water received 
 an addition of 4Jj degrees per minute, or altogether 162 
 degrees. If we suppose that it received as much per minute 
 during the whole time of boiling, the caloric which entered 
 into the water, and converted it into steam, would amount 
 to 4H multiplied by 20, which is 810 degrees. 
 
 271. Water may be heated, as already stated (257), to a 
 temperature of more than 212 degrees, by laying a force 
 upon it greater than that imposed by the atmosphere, or by 
 simply confining the steam (allowing no emission of steam 
 whatsoever), which has the same elfect. By heating water 
 in a strong cylindrical copper vessel, perfectly closed, called 
 a Papin’s Digester, the temperature of the water may be 
 raised to 400 degrees without boiling. If the mouth of the 
 vessel be suddenly opened while the water is in this state, 
 part of the water will rush out in tiie form of steam, but the 
 greater part remains in the form of water, and its tempera- 
 ture instantly sinks to 212 degrees; consequently, 188 
 degrees of heat have suddenly disappeared. This heat 
 must have been carried otf by the steam. Now, as only 
 about one-fifth of the water is converted into steam, that 
 one-fifth must contain not only its own 188 degrees, but 
 also the 188 degrees lost by each of the other four parts ; 
 that is to say, it must have contained five times 188 degrees, 
 or 940 degrees. Here, then, is a proof that steam contains 
 at least 943 degrees of heat. 
 
 272. If one part of steam, at 212 degrees, be mixed with 
 nine parts, by weight, of water at 62 degrees, the steam 
 
 200. What was Dr. Black’s experiment and its result ? 
 
 201. How may water be heated beyond the boiling point ! 
 
 202. By what instrument may this be done ? 
 
 203. What calculations are made here ? 
 
84 
 
 PNEUMATICS. 
 
 instantly assumes the form of water, and its temperature, 
 after mixture, is 1786 degrees; consequently, each of the 
 nine parts of water has received 116 6 degrees of caloric, 
 and the steam has lost nine times 1166 degrees, or 1044 
 degrees of caloric. But as the temperature of the steam is 
 diminished by 33-4 degrees, we must deduct this sum, 
 when there will remain rather more than 1000 degrees, 
 which is the quantity of heat in the steam. 
 
 273. If a gallon of water be transformed into steam, and 
 that steam allowed to mix with six gallons of cold water, 
 the whole will be raised to the boiling point. 
 
 274 From these and other philosophical experiments, it 
 has been ascertained that the latent heat in steam varies 
 from 940 degrees to 1044 degrees; usually, it is reckoned 
 to be about a medium between these extremes, or nearly 
 1000 degrees. 
 
 275. In proportion as steam is raised beyond a tempera- 
 ture of 212 degrees, the ratio of accumulation of latent 
 heat becomes the greater, just as the steam becomes more 
 dense and of greater elastic force. At a temperature of 
 290 degrees, steam will rush out, and deposit four times 
 as much heat as it would do at 212 degrees. This has 
 been ascertained by experiment. 
 
 276. To prove that all the heat above 212 degrees is 
 latent in steam, it is only necessary to place a thermo- 
 meter in a boiler, but in such a way that it can be seen 
 through a strong piece of glass, or that it will act upon an 
 external index. Thermometers with externally acting in- 
 dices are common in steam boilers. 
 
 277. We can now comprehend why scalds from steam 
 are so very violent. The steam, at 212 degrees, so long as 
 kept within the boiler, rises to a temperature of nearly 1000 
 degrees the instant it comes in contact with the air or any 
 substance on which it condenses itself. Our hand, there- 
 fore, on suffering a scald from steam, receives in less than 
 a moment of time 1000 degrees of heat, which is sufficient 
 to destroy the skin, and to inflict the severest pain. 
 
 204. What is the latent heat in steam ? 
 
 205. Explain the illustration here gixen. 
 
LATENT HEAT. 
 
 85 
 
 278. In the process of evaporation which is less or more 
 in constant activity over the globe, the aeriform moisture 
 carries off latent heat from the liquid substances from which 
 it rises. This is as perceptible by our sense of touch or 
 feeling, as the deposition of heat in a scald. If we wet 
 the back of our hand with water, we feel a sensation of 
 cold from the evaporation which immediately ensues. If 
 we use spirits instead of water, the evaporation will be 
 more active, and the sensation of cold the more intense. 
 The feeling of cold is caused by the withdrawal of heat 
 from the part, which heat becomes latent in the rising 
 vapour. Rooms are cooled by sprinkling water on the 
 floor; the coolness being caused by the withdrawal of heat 
 in the evaporation which ensues. 
 
 279. The principle of latent heat is essential in the econ- 
 omy of nature. The mode of its evolution and absorption 
 has the effect of preventing sudden alterations in the con- 
 dition of solids and liquids. Instead of water suddenly 
 exploding in steam on attaining the boiling point, the 
 process of transformation into air is gradual, on account 
 of the steam becoming the depository of the accumulating 
 heat. So, when water freezes, it does not do so instanta- 
 neously on attaining the freezing point, because it has to 
 absorb the heat in the water, and seal it up in a latent 
 state, ready to be developed again in a manner equally 
 gradual on the melting of the ice.* Thus the evolution 
 and absorption of latent heat form an important principle 
 in regulating change of condition in substances, both in 
 the economy of nature and of art. 
 
 PNEUMATICS CONTINUED. 
 
 ALTERATION OF TEMPERATURE IN AIR. 
 
 We have now to consider the influence of change of 
 temperature in air. 
 
 * Laws or Matter and Motion, paragraph 117. 
 
 206. What examples of latent heat are cited 7 
 
 207. How shown in nature and art 7 
 
86 
 
 PNEUMATICS. 
 
 280. Air, like water, is heated by the sun’s rays, and 
 also by artificial means. 
 
 281. The heat existing in any given bulk of air depends 
 on the quantity or weight of air in the bulk. 
 
 282. In some situations the air is dense, and in others 
 it is thin — it is most dense where the atmospheric pressure 
 is greatest, or at the level of the sea. 
 
 283. If we take a pound weight of air near the sea’s 
 level, and another pound weight at a spot a mile above the 
 sea, we shall tind that each pound contains precisely the 
 same quantity o! heat ; but in the case of that taken near 
 the sea, the air will feel warm, and in the case of the other, 
 the air will feel cool. This seems paradoxical, yet it is a 
 truth. A pound of air, taken near the sea, is compact in 
 substance, and goes into a comparatively small bulk; but 
 that taken from a high part of the atmosphere is thin, and 
 occupies a much larger space. 
 
 284. This explains why the thin air on high grounds is 
 seemingly colder than in low situations. Aloft, the air is 
 as warm as it is below, but there is less of it; the particles 
 are more widely asunder, and this produces the effect of a 
 greater coldness. Properly speaking, the cold in high 
 situations arises from the want of air, rather than from the 
 air itself. 
 
 285. In the warmest regions of the globe, the air is cold 
 at the tops of high mountains, merely because the air is 
 there thin, and incapable of forming a medium for the 
 retention of heat from the sun’s rays.* In every country 
 there is a point of altitude at which water freezes on all 
 occasions, whether summer or winter. In Europe, this 
 point — called by some the snow-line, or point of eternal 
 snow — is from five to six thousand feet above the level of 
 the sea; in the hot regions of Africa and America, it is at 
 
 * The thin air in the higher regions of the atmosphere is understood 
 to contain heat in a latent condition, but this no way affects the above 
 argument. 
 
 208. Bv what means is air heated 1 
 
 209. What relation between temperature and density J 
 
 210. How is the cold in high situations explained ? 
 
 21 1. What of the snow-line in different countries ? 
 
 I 
 
LATENT HEAT. 
 
 87 
 
 f >urteen thousand feet. At these points of altitude respec- 
 tively, snow lies constantly unmelted on the mountain 
 ridges and summits. The same effect is observable on 
 ascending in a balloon. In the warm region of Hindostan, 
 the atmosphere is as cool and pleasant at a certain height 
 on the Himalaya mountains as it is in the northern part of 
 Europe. 
 
 286. In this manner we see that atmospheric pressure 
 affects the temperature in the air around us. 
 
 2S7. Inasmuch as heated water, from its specific light- 
 ness rises to the top in any containing vessel, while the 
 colder particles of the liquid sink to the bottom (156), so 
 does heated air from precisely the same cause rush upwards, 
 while the colder atmosphere sinks to replace it. 
 
 288. It might be inferred from this that the heated air 
 near the sea and other low situations would mount into the 
 higher regions of the atmosphere, and there sustain a con- 
 siderable warmth. Heated air certainly rises into the upper 
 strata of the atmospuere, but on rising it expands, and by 
 that very circumstance its heat has no sensible effect in 
 meliorating the cold. According to the constitution of 
 things, it is impossible to warm the higher regions of the 
 air. The quantity of heat which daily ascends all over the 
 globe is immense, but it never in the smallest degree raises 
 the temperature of the upper air, being thrown off bv radia- 
 tion into surrounding space, or going into a latent condi- 
 tion. 
 
 289. The air differs in temperature at different parts on 
 the same level, in consequenceof the constant daily shining 
 and withdrawal of the sun’s rays. During the day the air 
 is warmed, during the night it becomes cool. 
 
 290. The difference of temperature produced in this or 
 any other manner, leads to constant disturbance in the at- 
 mosphere. Here the air is rising, there it is sinking or 
 rushing sidewise to supply the deficiency ; in short, its 
 motions are indescribably various, all in consequence of 
 the ever-shifting temperature of the atmosphere. 
 
 212. What analogy between liquids and gases ? 
 
 213. Why cannot the higher regions be heated ? 
 
 214. Explain the difference between day and night, and why 1 
 
88 
 
 PNEUMATICS. 
 
 AIR IN MOTION WINDS. 
 
 291. The currents of the air are called winds. Winds 
 originate from any cause which occasions a portion of the 
 atmosphere to expand or contract. Change of temperature, 
 as being the principal cause of these expansions and con- 
 tractions, is the principal cause of winds. The manner of 
 the origin of these winds is very simple, and is completely 
 exemplified within our daily experience. When the door 
 of a heated apartment is thrown open, a current of air is 
 thereby immediately produced : the warm air from the 
 apartment passing out and the cold air rushing in. 
 
 292. Some winds occur from the following cause : — 
 When a condensation of vapour in the atmosphere sudden- 
 ly takes place, giving rise to clouds which speedily fall in 
 rain, the temperature of the surrounding air is sensibly 
 altered, and the colder rushing in upon the warmer, gives 
 rise to a sudden gust of wind. For this reason, a cold 
 heavy shower passing overhead, with a hasty fall of snow 
 or hail, is often attended with a violent and sudden gust of 
 wind, which ceases when the cloud disappears, but is re- 
 newed when another cloud, sweeping along in the same 
 direction, brings with it a fresh blast. Accordingly, a gust 
 of the wind is universally considered to be a prognostic of 
 rain, because it indicates that a change is taking place in 
 the temperature of the atmosphere, owing to the vapour in 
 its higher regions being condensed into rain-clouds. 
 
 293. The winds which blow in Great Britain, the United 
 States, and other temperate parts of the earth, generally 
 originate in some atmospheric disturbance on the ocean or 
 in tropical climates, and therefore cannot possibly be prog- 
 nosticated with any degree of certainty. 
 
 294. The most remarkable winds are those which tra- 
 verse the ocean steadily in one direction, and are called 
 “ trade-winds,” from their use to mercantile navigation. In 
 order that we may distinctly understand the cause and na 
 
 215. Define wind and its causes. 
 
 216. Explain the connection between winds and rain. 
 
 217. Explain the trade-winds and their source. 
 
AIR IN MOTION WINDS. 81) 
 
 • 
 
 ture of the trade-winds, it is necessary to bear in mind that 
 the portion of the globe extending 23$ degrees north and 
 23£ degrees south from the equator, forming the torrid 
 zone, is constantly beat upon by the sun’s rays in a direc- 
 tion so little oblique, that the most intolerable heat might 
 there be anticipated. This being premised, and it being 
 also remembered that the earth revolves daily from west to 
 east, the cause of the trade-winds will be readily understood. 
 
 295. The rays of the sun as the earth passes round be- 
 neath them, obviously rarefy, by the heat they impart, the 
 air beneath, and the air so rarefied rises into the higher 
 regions of the atmosphere. While this takes place, the 
 colder air from the adjoining temperate zones rushes in to 
 supply its place. But it is from the polar regions, north 
 and south, that these colder currents originally come; and 
 did the earth remain at rest, such would be their obvious 
 direction. Instead of this, however, north of the equator 
 the direction of the trade-winds is from the north-east ; 
 south of the equator, from the south-east ; the cause of _ 
 which is thus explained : — The velocity with which the 
 surface of the earth revolves at the poles, is inconsiderable, 
 if at all appreciable, but increases as we advance, and is 
 at its maximum at the equator; the winds, in sweeping 
 from the poles, do not acquire a corresponding velocity 
 with the motion of the earth as they advance towards the 
 equator; therefore moving more slowly than the earth, they 
 are in some measure left behind, or appear to an observer 
 as if moving in a direction contrary to the rotation of the 
 earth, namely, from east to west. -While the trade-wind 
 thus blows upon the surface of the earth, there is no doubt 
 that an opposite current, that of the rarefied air which has 
 ascended, flows towards the poles at a great elevation in 
 the atmosphere. 
 
 296. The external limits of the trade-winds are 39 de- 
 grees north and 30 degrees south of the equator ; but each 
 limit diminishes as the sun advances to the opposite tropic. 
 The larger the expanse of ocean over which they sweep, 
 
 218. What theory is stated to account for them ? 
 
 219. What of their limits and how modified 1 
 
90 
 
 PNEUMATICS. 
 
 the more steadily do they blow; accordingly they are more 
 steady in the Pacific than in the Atlantic, and in the South 
 than in the North Atlantic Ocean. Within the region of 
 the constant trade-winds, rain seldom occurs, but it falls 
 abundantly in the adjoining latitudes. The reason is, that 
 rain is produced by the sudden mixture of air of ditferent 
 temperatures charged with moisture; but the constant 
 circulation and intermixture of the air from the upper 
 strata of the atmosphere, or ground current, maintains so 
 equal a temperature in these latitudes as not to occasion 
 the condensation of vapour which is necessary for the pro- 
 duction of rain. Besides which it is plausibly enough 
 alleged, that the aqueous vapour constantly flows off in the 
 current of the equatorial wind into the adjoining temperate 
 zones. \\ ithin the limits of the trade-winds, contrary to 
 what might have been anticipated from the latitude, the 
 atmosphere is peculiarly cool and refreshing. 
 
 SEA AND LAND BREEZES. 
 
 297. In most countries near the shores of the sea, but 
 particularly in tropical climates, there are periodical winds 
 called sea and land breezes; they occur in the following 
 manner: — During the day, the wind blows for a certain 
 number of hours from the sea to the land ; but when the 
 evening arrives, it changes its direction, and blows as many 
 hours from the land to the sea. In some countries the sea- 
 breeze sets tn about seven or eight in the morning, and is 
 strongest at noon, but continues very sensible until three 
 o’clock, when the surfice of the sea will be observed to 
 exhibit ripples of a deep blue colour. After this, at six in 
 the evening, the land-breeze commences. The sea now 
 assumes a greenish hue; and this breeze continues until 
 eio-ht the next morning. The cause of this alteration mav 
 be readily explained. During the day, the air over the 
 surface of the earth is more heated bv- the rays of the sun 
 than that over the surface of the sea ; because the earth, 
 from its greater density, comparative state of rest, d 
 
 220. What of' rain and the trade-winds ? 
 
 221. Explain the phenomena of sea and land breezes. 
 
SEA AND LAND BREEZES. 
 
 fH 
 
 numerous elevations, absorbs the sun’s rays sooner, and is 
 more heated than the sea, which, from its state of constant 
 motion and transparency, imbibes the warmth very inti- 
 mately, though more slowly. Accordingly, when the sun, 
 having risen above the horizon, has thus imparted a suffi- 
 cient degree of warmth to rarefy the body of air over the 
 land, the air so rarefied ascends into the higher regions of 
 the atmosphere, while that over the surface of the sea, 
 being scarcely at all rarefied, rushes in to supply its place. 
 Hence, a sea-breeze, or current of air from the sea to the 
 land, at this time prevails : but when the sun again begins 
 to sink below the horizon, the body of air over the surface 
 of the land becomes rapidly cold, because the earth itself, 
 by radiation, parts very quickly with the warmth it had 
 absorbed. Then the land air, being below the temperature 
 of the sea air, rushes in to supply its place, and thus, during 
 the night, a land-breeze, or a current of air from the land 
 to the sea, is produced. 
 
 2 98. When the sea-breeze first sets in, it commences 
 very near the shore, and gradually extends itself farther out 
 at sea, and, as the day advances, becomes more or less hot. 
 Hence, the sails of ships have been observed quite becalmed 
 six or eight miles out at sea, while at the same time a fresh 
 sea-breeze has been blowing upon the shore. The cause 
 of this is obvious ; for it is natural to suppose that the mass 
 of air nearest the land will be the first to rush in, for the 
 purpose of supplying the place of the air which is rarefied 
 immediately above it. On this account the effect of the 
 sea-breeze is said not to be perceptible at a distance of 
 more than five or six leagues from the shore, and for the 
 most part becomes fainter in proportion to its distance from 
 land. The distance, on the other hand, to which the land- 
 breeze extends in blowing across the sea, depends on the 
 more or less exposed aspect of the coast from which it 
 proceeds. In some places this breeze was found by Dam- 
 pier brisk three or four leagues off shore; in other places 
 not so many miles; in others, again, it scarcely extended 
 without the rocks. The sea-breeze, from blowing over a 
 
 222. What peculiarities in these sea breezes T 
 
92 
 
 PNEUMATICS. 
 
 more open tract, is always stronger than the land-breeze ; 
 but it is observed that the land-breeze is much colder than 
 the sea-breeze. Furthermore, it has been noticed that the 
 tendency of the land-breeze at night has almost invariably 
 a correspondence with the sea-breeze of the preceding or 
 following day. Unless for the periodical refreshing cool 
 breezes iroin the sea, the West India islands, and generally 
 all hot countries, would scarcely be habitable for the white 
 races of men. 
 
 299. The most dangerous winds to the navigator are 
 those which occur in sudden gusts, or squalls, and for the 
 approach of which the sharpest outlook is required. When 
 the squall is in the form of a violent tempest, accompanied 
 by rain, lightning, and thunder, it receives the name of a 
 hurricane. Hurricanes' occur most frequently and with 
 the greatest violence in tropical climates, because, in con- 
 sequence of the very great heat which there prevails, the 
 rarefaction of the air, and also the condensation of the 
 vapour it contains into rain-drops, take place more suddenly 
 and completely than in more temperate regions. By this 
 means the electricity of the atmosphere — ill it subtle fluid 
 which seems to pervade all bodies, and which universally 
 seeks its own equilibrium — is disturbed, and no longer 
 maintains an equal distribution through the aerial vapour. 
 It accumulates in vast quantities in one mass of vapour or 
 cloud, while in another it is deficient; and, consequently, 
 to regain its equilibrium, it flashes in the form of lightning 
 from the surcharged cloud, to the cloud that is under- 
 charged, or to the eartli itself. Hence, hurricanes are 
 always attended ufith electrical manifestations, which add 
 greatly to the tragical horrors of the spectacle they exhibit. 
 
 VENTILATION. 
 
 300. Ventilation (from Ventus. the Latin word for wind) 
 is the art of preserving the air of apartments in a pure con- 
 dition. 
 
 223. What of hurricanes and their causes ? 
 
 224. What agency has electricity in these ? 
 
 225. Define ventilation and its importance. 
 
VENTILATION. 
 
 9) 
 
 301. This is an arrangement of the utmost importance 
 to health and comfort. A plentiful supply of pure air is 
 necessary for respiration, because the air on being used by 
 the lungs is expelled in a deteriorated condition, and unfit 
 for being- again inhaled.* If apartments, therefore, are 
 not properly ventilated, the air becomes foul from the 
 respired air, as well as, perhaps, from impure exhalations 
 and rarefaction from heat. 
 
 302. The air so deteriorated may not commonly, produce 
 immediate death, but it injures the health of those who live 
 amongst it, and is the fertile cause of deadly distempers, 
 such as fevers, cholera, and plague. 
 
 303. Besides being indispensable for breathing, pure air 
 is necessary for the support of combustion. Any fire de- 
 prived of a supply of air languishes and becomes extinguished. 
 The kind of air best adapted for the supply of a fire is that 
 which is most pure and cold, as it contains more oxygen 
 in any given quantity. Oxygen is the essential element 
 both for breathing and combustion ; and when it is supplied 
 
 * It is calculated that a man in ordinary circumstances consumes 
 about 45,000 cubic inches, or nearly 15,000 grains, of oxygen in twen- 
 ty-four hours. A quantity of carbonic acid gas is produced in some 
 measure proportionate to this consumption. All the oxygen which is 
 inhaled is not consumed; a small portion returns with the breath. The 
 nitrogen of the air undergoes little or no change by being drawn through 
 and expelled from the lungs. 
 
 “ In combustion or burning, it is [also] the oxygen of the air alone 
 which is used, the nitrogen remaining unaltered. It is in consequence 
 of a chemical attraction subsisting between the burning body and the 
 oxygen of the air, that the burning goes on, the oxygen undergoing a 
 change from being chemically united with the combustible body, and 
 being no longer able to support the combustion of that substance, 
 while, at the same time, the combustible body is altered from being 
 united to oxygen. Hence the reason why a lighted candle is immedi- 
 ately extinguishad if placed in a quantity of air from which the oxygen 
 has been withdrawn, or in almost any situation where it cannot procure 
 free oxygen ready to combine with the combustible body. 
 
 “ Oxygen may be considered the essential, the active part of the air, 
 the part which does every thing. It is the oxygen chiefly which is 
 engaged, and becomes altered in all those chemical operations in which 
 the air is concerned ; the nitrogen seldom undergoes any alteration, 
 acting chiefly as a damper, moderating the action of the oxygen, and 
 preventing it from doing too much .” — Hugo Reid's Chemistry of Nature. 
 
 226. What dangers result from a want of it ? 
 
 227. What element in air is essential to combustion ? 
 
94 
 
 PNEUMATICS. 
 
 111 a sufficient quantity, the fire burns rapidly and brightly. 
 The intense combustion produced by blowing a current of 
 air into a fire by means of a pair of bellows, is well known. 
 This intense combustion is produced by the extraordinary 
 quantity of oxygen which is forced into the burning mass. 
 
 3D4. Fire deteriorates pure air as effectually as breathing 
 i The oxygen is consumed, and by a chemical change 
 m substance, carbonic acid gas, which is unfit for respira- 
 tion or combustion, is produced. Fire also heats and 
 causes to expand the air which passes unconsumed through 
 or near it. This expanded air, from its specific lightness, 
 mounts upward, and endeavours to escape by any opening 
 made for ii above the fire place, while colder and more 
 dense air rushes in to supply the deficiency. 
 
 305. Although carbonic acid gas is considerably heavier 
 than pure air (171), it has a tendency when heated and 
 expanded to mount upward along with the air which has 
 been simply heated in its passage near the fire. Thus, by 
 a fortunate provision, all impure air whatsoever may be 
 carried off by expanding it by heat : in other words, the 
 tendency which a heavy impure air has to sink, is overcome 
 by increase of temperature; and in this manner our warmed 
 breath and the warm bad air from our fires are equally 
 caused to escape upwards, and leave room for a fluid suita- 
 ble to our necessities. 
 
 306. Let it now be observed that a constant supply of 
 air is necessary in apartments for two purposes — breathing, 
 and combustion in the fire which is employed for heating 
 or cooking; and let it further be noted, that means must 
 be provided for the escape of the air after it has performed 
 its office. 
 
 307. In common circumstances, the supply, such as it is, 
 is kept up by means of the occasional opening of the door, 
 and crevices in the floor and windows; the whistling of the 
 air through the keyhole and other small openings, is an 
 example of the activity of the atmosphere in rushing to 
 supply the internal deficiency. The chimney is usually 
 the only outlet. 
 
 228. What analogy between this and respiration ? 
 
 220. Whence is our ordinary supply of air, and how changed ? 
 
VENTILATION. 
 
 308. When a fire is lighted in an apartment.it heats and 
 expands a certain quantity of air near it : the heated and 
 expanded air rises : this causes a partial deficiency or 
 vacuum around : the air at a distance rushes to restore the 
 equilibrium : this rushing is in the form of a current towards 
 the fire and chimney, and is commonly called draught. 
 
 30T The current of air so sustained through an apart- 
 ment is generally sufficient for ventilation, but by coming 
 in a sharp cold stream, it chills the person who is exposed 
 to it ; and hence many serious colds, rheumatisms, and 
 similar affections. Where it can be conveniently done, it 
 is better to supply air to the fire by a tube direct from the 
 atmosphere, or at least to warm the air in a lobby, before 
 entering the room. 
 
 3Kb In whichever manner air is supplied to the fire in 
 an apartment, it is necessary that it have a passage sufficient 
 lor entry and dismission. If .the room lie 
 so close as to be without the means of pas- 
 sage in and out lor the air, the fire will 
 speedily heat the air in an uniform degree, 
 like that in a confined oven, and ultimately 
 consume it, when the fire will go out. 
 
 3! I. If all passages into the apartment 
 be closed except the chimney, the fire will 
 necessarily supply itself with fresh air by 
 that channel, as in figure 37, in which the 
 heated air is observed to be ascending di- 
 rectly over the fire, while a stream of pure and cold air is 
 o;i each side descending the chimney to the 
 fireplace beneath. This process of ascend- 
 ing and descending continues as long as no 
 other inlet is allowed for the introduction 
 of air to the fire. 
 
 312. When a free passage is left for the 
 entrance of air, and also a proper outlet 
 above the fire, the air moves rapidly to the 
 seat of combustion, passes through the fire, 
 
 . 38. and ascends in an expanded volume in the 
 
 230. What of a draught ? 
 
 231. Explain the diagram. 
 
06 
 
 PNEUMATICS. 
 
 chimney. A representation of this process of supply and 
 emission is given in Figure 3S. In such a case the chim- 
 ney is said to have a good draught or to draw well; but 
 these terms are not correct. The draught is only the 
 rushing of the air to fill the partial vacuum over the fire 
 and in the chimney. 
 
 313. Such is the rapid consumption of fresh air in a fire, 
 and the force with which a current moves to supply the de- 
 ficiency, that air from the outer atmosphere will penetrate 
 any accessible channel to get to the seat of consumption. 
 In this respect, the air resembles water when any part of 
 its volume is removed : the rest of the water hastens to re- 
 store a level throughout its mass. 
 
 314. In Figure 39 we have an example of this activity 
 in the air, which represents a closed 
 apartment with a channel for intro- 
 ducing fresh air behind the fire- 
 place. The air rushes down this 
 channel, passes through the fire, 
 and then ascends in the chimney, 
 and escapes. In this, as in simi- 
 lar cases, the air shows no reluc- 
 tance to descend the channel ; it 
 indeed is compelled to do so, be- 
 cause the consumption caused by the fire has thinned the 
 air, or caused a partial emptiness of air in the apartment, 
 and the outer air being dense, must sink down to restore 
 the equilibrium. 
 
 315. Smokiness in an apartment arises from various 
 causes, but in most cases it can be traced to some impro- 
 priety in ventilation or malconstruction of chimney. Smoke 
 consists of exceedingly small particles of coal or culm, and 
 the vapourof bituminous matter and water, which are carried 
 upward along with the ascending heated air from the fire : 
 as long as the united mass retains its heat, the smoke is 
 seen to rise in a compact body from the top of the chimney ; 
 
 232. What analogy is referred to ? 
 
 233. Explain the first diagram. 
 
 234. Define smoke and its source. 
 
VENTILATION. 
 
 f.7 
 
 shortly after which the heat is withdrawn by coming in 
 contact with the cool external atmosphere, and the particles 
 of culm, no longer supported, fall by their natural gravity 
 to the earth. 
 
 316. One common cause of smokiness in an apartment 
 is the want of a sufficient supply of air to the fire by the 
 door, windows, or other lower openings. In common lan- 
 guage, the room is too close. In this 
 case the fire, as already stated, draws 
 its supply from the chimney. While 
 the heated air ascends, a stream of 
 cold air descends, as in Figure 40, 
 and in its descent it entangles the 
 heated air loaded with smoke, and 
 so brings down along with it a por- 
 tion of the smoke into the apartment. 
 
 Fig. 40. An additional and properly situated 
 
 opening in the room, will generally remove this cause of 
 smokiness. 
 
 317. Another common cause of smokiness is too great a 
 width of chimney, particularly beneath or near the fireplace. 
 If the chimney be too wide throughout its length, the volume 
 of heated air from the fire is insufficient to fill it; conse- 
 quently it mounts sluggishly, is entangled with cold air en- 
 tering both from above and beneath, and so partially returns, 
 on the occurrence of winds, into the room It is important 
 for riddance of smoke that the chimney should contain only 
 a heated column of air, which has a tendency to shoot 
 rapidly upwards and escape. The longer such a column 
 is (that is, the taller the chimney), the more difficult is it 
 for the cold air above to retard its emission. 
 
 318. The most common cause o smokiness is the im- 
 proper construction of the fireplace and lower part of the 
 chimney. These are made so wideband open that cold air 
 rushes into the chimney from the room without passing 
 through or near the fire. This cold or heavy air mingles 
 
 235. Explain the next diagram. 
 
 236. What other cause of smokiness is named ? 
 
 237. Name the most common cause. 
 
98 
 
 PNEUMATICS. 
 
 with the heated smoky air, cools it, and brings back a por- 
 tion of it into the room, in which the air is less dense than 
 the external air. The remedy for this consists in narrow- 
 ing the fireplace and throat of the chimney, so that all air 
 shall first be heated before it commences its ascent. By 
 doing so, the tendency in the heated air to rise completely 
 overcomes the falling tendency in the particles of culm. 
 
 319. Smoke sometimes descends a chimney into a room 
 from an adjacent chimney top, in which case it is usually 
 called back smoke. This happens when the chimney and 
 room contain air specifically lighter than the external at- 
 mosphere, and no inlet is allowed to restore the balance 
 except the chimney. The air in the chimney cools and 
 sinks, carrying an odour of soot with it into the room ; and 
 this being still insufficient to restore the equilibrium, a cer- 
 tain portion of atmospheric air also descends, bringing with 
 it the smoke of the next house. If a room be left with an 
 open chimney in summer, such a phenomenon is certain to 
 occur. The air being warmer or more light outside during 
 the day, the air of the room rushes up the chimney, leaving 
 a partial emptiness; and at night there is a reverse motion, 
 which brings the odour of soot, or perhaps smoke, along 
 with it. 
 
 320. Smokiness may occur from the peculiar situation 
 of a house,' as for instance in a low dwelling near a tall pile 
 o ' building, over which the wind is apt to gush with rapidity 
 into the low chimney, as water falls over a precipice, and 
 so overcoming all obstacles before it. But in by far the 
 greater number of cases, the smokiness is dependent on 
 those circumstances above mentioned, and might be en- 
 tirely remedied by proper attention to a few simple rules in 
 pneumatics. It must always be borne in mind that the 
 cause of the smoke is something connected with the air ; 
 the smoke itself acting only a secondary part in the phe- 
 nomenon. 
 
 321. Large apartments, such as churches, halls of public 
 assembly, and schools, in which there is a large consump- 
 
 238. What of smoke from the next house 1 
 
 239. What of the relative situation of houses 1 
 
VENTILATION. 
 
 9J 
 
 tioii of air by respiration, require to be ventilated in a par- 
 ticular manner. The chimney, if they have one, is incom- 
 petent to carry off the foul air; and if they have no such 
 outlet, the case becomes the more urgent. In many 
 instances, the only means of ventilation which are em- 
 ployed is to let down the upper sashes of the windows; 
 but this is a very clumsy mode of procedure, and may have 
 dangerous effects from the currents of cold air which rusii 
 into the room. Besides, the plan is inefficacious in war n 
 weather, when ventilation is most required, because the air 
 outside being at the same temperature as that inside, there 
 will be no rush either way : the whole will be in a state 
 of stagnation. 
 
 322. To ventilate properly in these cases, the equilibrium 
 of the air must be destroyed, in order to cause the foul air 
 in the apartment to rush away to restore the atmospheric 
 balance, and in doing so leave the room to be filled with 
 fresh air. To accomplish this sure method of ventilation, 
 the floor or some other lower part of the room must be 
 perforated with innumerable small holes, through which 
 currents of fresh air will be introduced from the exterior 
 of the building. The ceiling must be similarly perforated 
 
 240. What oflarge apartments ? 
 
 241. Explain the diagram. 
 
rjo 
 
 PNEUMATICS. 
 
 with holes to carry off the ascending streams of breathed 
 warm air. From above the ceiling, the air is carried along 
 and down a channel to a fire, which highly rarefies it, and 
 shoots it up a chimney along with the smoke from the fire. 
 A representation of this method of ventilation, which is a 
 device of the eminent chemist Dr. D. B. Reid, is given in 
 Figure 41. The air enters by a channel a b r, thence ascends 
 into the room, passes off at the ceiling, and is conveyed to 
 the fire k, after which it ascends into the atmosphere. Valves 
 or dampers may be placed in the channels to regulate the 
 admission and emission of the air. 
 
 323. By thus establishing a fire somewhere adjacent, 
 and opening a communication to it from an apartment, any 
 kind of foul air may be effectually drawn off. On the same 
 principle, a deep vat or pit containing carbonic acid gas, 
 or any other air specifically heavier than the atmosphere, 
 may be drained of its contents by plunging the lower ex- 
 tremity of a tube into it, and directing the other end to a fire. 
 The fire will thus draw a portion of its supply of air from 
 the pit, and so carry oft’ the deletorious vapour. 
 
 324. When it would be inconvenient to ventilate by 
 means of a fire, force may be employed to propel pure air 
 into a confined apartment. We have an example of this 
 in the case of the diving-bell. 
 
 THE DIVING-BELL. 
 
 325. The diving-bell is an iron box or apartment let 
 down into water, and containing two or more men who 
 are to be employed in some kind of mechanical operation 
 at the bottom. It is chiefly used in building the founda- 
 tions of piers in the sea, at a depth of from twelve to twenty 
 feet below the surface, and in gathering at a much greater 
 depth the valuable relics of vessels which have been wrecked 
 and sunk. 
 
 326. Originally, the machine resembled a bell in figure ; 
 it is now generally shaped like a square box, narrower at 
 the top than the bottom. It is made of iron, is perfectly 
 
 242. Describe the use of a fire for ventilation. 
 
 243. Define a diving-bell and its use. 
 
THE DIVING-BELL. 
 
 101 
 
 cl >se except in the bottom or mouth, which is open, and is 
 suspend d by a strong chain from a crane on the deck of 
 a vessel. It is from six to eight feet in height, with two or 
 more glass lenses on the top to admit light from above 
 when it is sunk, and there is a sent round the interior for 
 the accommodation of those who descend. 
 
 327. Figure 42 is an outline representation of a diving-bell 
 
 r T C and its apparatus. B is the 
 
 bell containing two men, 
 one on the seat, and the 
 other in the act of tying a 
 rope R to a prostrate can- 
 non, which, on giving a 
 preconcerted signal, will 
 be hauled up to a vessel 
 on the surface of the water. 
 C is the chain by which 
 the bell is suspended, and 
 T is a flexible leather tube 
 by which fresh air is ad- 
 mitted into the bell. There 
 is a stopcock on the mouth 
 of the tube, by which the 
 Fig- 42. men can regulate the ad- 
 
 mission of air at pleasure. The bell does not touch the 
 bottom, but hangs within a few inches or perhaps one or 
 two fcet of it, and therefore the men are provided with long 
 leather boots, to protect them while they stand upon the 
 bottom in the water. 
 
 328. Tiie manner in which the diving bell is supplied 
 with fresh air, and freed from that which is impure, is most 
 deserving of our attention. 
 
 329. When the bell is lowered, so as to touch and sink 
 beneath the surface of the sea, it may be compared to the 
 dipping of a tumbler, mouth downwards, in a vessel of 
 water. In the same manner as the air within the tumbler 
 keeps the liquid from filling it, so does the air within the 
 
 244. Explain the diagram. 
 
 245. How is a diving-bell supplied with air ? 
 
102 
 
 PNEUMATICS. 
 
 bell prevent the water from rising beyond a certain height. 
 As the bell sinks, the air which it contains becomes gra- 
 dually more compressed in bulk by the intrusion of water, 
 and at a depth of thirty-four feet, the air is condensed into 
 one-half of its natural dimensions. At this point, therefore, 
 if no precautions were used, the bell would be half-filled 
 with water. The means adopted to keep the water out 
 consists in forcing in air through the already mentioned 
 tube. On the deck of the superintending vessel is placed 
 a powerful air cendensing-pump, wrought by one or two 
 men inconstant attendance; and by this machine fresh 
 air is injected into the bell, and kept at such a density as 
 forces the water entirely out, or very nearly so. 
 
 330. The bell is freed of impure air by. means of a sep- 
 arate tube and stopcock, fixed in its upper part; but in 
 some cases such an arrangement is not considered neces- 
 sary, as the expired air on becoming cool, and consisting 
 chiefly of carbonic acid gas, descends by its greater weight 
 to the bottom, and escapes round the low : er edges of the 
 bell, whence it rises in bubbles to the surface. 
 
 PNEU I ATICS— CONCLUDED. 
 
 BUOYANT PROPERTY OF AERIFORM FLUIDS. 
 
 331. The atmosphere, as has been stated, possesses the 
 property of buoying up bodies which, bulk for bulk, are 
 lighter than itself. The law governing bouyancy in liquids 
 is precisely the same as that governing bouyancy in aeri- 
 form fluids, and may here be repeated in reference to air. 
 
 332. First . — Any solid body immersed in a fluid dis- 
 places exactly its own bulk of fluid, and the force with 
 which the body is buoyed up is equal to the weight of the 
 fluid which is displaced. This refers to bodies of less 
 density than air. 
 
 333. Second . — Any solid body of a greater density than 
 air, when w'holly immersed in that fluid, loses exactly as 
 
 246. How is impure air removed ? 
 
 247. - What of the buoyancy of air ? 
 
 24S. What analogy between air and water t 
 
BUOYANT PROPERTY OF AERIFORM FLUIDS. 1 13 
 
 much of its weight as the weight of ail equal bulk of air — 
 tic: t is, i f she air which it displaces. 
 
 As these propositions have been sufficiently exemplified 
 in a preceding part of the present work, from paragraph 83 
 to 108, and as the fluid support of air is in principle the 
 same as that of water, little additional explanation is here 
 required upon the subject. 
 
 334. The support afforded to bodies in the atmospheric 
 fluid by its resistance is very evident from • many appear- 
 ances in nature, as the support of vapours or clouds, the 
 rising of smoke and fine particles of dust, and the flying of 
 birds ; in art, it is exemplified by the flying of a boy’s paper 
 kite, the rising of soap-bubbles, and its buoyant, property 
 by the floating of balloons. 
 
 335. The flight of birds is not accomplished altogether 
 by the buoyant property in the air. These animals support 
 themselves by striking their wings against the fluid through 
 which they are passing, and this friction, along with the 
 property of buoyancy in the atmosphere, sustains them at 
 any height to which they are pleased to ascend. Birds do 
 not generally fly above half a mile in height, and seldom 
 above a few hundred yards. At considerable elevations 
 the air is so specifically light, as to be unsuitable for their 
 easy support. Those which rise to the higher regions of 
 the atmosphere, as for instance the eagle, are provided with 
 large wings, which enahle them to support themselves in 
 the comparatively thin fluid in which they move. A small 
 bird, when let out from a balloon, at the height of three 
 miles, drops almost like a plummet, till it arrive in a fluid 
 against which its little wings can take effect. 
 
 336. The buoyant property of the air thus obviously 
 diminishes in proportion as it becomes less dense ; and 
 there is a point above which the lightest imaginable body 
 or particle of matter would inevitably sink. By this means, 
 independently of terrestrial attraction, an effectual limit has 
 
 249. What examples of buoyancy are named 1 
 
 250. What of the flight of birds ? 
 
 251. What of the higher regions of the air 1 
 
104 
 
 PNEUMATICS. 
 
 been set to the distance attainable by substances from the 
 surface of our planet. Not an atom of matter, since the 
 period of the creation, has been suffered to escape beyond 
 the higher regions of the atmosphere, or which has not in 
 making the attempt been brought back to the earth. 
 
 337. The support given to bodies by the atmosphere 
 diminishes their apparent weight, in the same manner as 
 the apparent weight of bodies is diminished in water. A 
 stone is moved more easily in water than in air, and so 
 likewise is it moved more easily in air than in a vacuum. 
 
 338. The diminution in weight of a body in air,.a3 
 already stated (334), is equal to the weight of the bulk of 
 air displaced. Thus, if an object which displaces one grain 
 of air, weigh a pound in a vacuum, it will weigh one grain 
 less than a pound in air, and therefore one gr in will require 
 to be added to it to make up the apparent deficiency. 
 
 339. The weight of air displaced by any merchantable 
 object is so exceedingly trifling as not to be worth reckon 
 ing in ordinary circumstances. Strictly speaking, however, 
 that weight of air has an influence in the value of the trans- 
 action. In all cases in which the object weighed is more 
 bulky than the weight employed to balance it, a certain 
 quantity must be added to overcome the force with which 
 it is buoyed up by the atmospheric fluid. 
 
 340. A pound of leathers lightly piled together contains 
 somewhat more weight than a pound of lead. We may 
 prove that such is the case, by taking the apparent pound 
 of feathers and forcing them into a small bulk in an air- 
 tight covering, and then weighing them again, when it will 
 be perceived that they will weigh a little more than a pound. 
 In strict justice to seller and buyer, all commodities should 
 either be weighed in vacuo, or balanced against weights of 
 equal bulk. 
 
 BALLOONS. 
 
 3»1. The light heated air which escapes from a fire, 
 ascends, and is buoyed up by the more dense air beneath. 
 
 252. What of the weight of air, and the illustrations ? 
 
 253. Explain the principle of balloons. 
 
balloons. 
 
 105 
 
 Hydrogen or any other gas of a less specific gravity than 
 air, in the same manner ascends and floats in the atmo- 
 sphere at the height at which it finds air of its own specific 
 gravity. 
 
 342. On the same principle, if heated air or any light 
 gas be inclosed in a large silk bag, it will ascend in the 
 atmosphere till it reach a region of air which is incapable 
 of supporting it. Thus, a soap-bubble inclosing warm air 
 readily ascends to the ceiling of an apartment. If the bub- 
 ble be made with cold water, it will sink instead of rising. 
 
 343. A balloon is a bag made of fine varnished silk, and 
 of such a magnitude that the difference betwixt the weight 
 of its contents and that of the displaced air is sufficient to 
 support the weight of the silk and the other parts of the 
 apparatus. 
 
 344. Balloons were originally made to rise by being 
 filled with heated air from a fire hung beneath them ; but 
 this dangerous and inconvenient practice was in course of 
 time superseded by the use of hydrogen gas, one of the 
 lightest airs which can be prepared. Hydrogen gas has 
 latterly been succeeded by carburetted hydrogen, which 
 though not so light, is more easily obtained, being the gas 
 with which towns are now generally lighted. 
 
 345. Employing a moderately pure and light gas, the 
 contents of a balloon may be estimated to weigh only an 
 eighth of the weight of the atmosphere, bulk for bulk ; and 
 hence, after adding another eighth for weight of apparatus, 
 it will ascend with a force of six-eighths; in other words, 
 if the gas and apparatus weigh two pounds, the balloon will 
 lift from the ground a weight of other six pounds. 
 
 346. The force with which a balloon will ascend is there- 
 fore to be calculated by measuring its capacity in cubic 
 feet, and comparing the result with an equal bulk of ainm- 
 spheric air: the difference of weight is the buoyant fi'rce 
 of the balloon 
 
 254. How were they formerly made to rise ? 
 
 255. What ^as is now employed, and why ? 
 
 256. How is its force of ascent calculated ? 
 
106 
 
 PNEUMATICS. 
 
 347. Of aerostation, or the art of moving through the 
 air in balloons, great expectations were originally entertain- 
 ed, but the experience of half a century has proved that it 
 is of no practical value. Its only use is the exhibition of 
 an interesting principle in pneumatics. A balloon con- 
 structed in the best known manner, and moving upwards 
 with a powerful force, is subject to the following draw- 
 backs : — 
 
 348. As the balloon ascends, its contents expand in con- 
 sequence of the increasing rarefaction of the atmosphere; 
 if, therefore, it has been entirely filled when on the ground, 
 a portion of the gas must be allowed to escape as it rises, 
 otherwise it will burst. At the height of 3000 feet, the 
 atmosphere is a tenth degree less dense than on the surface 
 of -the earth; hence the gas expands a tenth in bulk, and a 
 tenth must be suffered to escape. This amounts to 8000 
 feet of gas in a balloon containing 80,000 feet; calculating 
 the gas at 36 lbs. per 1000 cubic feet, the loss incurred by 
 the escape at this limited height would be equal to 288 lbs. 
 of buoyant power. As the atmosphere becomes the more 
 rare as the machine ascends, the expansion proceeds, more 
 gas must be emitted, and more buoyant power lost. 
 
 349. Again, at the approach of night, upon the passage 
 through clouds, or under the influence of a shower of rain, 
 a large quantity of moisture becomes absorbed by the net 
 which encloses the balloon and other apparatus, frequentlv 
 to the extent of two or three hundred-weight, requiring an 
 immediate discharge of ballast to that amount, to prevent 
 the balloon from being borne to the ground. As the morn- 
 ing approaches, or the influence of increasing heat begins 
 to be felt, the moisture becomes dissipated ; and there being 
 no means of recovering the lost ballast, the balloon rapidly 
 rises in the air, its contents expanding in the ascent, and 
 rendering further liberations of gas necessary to prevent 
 explosion. These alternations continuing to operate more 
 or less frequently, it is evident that they must soon put an 
 end to the buoyant pow'er, however great originally, and 
 
 257. What disadvantages attend upon balloons ? 
 
BALLOONS. 
 
 107 
 
 forcibly terminate the excursion through the air. Such are 
 the principal causes which affect the continuance of aerial 
 voyages for any length of time, and along with the contend- 
 ing eifects of winds, against which there can be no pre- 
 ventive, render aerostation only a matter of amusement to 
 a public assemblage. 
 
DAVIES’ SYSTEM OF MATHEMATICS. 
 
 MAMEMMETCAlt W©iM: 
 
 DESIGNED FOR SCHOOLS, ACADEMIES, AND COLLEGES. 
 
 BY CHARLES DAVIES, LL.D. 
 
 PUBLISHED BY A. S. BARNES & CO.. 
 
 51 JOHN-STREET, NEW YORK. 
 
 ELEMENTARY COURSE. 
 
 Pnea 
 
 UAVTES’ PRIMARY TABLE BOOK IS 
 
 DAVIES’ FIRST LESSONS IN ARITHMETIC ......' 18 
 
 DAVIES’ SCHOOL ARITHMETIC Ncu> Edition, 38 
 
 KEY TO DAVIES’ SCHOOL ARITHMETIC 38 
 
 DAVIES’ UNIVERSITY ARITHMETIC 12mo. aheep, 75 
 
 KEY TO^DAVIES’ UNIVERSITY ARITHMETIC 50 
 
 DAVIES’ ELEMENTARY ALGEBRA 12mo. aheep, 84 
 
 KEY TO DAVIES’ ELEMENTARY ALGEBRA 50 
 
 DAVIES’ ELEMENTARY GEOMETRY I2mo. aheep, 75 
 
 DAVIES’ DRAWING AND MENSURATION 12mo. sheep, 84 
 
 ADVANCED COURSE. 
 
 * Price. 
 
 DAVIES’ BOURDON'S ALGEBRA— BeiDg an abridgment of the work 
 
 of M. Bourdon 8 vo. aheep. 1 50 
 
 DAVIES’ LEGENDRE’S GEOMETRY AND TRIGONOMETRY— 
 
 Being an abridgment of the work of M. Legendre 8uo. sheep. I 50 
 
 DAVIES’ ELEMENTS OF SURVEYING— With a description and Plate? 
 
 of the Theodolite, Compass, Plane Table, and Level 8vo. aheep. 1 50 
 
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 the Point and Straight Line ; a System of Conic Sections ; the Equa- 
 tions of the Line and Plane in Space, &c 8vo. sheep. 1 50 
 
 DAVIES’ DIFFERENTIAL AND INTEGRAL CALCULUS— Embra- 
 cing the Rectification and Quadrature of Curves, the Mensuration of 
 Surfaces, and the Cubature of Solids 8no. sheep. 1 50 
 
 DAVIES’ DESCRIPTIVE GEOMETRY— With its application to Spheri- 
 cal Projections s. n . sheep, 2 08 
 
 DAVIES’ SHADES, SHADOWS, AND LINEAR PERSPECTIVE — 
 
 VV,tb numerous Plates bvo calf back, 2 54 
 
 (a) 
 
Davies’ System of Mathematics. 
 
 TO THE FRIENDS OF EDUCATION. 
 
 The publishers of this series of mathematical works by Professor 
 Chahi.es Davies, heir leave respectfully to ask of teachers and the 
 friends of education a careful examination of these works. It is 
 not their intention to commend, particularly, this Course of Math- 
 ematics to public favor ; and especially, it is not their design to 
 disparage other works on the same subjects. They wish simply 
 to explain the leading features of this system of Text-Books — the 
 place which each is intended to fill in a system of education — the 
 general connection of the books with each other — and some of the 
 advantages which result from the study of a uniform series of math- 
 ematical works. 
 
 It may, perhaps, not be out of place, first, to remark, that the 
 author of this series, after graduating at the Military Academy, 
 entered upon the duties of a permanent instructor in that institution 
 in the year 1816, and was employed for the twenty following years 
 in the departments of scientific instruction. At the expiration of 
 that period he visited Europe, and had a full opportunity of com- 
 paring the systems of scientific instruction, both in F^.nce and 
 England, with that which had been previously adopted at the Mili- 
 tary Academy. 
 
 This series, combining all that is most valuable in the various 
 methods of European instruction, improved and matured by the 
 suggestions of more than thirty years’ experience, now forms the 
 only complete consecutive course of Mathematics. Its methods, 
 harmonizing as the works of one mind, carry the student onward 
 by the same analogies and the same law's of association, and are cal- 
 culated to impart a comprehensive knowledge of the science, com- 
 bining clearness in the several branches, and unity and proportion 
 in the whole. Being the system so long in use at West Point, and 
 through which so many men, eminent for their scientific attain- 
 ments, have passed, it may be justly regarded as our National 
 System of Mathematics. Scholars and students who have pur- 
 sued this course, w'ill everywhere stand on the highest level with 
 reference to the estimates which themselves and others will form 
 of this part of their education. 
 
 The series is divided into three parts, viz. : First — Arithmeti- 
 cal Course for Schools. Second — Academical Course. Turd 
 —Collegiate Course. 
 
 (3) 
 
Davies' System if Mathematics. 
 
 The Arithmetical Course for Schools. 
 
 I. PRIMARY TABLE-BOOK. 
 
 II. FIRST LESSONS IN ARITHMETIC. 
 
 III. SCHOOL ARITHMETIC. (Key separated 
 
 PRIMARY TABLE-BOOK. 
 
 The leading feature of the plan of this work is to teach the reading of figures 
 that is, so to train the mind that it shall, by the aid of the eye alone, catch in 
 stantly the idea which any combination of figures is intended to express. 
 
 The method heretofore pursued has aimed only at presenting the combinations 
 by means of our common language : this method proposes to present them pure- 
 ly through the arithmetical symbols, so that the pupil shall not be obliged to pause 
 at every step and translate his conceptions into common language, and then re- 
 translate them into the language of arithmetic. 
 
 For example, when he sees two numbers, as 4 and 8, to be added, he shall not 
 pause and say, 4 and 8 are 12, but shall be so trained as to repeat 12 at once, as is 
 always done by an experienced accountant. So if the difference of these num- 
 bers is to be found, he shall at once say 4, and not 4 from 8 leaves 4. If he de- 
 sires their product, he will say 32 , if their quotient, 2 : and the same in all simi- 
 lar cases. 
 
 FIRST LESSONS IN ARITHMETIC. 
 
 The First Lessons in Jliilhmetic begin with counting, and advance step by step 
 through all the simple combinations of numbers. In order that the pupil may be 
 impressed with the fact that numbers express a collection of units, or things of 
 the same kind, the unit, in the beginning, is represented by a star, and the child 
 should be made to count the stars in all cases where they are used Having once 
 fixed in the mind a correct impression of numbers, it was deemed no longer 
 necessary to represent the unit by a symbol ; and hence the use of the star was 
 discontinued. In adding 1 to each number from 1 to 10, we have the first ten 
 combinations in arithmetic. Then by adding 2 in the same way, we have the 
 second ten combinations, and so on. Each ten combinations is arranged in a 
 separate lesson, throughout, the four ground rules, and each is illustrated either 
 by unit marks or a simple example. Thus the four hundred elementary combi- 
 nations are presented, in succession, in forty lessons, — a plan not adopted in any 
 other elementary book. 
 
 SCHOOL ARITHMETIC. 
 
 This work begins with the simplest combination of numbers, and contains all 
 that is supposed to be necessary for the average grade of classes in schools. It 
 is strictly scientific and entirely practical in its plan Each idea is first presented 
 to the mind either by an example or an illustration, and then the principle, or 
 abstract idea, is stated in general terms. Great care has been taken to attain 
 simplicity and accuracy in the definitions and rules and at the same time so to 
 frame them as to make them introductory to the higher branches of mathematica. 
 science. No definition or rule is given until the mind of the pupil has been 
 brought to it by a series of simple inductions, so that mental training may begin 
 wnh the first intellectual efforts in numbers 
 
 4 
 
Danes ’ System of Mathematics. 
 
 The Academic Course. 
 
 I. THE UNIVERSITY ARITHMETIC. (Key separate.) 
 
 II. PRACTICAL GEOMETRY AND MENSURATION. 
 
 III. ELEMENTARY ALGEBRA. (Key separate,) 
 
 IV. ELEMENTARY GEOMETRY. 
 
 V. DAVIES’ ELEMENTS OF SURVEYING. 
 
 Those who are conversant with the preparation of elementary 
 text-hooks, have experienced the difficulty of adapting them to the 
 wants which they are intended to supply. The institutions of in- 
 struction are of all grades from the college to the district school, 
 and although there is a wide difference between the extremes, the 
 level in passing from one grade to the other is scarcely broken. 
 Each of these classes of seminaries requires text-books adapted to 
 its own peculiar wants ; and if each held its proper place in -its 
 own class, the task of supplying suitable text-books would not be 
 so difficult. An indifferent college is generally inferior, in the 
 system and scope of instruction, to a good academy or high-school ; 
 while the district-school is often found to be superior to its neigh- 
 boring academy. 
 
 Although, therefore, the University Arithmetic and the Practical 
 Geometry and Mensuration, have been classed among the books 
 appropriate for academies, they may no doubt be often advantage- 
 ously studied in the common-school ; so also with the Algebra and 
 Elementary Geometry. The Practical Geometry and Mensura- 
 tion, containing so much practical matter, can hardly fail to be a 
 useful and profitable study. 
 
 DAVIES’ UNIVERSITY ARITHMETIC. 
 
 The scholar in commencing this work, is supposed to be familiar with the oper 
 ations in the four ground rules, which are fully taught both in the First Lessons 
 and in the School Arithmetic. This being premised, the language of figures, 
 which are the representatives of numbers, is carefully taught, and the different 
 significations of which the figures are susceptible, depending on the places in 
 which they are written, are fully explained. It is shown, for example, that the 
 simple numbers in which the unit increases from right to left according to the 
 scale of tens, and the Denominate or Compound Numbers, in which it increases 
 according to a different scale, belong in fact to the same class of numbers, and 
 that both may be treated under a common set of rules. Hence, the rules for No- 
 tation, Addition, Subtraction, Multiplication, and Division, have been so con- 
 structed as to apply equally to all numbers. This arrangement is a new one, and 
 is deemed an essential improvement in the science of numbers 
 
 l.i developing the properties of numbers, from their elementary to their highest 
 combinations, great labor has been bestowed on classification and arrangement. 
 It has been a leading object to present the entire subject of arithmetic as forming 
 
Dueled System of Mathematics. 
 
 a series of dependent and connected propositions ; so that the pupil, while ac- 
 quiring useful and practical knowledge, may at the same time be introduced to 
 those beautiful methods of exact reasoning which science alone can teach. 
 
 Great care has been taken to demonstrate fully all the rules, and to explain the 
 reason of every process, from the most simple to the most difficult. The demon- 
 stration of the rule for the division of fractions, on page 147, is new and consid- 
 ered valuable. 
 
 The properties of the 9’s, explained at page 93, and the demonstration of the 
 four ground rules by means of those properties, are new in their present form, 
 and are thought worthy of special attention. 
 
 In the preparation of the work, another object has been kept constantly in 
 view ; viz., to adapt it to the business wants of the country. For this purpose, 
 much pains nave been bestowed in the preparation of the articles on Weights 
 and Measures, foreign and domestic — on Banking, Bank Discount, Interest, Coins 
 and Currency, Exchanges, Book-keeping, &c. In short, it is a full treatise on 
 the subject of Arithmetic, combining the two characteristics of a scientific and 
 practical work. 
 
 Recommendation from the Prof es. tors of the Mathematical Department of the 
 United States Military Academy 
 
 In the distinctness with which the various definitions are given— the clear and 
 strictly mathematical demonstration of the rules — the convenient form and well- 
 chosen matter of the tables, as well as in the complete and much desired appli- 
 cation of all to the business of the country, the “ University Arithmetic” of 
 Prof. Davies is superior to any other work of the kind with which we are ac- 
 quainted. These, with the many other improvements introduced by the ad- 
 mirable scientific arrangement and treatment of the whole subject, and in par- 
 ticular those of the generalization of the four ground rules, so as to include 
 “ simple and denominate” numbers under the same head, and the very plain 
 demonstration of the rule for the division of fractions— both of which are, to us, 
 original — make the work an invaluable one to teachers and students who are de- 
 sirous to teach or study arithmetic as a science as well as an art. 
 
 '.Signed.) D H. MAHAN, Prof. Engineering. 
 
 W. H. O. BARTLETT, Prof. Nat. Phil. 
 
 A. E. CHURCH, Prof. Mathematics. 
 
 United States Military Academy , Jan. 18, 1847. 
 
 PRACTICAL GEOMETRY AND MENSURATION. 
 
 The design of this work is to afford schools ana academies an Elementary 
 Text- Book of a practical character. The introduction into our schools, within 
 the last few years, of the subjects of Natural Philosophy, Astronomy, Mineralo- 
 gy, Chemistry, and Drawing, has given rise to a higher grade of elementary 
 studies ; and the extended application of the mechanic arts calls for additional 
 information among practical men. In this work all the truths of Geometry are 
 made accessible to the general reader, by omitting the demonstrations altogether, 
 and relying for the impression of each particular truth on a pointed question and 
 an illustration by a diagram. In this way it is believed that all the important 
 properties of the geometrical figures may be learned in a few weeks ; and after 
 these properties have been once applied, the mind receives a conviction of their 
 truth little short of what is afforded by rigorous demonstration. The work is 
 divided into seven books, and each book is subdivided into sections. 
 
 In Hook 1 , the properties of the geometrical figures are explained bv questions 
 and illustrations. 
 
 
Davies System uj Mathematics. 
 
 In Book II. are explained the construction and uses of the various scales ; and 
 also the construction of geometrical figures. It is, as its title imports, Practica. 
 Geometry. 
 
 Book III. treats of Drawing. Section I„ of the Elements of the Art ; Section 
 II., of Topographical Drawing ; and Section III., of Plan D rawing. 
 
 Book IV. treats of Architecture — explaining the different orders, both by de- 
 scriptions and drawings. 
 
 Book V. contains the application of the principles of Geometry to the Mensu- 
 ration of Surfaces and Solids. A separate rule is given for each case, and the 
 whole is illustrated by numerous and appropriate examples. 
 
 Book VI. contains the application of the preceding Books to Artificers’ and Me- 
 chanics’ work. It contains full explanations of all the scales — the uses to which 
 they are applied— and specific rules for the calculations and computations which 
 are necessary in practical operations. 
 
 Book VII. is an introduction to Mechanics. It explains the nature and proper- 
 ties of matter, the laws of motion and equilibrium, and the principles of all the 
 simple machines. 
 
 ELEMENTARY ALGEBRA. 
 
 This work is intended to form a connecting link between Arithmetic and Alge 
 bra, and to unite and blend, as far as possible, the reasoning on numbers with tho 
 more abstract method of analysis. It is intended to bring the subject of Algebra 
 within the range of our common schools, by giving to it a practical and tangible 
 form. It begins with an introduction, in which the subject is first treated men- 
 tally, in order to accustom the mind of the pupil to the first processes ; after 
 which, the system of instruction assumes a practical form. The definitions and 
 rules are as concise and simple as they can be made, and the reasonings are as 
 clear and concise as the nature of the subject will admit. The strictest scientific 
 methods are always adopted, for the double reason, that what is learned should 
 be learned in the right way, and because the scientific methods are generally the 
 most simple. 
 
 ELEMENTARY GEOMETRY. 
 
 This work is designed for those whose education extends beyond the aequisi 
 tion of facts and practical knowledge, but who have not the time to go through 
 a full course of mathematical studies. It is intended to present the striking and 
 important truths of Geometry in a form more simple and concise than is adopted 
 in Legendre, and yet preserve the exactness of rigorous reasoning. In this sys- 
 tem, nothing has been omitted in the chain of exact reasoning, nothing has been 
 taken for granted, and nothing passed over without being fully demonstrated 
 The work also contains the applications of Geometry to the Mensuration of Sur 
 faces and Solids. 
 
 SURVEYING. 
 
 In this work it was the intention of the author to begin with the very elements 
 of the subject, and to combine those elements in the simplest manner, so as to 
 render the higher branches of Plane Surveying comparatively easy. All the in- 
 struments needed for plotting have been carefully described, and the uses of those 
 required for the measurement of angles are fully explained. The Conventional 
 Signs adopted by the Topographical Bureau, and which are non used by the li nitea 
 States Engineers in all their charts and maps, are given in full. An account is also 
 given of the manner of surveying the public lands : and although the method is sim 
 pie, it has nevertheless been productive of great results. The work also contains 
 a Table of Logarithms— a Table of Logarithmic Sines— a Traverse Table, and a 
 Table of Natural Sines— being all the Tables necessary for Practical Surveying 
 
 n\ 
 
Davies’ System of Mathematics. 
 
 The Collegiate Course. 
 
 I. DAVIES’ BOURDON’S ALGEBRA. 
 
 II. DAVIES’ LEGENDRE’S GEOMETRY AND TRIGONOMETRY. 
 
 III. DAVIES’ ANALYTICAL GEOMETRY. 
 
 IV. DAVIES’ DESCRIPTIVE GEOMETRY. 
 
 V. DAVIES’ SHADES, SHADOWS, AND PERSPECTIVE. 
 
 VI. DAVIES’ DIFFERENTIAL AND INTEGRAL CALCULUS. 
 
 The works embraced under the head of the “ Collegiate Course,” 
 were originally prepared as text-books for the use of the Military 
 Academy at West Point, where, with a single exception, they are 
 still used. Since their introduction into many of the colleges of 
 the country, they have been somewhat modified, so as to meet the 
 wants of collegiate instruction. The general plan on which these 
 works are written, was new at the time of their appearance. Its 
 main feature was to unite the logic of the French School of 
 Mathematics with the practical methods of the English, and the 
 two methods are now harmoniously blended in most of our systems 
 of scientific instruction. 
 
 The introduction of these works into the colleges was for a 
 long time much retarded, in consequence of the great deficiency in 
 the courses of instruction in the primary schools and academies : 
 and this circumstance induced Professor Davies to prepare his 
 Elementary Course. 
 
 The series of works here presented, form a full and complete 
 course of mathematical instruction, beginning with the first com- 
 binations of arithmetic, and terminating in the higher applications 
 of the Differential Calculus. Each part is adapted to all the 
 others. The Definitions and Rules in the Arithmetic, have 
 reference to those in the Elementary Algebra, and these to similar 
 ones in the higher books. A pupil, therefore, who begins this 
 course in the primary school, passes into the academy, and then 
 into the college, under the very same system of scientific in- 
 struction. 
 
 The methods of teaching are all the same, varied only by the 
 lature and difficulty of the subject. He advances steadily from 
 one grade of knowledge to another, seeing as he advances the con 
 nection and mutual relation of all the parts : and when he reacnej 
 the end of his course, he finds indeed, that “ science is but know 
 ledge reduced to order.” 
 
 (81 
 
Davies' System of Mathematics. 
 
 DAVIES’ BOURDON. 
 
 The Treatise on Algebra by M. Bourdon, is a work of singular excellence 
 and merit. In France it is one of the leading text-books. Shortly after its first 
 publication it passed through several editions, and has formed the basis of every 
 subsequent work on the subject of Algebra. 
 
 The original work is, however, a full and complete treatise on the subject of 
 Algebra, the later editions containing about eight hundred pages octavo. The 
 time given to the study of Algebra in this country, even in those seminaries where 
 the course of mathematics is the fullest, is too short to accomplish so volumin- 
 ous a work, and hence it has been found necessary either to modify it, or to 
 abandon it altogether. The Algebra of M. Bourdon, however, has been regarded 
 only as a standard or model, and it would perhaps not be just to regard him as 
 responsible for the work in its present form. 
 
 In this work are united the scientific discussions of the French with the prac- 
 tical methods of the English school, so that theory and practice, science and art, 
 may mutually aid and illustrate each other. A great variety of examples have 
 also been added in the late editions. 
 
 DAVIES’ LEGENDRE. 
 
 Legendre’s Geometry has taken the place of Euclid, to a great extent, both in 
 Europe and in this country. In the original work the propositions are not 
 enunciated in general terms, but with reference to, and by the aid of, the par- 
 ticular diagrams used for the demonstrations. It was supposed that this de 
 parture from the method of Euclid had been generally regretted, and among the 
 many alterations made in the original work, to adapt it to the systems of i e- 
 struction in this country, that of enunciating the propositions in general terms 
 should be particularly named ; and this change has met with universal acceptance. 
 
 To the Geometry is appended a system of Mensuration of Planes and Solids— 
 a full treatise on Plane and Spherical Trigonometry— and a table of Logarithms, 
 and Logarithmic Sines, Tangents, and Secants. The whole forms a complete 
 system of Geometry with its applications to Trigonometry and Mensuration, 
 together with the necessary tables. 
 
 ANALYTICAL GEOMETRY. 
 
 This work embraces the investigation of the properties of geometrical figures 
 oy means of analysis. It commences with the elementary principles of the sci- 
 ence, discusses the Equation of the Straight Line and Circle — the Properties of 
 the Conic Sections — the Equation of the Plane — the Positions of Lines in Space, 
 and the Properties of Surfaces. 
 
 DESCRIPTIVE GEOMETRY. 
 
 Descriptive Geometry is intimately connected with Architecture and Civil 
 Engineering, and affords great facilities in all the operations of Construction. 
 
 As a mental discipline, the study of it holds the first place among the various 
 branches of Mathematics. 
 
 SHADES, SHADOWS, AND PERSPECTIVE. 
 
 This work embraces the various applications of Descriptive Geometry to 
 Drawing and Linear Perspective. 
 
 DIFFERENTIAL AND INTEGRAL CALCULUS. 
 
 This treatise on the Differential and Integral Calculus, was intended to supp.y 
 the higher seminaries of learning with a text-book on that branch of science. It 
 is a work after the French methods of teaching, and in which the notation of tin 
 French school is adopted. 
 
 fP 
 
Davies’ Mathematical Works. 
 
 A CATALOGUE 
 
 OF THE 
 
 COLLEGES AND UNIVERSITIES 
 
 THAT HAVE ADOPTED 
 
 DAVIES’ MATHEMATICAL WORKS. 
 
 (THE WHOLE SERIES, OR IN PART.) 
 
 THE UNITE!) STATES MILITARY ACADEMY. 
 
 Dartmouth College, 
 
 University of Vermont, 
 Norwich University, 
 
 Brown University, 
 
 Washington College, 
 
 Wesleyan University, 
 
 Columbia College, 
 
 Union College, 
 
 Hamilton Lit. and Theol. Instil. 
 Geneva College, 
 
 University of New York, 
 College of New Jersey, 
 University of Pennsylvania, 
 Lafayette College, 
 
 Marsh ill College, 
 
 Dickinson College, 
 
 Jefferson College, 
 
 Washington College, 
 
 Alleghany College, 
 
 Western University, 
 
 Newark College, 
 
 Georgetown College, 
 Columbian College, 
 
 St. John’s College, 
 
 St. Mary’s College, 
 
 Mount St. Mary’s College, 
 Washington College, 
 
 Hanover, 
 
 New Hampshire 
 
 Burlington , 
 
 Vermont. 
 
 Norwich, 
 
 
 Providence, 
 
 Rhode Island. 
 
 Hartford, 
 
 Connecticut. 
 
 Middletown, 
 
 “ 
 
 New York, 
 
 New York. 
 
 Schenectady, 
 
 14 ,4 
 
 Hamilton, 
 
 “ “ 
 
 Geneva, 
 
 .4 
 
 New York, 
 
 4. .4 
 
 Princeton. 
 
 New Jersey. 
 
 Philadelphia, 
 
 Pennsylvania. 
 
 Easton, 
 
 4* 
 
 Mercersburg, 
 
 U 
 
 Carlisle, 
 
 44 
 
 Canonsburg. 
 
 44 
 
 Washington, 
 
 44 
 
 Meadville, 
 
 44 
 
 Pittsburg, 
 
 44 
 
 Newark, 
 
 Delaware. 
 
 Georgetown . 
 
 Dist. of Columrl 
 
 Washington, 
 
 It 4* 
 
 Annapolis, 
 
 Maryland, 
 
 Baltimore, 
 
 “ 
 
 Emmettsburg, 
 
 “ 
 
 Lexingtgn, 
 
 Virginia. 
 
 10 
 
Davies’ Mathematical Works. 
 
 Hamp>den-Sydney College, 
 University of Virginia, 
 Randolph Macon College, 
 University of North Carolina, 
 Davidson College, 
 
 College of South Carolina, 
 University of Alabama, 
 Lagrange College, 
 
 Louisiana College, 
 
 Jefferson College, 
 
 Oakland College, 
 
 University of Tennessee, 
 
 St. Joseph’s College, 
 
 Centre College, 
 
 Augusta College, 
 
 Cumberland College, 
 Georgetown College, 
 
 Bacon College, 
 
 University of Ohio, 
 
 Western Reserve College, 
 Oberlin Institute, 
 
 Miami University, 
 
 Franklin College, 
 
 Kenyon College, 
 
 Granville College, 
 
 Cincinnati College, 
 Woodward College, 
 
 Indiana College, 
 
 South Hanover College, 
 Wabash College, 
 
 Illinois College, 
 
 Shurtleff College, 
 McKendroan College, 
 University of St. Louis, 
 
 St. Charles College, 
 
 Michigan University, 
 
 Tbe Miiitary Academy, 
 Charleston College, 
 
 Prince Ed Co. 
 
 Virginia. 
 
 Charlottesville, 
 
 “ 
 
 Boydtown, 
 
 U 
 
 Chapel-Hill, 
 
 North Carolina 
 
 Mecklenburg, 
 
 tl 
 
 Columbia, 
 
 South Carolina 
 
 Tuscaloosa, 
 
 Alabama. 
 
 Lagrange, 
 
 “ 
 
 Jackson, 
 
 Louisiana. 
 
 Washington, 
 
 Mississippl 
 
 Oakland, 
 
 W 
 
 Nashville, 
 
 Tennessee. 
 
 Bardstown, 
 
 Kentucky. 
 
 Danville, 
 
 (* 
 
 Augusta, 
 
 “ 
 
 Princeton, 
 
 1C 
 
 Georgetown, 
 
 “ 
 
 Harrodsburgh, 
 
 “ 
 
 Athens, 
 
 Ohio. 
 
 Hudson, 
 
 U 
 
 Oberlin, 
 
 it 
 
 Oxford, 
 
 “ 
 
 New Athens, 
 
 - 
 
 Gambier, 
 
 a 
 
 Granville, 
 
 - 
 
 Cincinnati, 
 
 - 
 
 Cincinnati, 
 
 “ 
 
 Bloomington, 
 
 Indiana 
 
 South Hanover, 
 
 “ 
 
 Crawford sviUe, 
 
 “ 
 
 Jacksonville, 
 
 Illinois 
 
 Upper Alton, 
 
 “ 
 
 Lebanon, 
 
 it 
 
 St. Louis, 
 
 Missouri 
 
 St. Charles, 
 
 ■ U 
 
 Ann Arbour, 
 
 Michigan 
 
 Georgetown, 
 
 Kentucky. 
 
 Charleston , i 
 
 South Carolina 
 
 11 
 
Parker' a Natural riulosophy. 
 
 NATURAL AND EXPERIMENTAL PHILOSOPHY 
 
 FOR SCHOOLS AND ACADEMIES, 
 
 BY R. G. PARKER, A. M. 
 
 PRINCIPAL OF THE JOHNSON GRAMMAR SCHOOL, BOSTON, AUTHOR OF AIDS 
 TO ENGLISH COMPOSITION, ETC., ETC. 
 
 I. PARKER’S FIRST LESSONS IN NATURAL PHILOSOPHY. 
 
 II. PARKER’S COMPENDIUM OF NATURAL AND EXPERIMENTAL 
 PHILOSOPHY. 
 
 PARKER’S FIRST LESSONS IN NATURAL PHILOSOPHY, 
 Embracing the Elements of the Science. Illustrated with numerous 
 engravings. Designed for young beginners. Price 38 cts. 
 
 It is the design of this Utile book, to present to the minds of the 
 youth of the country a view of the laws of Nature— as they are 
 exhibited in the Natural World. 
 
 Reading books should be used in schools for the double object of 
 teaching the child to read, and storing his mind with pleasant and 
 useful ideas. 
 
 The form of instruction by dialogue, being the simplest, has 
 been adopted — and by means of the simple question and the ap- 
 propriate answer, a general view of the laws of the physical uni- 
 verse has been rendered so intelligible, as to be easily understood 
 by children who are able to read intelligibly. 
 
 It is confidently believed that this book will form an importanl 
 eia in the progress of common-school education 
 
 PARKER’S COMPENDIUM OF NATURAL AND EXPERIMENTAL 
 PHILOSOPHY. 
 
 Embracing the Elementary principles of Mechanics, Hydrostatics, Hy- 
 draulics, Pneumatics, Acoustics, Pyronomics, Optics, Astronomy, 
 Galvanism, Magnetism, Electro-Magnetism, Magneto-Electricity, 
 with a description of the Steam and Locomotive Engines. Illustrated 
 by numerous diagrams. Price $1.00. 
 
 The use of school apparatus for illustrating and exemplifying 
 the principles of Natural and Experimental Philosophy, has, with- 
 in the last few years, become so general as to render necessary a 
 work which should combine, in the same course of instruction, the 
 theory, with a full description of the apparatus necessary for illus- 
 tration and experiment. 
 
 The work of Professor Parker, it is confidently believed, fully 
 oiwets that requirement. It is also verv full in the general facts 
 
 (U) 
 
Parker's Natural Philosophy. 
 
 which it presents — clear and concise in its style, and entirely 
 scientific and natural in its arrangement. The following features 
 will, it is hoped, commend the work to public favor. 
 
 1. It is adapted to the present state of natural science ; embraces 
 a wider field, and contains a greater amount of information on the 
 respective subjects of which it treats, than any other elementary 
 treatise of its size. 
 
 2. It contains an engraving of the Boston School set of philn 
 sophical apparatus ; a description of the instruments, and an ac- 
 count of many experiments which can he performed by means ot 
 the apparatus. 
 
 3 It is enriched by a representation and a description of the 
 Locomotive and the Stationary Steam Engines , in their latest and 
 most approved form3. 
 
 4. Besides embracing a copious account of the principles ol 
 Electricity and Magnetism, its value is enhanced by the introduc- 
 tion of the science of Pyronomics, together with the new science 
 of Electro-Magnetism and Magneto-Electricity. 
 
 5. It is peculiarly adapted to the convenience of study and of 
 recitation, by the figures and diagrams being first placed side by 
 side with the illustrations, and then repeated on separate leaves at 
 the end of the volume. The number is also given, where each 
 principle may be found, to which allusion is made throughout the 
 volume. 
 
 6. It presents the most important principles of science in a 
 larger type ; while the deductions from these principles, and the 
 illustrations, are contained in a smaller letter. Much useful and 
 interesting matter is also crowded into notes at the bottom of the 
 page. By this arrangement, the pupil can never be at a loss to 
 distinguish the parts of a lesson which are of primary importance ; 
 nor will he be in danger of mistaking theory ami conjecture for fact. 
 
 7. It contains a number of original illustrations, which the author 
 has found more intelligible to young students than those which he 
 has met elsewhere. 
 
 8. Nothing has been omitted which is usually contained in an 
 elementary treatise. 
 
 9. A full description is given of the Magnetic Telegraph, and the 
 principles of its construction are fully explained. 
 
 10. For the purpose of aiding the teacher in conducting an ex- 
 amination through an entire subject, or indeed, through the whole 
 book, if necessary, all the diagrams have been repeated at the 
 end of the work, and questions proposed on the left-hand page im- 
 mediately opposite. This arrangement will permit ihe pupil to 
 use the figure, in his recitation, if he have not time to make it on 
 the black-boa. d. and will also enable him to review several lessons 
 and rec all all the principles by simply reading the questions, and 
 analyzing the diagrams. 
 
Parker's Natural Philosophy. 
 
 From the Wayne County Whig. 
 
 After a careful examination of this work, we find that it is well calculated for 
 the purpose for which it is intended, and better adapted to the state of natural 
 science at the present time, than any other similar production with which we 
 are acquainted. The design of the author, in the preparation of this work, was 
 to present to the public an elementary treatise unencumbered with matter that is 
 not intimately connected with this science, and to give a greater amount of in- 
 formation on the respective subjects of which it treats, than any other school- 
 book of an elementary character. The most remarkable feature in the style of 
 this work is its extreme brevity In the arrangement of the subject and the man 
 ner of presenting it, there are some peculiarities which are, in our opinion, de- 
 cided improvements. The more important principles of this interesting science 
 are given in a few words, and with admirable perspicuity, in a larger type ; while 
 the deductions from these principles, and the illustrations are contained in a 
 smaller letter. Much useful and interesting matter is also given in notes at the 
 oottoin of the page. 
 
 This volume is designed expressly to accompany the Boston School Srt of Philo- 
 sophical .Apparatus ; but the numerous diagrams with which it is illustrated, are 
 so well executed and so easily understood, that the assistance of the Apparatus 
 is hardly necessary to a thorough knowledge of the science. The trustees of the 
 Lyons Union School having recently procured a complete set of the above Ap- 
 paratus, this work will now be used as a text-book in that institution. 
 
 Leicester Academy, April 12, 1848. 
 
 Messrs. A. S. Barnes & Co.: 
 
 Sirs : — I have examined Parker’s Natural Philosophy, and anj much pleased 
 with it. 1 think I shall introduce it into the academy the coining term. It seems 
 to me to have hit a happy medium betw een the too simple and the too’abstract. 
 The notes containing facts, and showing the reasons of many things that are of 
 common occurrence m every-day life, seem to me to be a valuable feature of the 
 work. 
 
 Very respectfully, yours, B. A. SMITH. 
 
 From the New York Evening Post. 
 
 Professor Parker’s book embraces the latest results of investigation on the sul 
 'ects of which it treats. It has a separate title for the laws of heat, or Pyronom 
 lcs, which have been lately added to the list of sciences, as well as electro mag- 
 netism and magneto electricity. The matter is well arranged, and the style of 
 statement clear and concise. The figures and diagrams are placed side by side 
 with the text they illustrate, which is greatly for the convenience of the student- 
 We cheerfully commend the book to the favorable attention of the public. 
 
 From the Jllbany Spectator. 
 
 'I his is a school-book of no mean pretensions and of no ordinary value. It is 
 admirably adapted to the present state of natural science ; and besides contain- 
 ing engravings of the Boston school set of philosophical apparatus, embodies 
 >ii ire information on every subject on which it treats than any other elementary 
 '*■ rk of its size that we have examined It abounds with all the necessary heips 
 m 'rosecuting the study of the science, and as its value becomes known it can- 
 f aii to be generally adopted as a text-book 
 
 14 
 
Parker $ Natural Philosophy. 
 
 From the Newark Daily Advertiser. 
 
 A work adapted to the present state of natural science is greatly needed in all 
 our schools, and the appearance. of one meeting all ordinary wants must be hailed 
 with pleasure by those who feel an interest in the cause of education. Mr. Par- 
 ker’s work embraces a wider field, and contains a greater amount of information 
 on the respective subjects of which it treats, than any other elementary treatise 
 of its size, and is rendered peculiarly valuable by the introduction of the science of 
 Pyronomics, together with the new sciences of Electro-Magnetism and Magneto 
 Electricity. We have seldom met wdth a work so well adapted to the conveni- 
 ence of study and recitation, and regard as highly worthy of commendation the 
 care which the author has taken to prevent the pupil from mistaking theory and 
 conjecture for fact. We predict for this valuable and beautifully printed w 
 the utmost success. 
 
 From the New York Courier and Enquirer 
 
 “ A School Compendium of Natural and Experimental Philosophy,” by Richard 
 Green Parker, has just been issued by Barnes &. Co. Mr. Parker has had a good 
 deal of experience in the business of practical instruction, and is, also, the author 
 of works which have been widely adopted in schools. The present volume strikes 
 us as having very marked merit, and we cannot doubt it will be well received. 
 
 New York, May . 1848. 
 
 Messrs. A. S. Barnes & Co.-. 
 
 Gent . I have no hesitation in saying that Parker’s Natural Philosophy is the 
 most valuable elementary work I have seen : the arrangement of the subjects 
 and the clearness of the definitions render it an excellent adjunct to a teacher. 
 For the last seven years I have used it in various schools as a text-book for my 
 lectures on Natural Philosophy, and am happy to find that in the new edition 
 much important matter is added, more especially on the subjects of Electricity 
 and Electro-Magnetism. 
 
 With respect, Gentlemen, 
 
 Your obedient servant, 
 
 GILBERT LANGDON HUME, 
 Teacher of Natural Philosophy and Mathematics in N. Y. city. 
 
 New York, May 2, 1848 
 
 We have used Parker’s Compend of Natural Philosophy for many years, and 
 consider it an excellent work on the various topics of which it treats. 
 
 Yours, &c. FORREST &. McELLIGOTT, 
 
 Principals of the Collegiate School 
 
 From the Lynchburg Virginian. 
 
 The volume before us strikes us as containing more to recommend it than any 
 one of its class with which we are acquainted. It is adapted to the present state 
 of natural science ; embraces a wider field, and contains a greater amount of in- 
 formation on the respective subjects of which it treats, than any other clement. iry 
 treatise of its size. It contains descriptions of the steam-engine, stationery and 
 locomotive, and of the magnetic telegraph. It embraces a copious account o' 
 the principles of electricity and magnetism, under all their modifications, and is 
 embellished by a vast number of illustrations and diagrams. There is appended 
 a series of questions for examination, copious and pertinent 
 
 15 
 
Gillespie's Manna 1 of Road- Making. 
 
 ROADS AND RAILROADS. 
 
 A MANUAL OF ROAD-MAKING: 
 
 Comprising the principles and practice of the Location, Construe • 
 tion, and Improvement of Roads, (common, macadam, paved 
 plank, &c.,) and Railroads. By W. M. Gillespie, A. M., 
 Professor of Civil Engineering in Union College. Price $1.50. 
 
 Recommendation from Professor Mahan . 
 
 I have very carefully looked over Professor Gillespie’s Manual of Road- 
 Making. It is, in all respects, the best work on this subject with which I am ac- 
 quainted ; being, from its arrangement, comprehensiveness and clearness, equally 
 adapted to the wants of Students of Civil Engineering, and the purposes of per 
 sons in any way engaged in the construction or supervision of roads. The ap- 
 pearance of such a work, twenty years earlier, would have been a truly national 
 benefit, and it is to be hoped that its introduction into our seminaries may be so 
 general as to make a knowledge of the principles and practice of this branch of 
 engineering, as popular as is its importance to all classes of the community. 
 
 (Signed,) 
 
 D. H. MAHAN, 
 
 Professor of Civil Engineering in the Military ) 
 Academy of the United States. j 
 
 From a Report of a Committee of the American Institute. 
 
 This work contains in a condensed form, all the principles, both ancient and 
 modern, of this most important art ; and almost every thing useful in the great 
 
 mass of writers on this subject Such a work as this performs a great 
 
 service for those who are destined to construct roads — by showing not only what 
 ought to be done, but what ought not to be done ; thus saving immense outlay of 
 money, and loss of time in experiments The committee therefore, recom- 
 
 mend it to the public. 
 
 From the American Railroad Journal. 
 
 The views of the author are sound and practical, and should be read by the 
 people throughout the entire length and breadth of the land. . . . We recom- 
 mend this Manual to the perusal of every tax-payer for road-making, and to the 
 young men of the country, as they will find useful information in relation to each 
 department of road-making, which will surely be useful to them in after-life. 
 
 From Silli man's American Journal of Science. 
 
 If the well-established principles of Road-Making, which are so plainly set 
 forth in Prof. Gillespie’s valuable work, and so well illustrated, could be once 
 pat into general use in this country, every traveller would bear testimony to the 
 fact that the author is a great public benefactor. 
 
 From the Journal of the Franklin Institute. 
 
 This small volume contains much valuable matter, derived from the best 
 authorities, and set forth in a clear and simple style. For the want of informa- 
 tion which is contained in this Manual, serious mistakes are frequently made, 
 and roads are badly located and badly constructed by persons ignorant of the 
 
 (Id) 
 
Gillespie's Manual of Road- Making. 
 
 principles which ought to govern in such cases. By the extensive circulati of 
 such books as that now before us, and the imparting of sound views on tin it- 
 ject to the students of our collegiate institutions, we may hope for a chani for 
 .he better in this respect. 
 
 From the Albany Cultivator. 
 
 The author of this work has supplied a desideratum which has long existed 
 Perhaps there is no subject on which information is more needed by the country 
 in general than that of Road-Making. Prof. Gillespie has taken up the subject 
 in a proper manner, beginning the work at the right place, and prosecuting it in 
 systematic order to' its completion. 
 
 From the New York Tribune. 
 
 It would astonish many “ path-masters” to see how much they don’t know 
 with regard to the very business they have considered themselves such adepts in. 
 Yet all is so simple, so lucid, so straightforward, so manifestly true, that the 
 most ordinary and least instructed mind cannot fail to profit by it. We trust this 
 useful and excellent volume may find its way into every village library if not 
 into every school library, as well as into the hands of every man interested in 
 road-making. Its illustrations are very plain and valuable, and we cannot doubt 
 that the work will be a’ welcome visiter in many a neighborhood, and that bad 
 roads will vanish before it. 
 
 From the Newark Daily Advertiser. 
 
 This elaborate and admirable work combines in a systematic and symmetrical 
 form the results of an engineering experience in all parts of the Union, and of an 
 examination of the great roads of Europe, with a careful digestion of all acces- 
 sible authorities. The six chapters into which it is divided comprehend a 
 methodical treatise upon every part of the whole subject ; showing what roads 
 ought to be in the vital points of direction, slopes, shape, surface, and cost, and 
 giving methods of performing all the necessary measurements of distances, di 
 rections, and heights, without the use of any instruments but such as any 
 mechanic can make, and any farmer use. Bridges, Railroads, and City Streets 
 are also treated of at length and with good sense. 
 
 From the Vermont Chronicle. 
 
 To selectmen and others who may have any thing to do with these improve- 
 ments, we would earnestly recommend the book named above. The author is a 
 man of science, (Professor of Civil Engineering at Union College,) and his work 
 embraces a full discussion of both the principles and practice of Road-Making 
 A little study of this work may often lead to results of importance to whole towns 
 and counties. 
 
 From the Home Journal. 
 
 The author of this book holds a quill so skilful and dair tv in light literature, 
 that we were not prepared with laurels to crown him for a scientific work but 
 we see, by the learned critics, that this fruit of his study of his profession as an 
 engineer, is very worthy of high commendation, and a valuable addition to the 
 useful literature of the day. 
 
Willard’s Series of School Histories and Charts. 
 
 MRS. EMMA WILLARD’S 
 
 SERIES OF SCHOOL HISTORIES AND CHARTS. 
 
 I. WILLARD’S HISTORY OF THE UNITED STATES, OR RE- 
 PUBLIC OF AMERICA. 8vo. Price $1.50. 
 
 II. WILLARD’S SCHOOL HISTORY OF THE UNITED STATES. 
 
 III. WILLARD'S AMERICAN CHRONOGRAPHER, $1.00. 
 
 A Chart op American History. 
 
 I. WILLARD’S UNIVERSAL HISTORY IN PERSPECTIVE. $1.50. 
 II. WILLARD’S TEMPLE OF TIME, $1.25. 
 
 A Chart of Universal History 
 
 WILLARD’S 
 
 HISTORY OF THE UNITED STATES. 
 
 The large work is designed as a Text-Book for Academies and 
 Female Seminaries: and also for District School and Family 
 Libraries. The small work being an Abridgment of the same, is 
 designed as a Text-Book for Common Schools. The originality 
 of the plan consists in dividing the time into periods , of which 
 the beginnings and terminations are marked by important events ; 
 and constructing a series of maps illustrating the progress of the 
 settlement of the country , and the regular advances of civilization. 
 The Chronographic Chart, gives by simple inspection, a view of 
 the divisions of the work, and the events which mark the be- 
 ginning and termination of each period into which it is divided. 
 A full chronological table will be found, in which all the events of 
 the History are arranged in the order of time. There is appended 
 to the work the Constitution of the United States, and a series ol 
 questions adapted to each chapter, so that the work may be used 
 in schools and for private instruction. 
 
 The Hon. Daniel Webster says, of an early edition of the above work, in a letter 
 to the author, 4 * 7 keep it near me, as a Booh of Reference , accurate in facts and dates. 1 * 
 
 0 8 
 
Willard’s Series of School Histories and Charts. 
 
 WILLARD’S 
 
 AMERICAN C H RONOGRAPH ER, 
 
 DESIGNED TO ACCOMPANY WILLARD’S HISTORY OP 
 THE UNITED STATER 
 
 To measure time by space is universal .among civilized nations, 
 and as the hours, and minutes, and seconds of a clock measure the 
 time of a day, so do the centuries, tens, and single years of this 
 Chronographer, measure the time of American History. A 
 general knowledge of chronology is as indispensable to history, as 
 a general knowledge of latitude and longitude is to geography. 
 But to learn single dates, apart from a general plan of chronology 
 addressed to the eye, is as useless as to learn latitudes and longi- 
 tudes without reference to a map. The eye is the only medium 
 of permanent impression. The essential point in a date, is to 
 know the relative place of an event, or how it stands in time com- 
 pared with other important events. The scholar in the school- 
 100m, or the gentleman in his study, wants such a visible plan of 
 time for the study of history, the same as he wants the visible 
 plan of space, viz., a map for the study of geography, or of books 
 of travels. Such is the object of Willard's Chronographer of 
 American History. 
 
 Extract from a Report of the Ward School Teachers ’ Association 
 of the City of New York. 
 
 The Committee on Books of the Ward School Association respectfully report . 
 
 That they have examined Mrs. Willard’s History of the United States with 
 peculiar interest, and are free to say, that it is in their opinion decidedly the best 
 treatise on this interesting subject that they have seen. * * 
 
 As a school-book, its proper place is among the first. The language is remark- 
 able for simplicity, perspicuity, and neatness ; youth could not be trained to a 
 better taste for language than this is calculated to impart. The history is so 
 written as to lead to geographical examinations, and impresses by practice the 
 habit to read history with maps. It places at once, in the hands of American 
 youth, the history of their country from the day of its discovery to tne present 
 time, and exhibits a clear arrangement of all the great and good deeds of the'r 
 ancestors, of which they now enjoy the benefits, and inherit the renown. The 
 struggles, sufferings, firmness, and piety of the first settlers are delineated with a 
 masterly hand. 
 
 The gradual enlargement of our dominions, and the development of our na- 
 tional energies, are traced with a minute accuracy, which the general plan of the 
 work, indicates. 
 
 The events and achievements of the Revolution and of the last war, are 
 brought out in a clear light, and the subsequent history of our national policy 
 and advancement striking! v portrayed, without being disfigured bv that tinge 
 
 (IT 
 
Willard's Series oj School Histories and Charts. 
 
 ol party bias which is so difficult to be guarded against by historians of their own 
 times. 
 
 The aetails of the discovery of this continent by Columbus, and of the early 
 settlements by the Spaniards, Portuguese, and other European nations, are all of 
 essential interest to the student of American history, and will be found sufficiently 
 minute to render the history of the continent full and complete. The different 
 periods of time, together with the particular dates, are distinctly set forth with 
 statistical notes on the margin of each page, — and these afford much inf rmation 
 without perusing the pages. 
 
 The maps are beautifully executed, with the locality of places where particular 
 events occurred, and the surrounding country particularly delineated. These 
 are admirably calculated to make lasting impressions on the mind. 
 
 The day has now arrived when every child should be acquainted with the his- 
 tory of his country ; and your Committee rejoice that a work so full and clear can 
 be placed within the reach of every one. 
 
 The student will leam, by reading a few pages, how much reason he has to be 
 proud of his country— of its institutions — of its founders — of its heroes and states- 
 men : and by such lessons are we not to hope that those who come after us w T n 
 be instructed in their duties as citizens, and their obligations as patriots 1 
 
 Your Committee are anxious to see this work extensively used in all the schools 
 in the United States. 
 
 (Signed,) 
 
 SENECA DURAND, 
 EDWARD McELROY, 
 JOHN WALSH. 
 
 The Committee would respectfully offer the following resolution : 
 
 Resolved, That Mrs. Emma Willard’s History of the United States be adopted 
 by this Association, and its introduction into our schools earnestly recom- 
 mended. 
 
 At a meeting of the Board of the Ward School Teacners’ Association, January 
 20th, 1847, the above Resolution was adopted. — (Copied from the Minutes.) 
 
 From the Boston Traveller. 
 
 We consider the work a remarkable one, in that it forms the best book for 
 general reading and reference published, and at the same time has no equal, in 
 our opinion, as a text-book. On this latter point, the profession which its author 
 has so long followed with such signal success, rendered her peculiarly a fitting 
 person to prepare a text-book. None but a practical teachei is capable of pre- 
 paring a good school-book ; and as woman has so much to do in forming our 
 early character, why should her influence cease at the fireside — why not en- 
 courage her to exert her talents still, in preparing school and other books for 
 after years 1 No hand can do it better. 
 
 The typography of this work is altogether in good taste. 
 
 From the Cincinnati Gazette. 
 
 Mrs. Willard’s School History of the United States.— It is one of those 
 rare things, a good schuol-book ; infinitely better than any of the United States 
 Histones fitted for schools, which we have at present. It is quite full enough, 
 and yet condensed with great care and skill. The style is clear and simple — 
 Mrs. Willard having avoided those immense Johnsonian words w hich Gnmshaw 
 and other writers for children love to put into their works, while, at the same 
 time there is nothing of the pap style about it. The arrangement is exoellen' 
 
 ( 20 ) 
 
Willard’s Series of Sc ho >/ Histories and Charts. 
 
 the chapters of a good length ; every page is dated, and a marginal index makes 
 reference easy. But the best feature in the work is its series of maps ; we have 
 the country as it was when filled with Indians ; as granted to Gilbert . as di- 
 vided at the time the Pilgrims came over; as apportioned in 1643; the West 
 w hile in possession of France ; the Atlantic coast in 1T33 ; in 1763 ; as in the 
 Revolution, with the position of the army at various points ; at the close of the 
 Revolutionary War ; during the war of 1812-15 ; and in 1840 : making eleven 
 most excellent maps, such as every school history should have. When we 
 think of the unintelligible, incomplete, badly written, badly arranged, worthless 
 work of Grimshaw which has been .so long used in our schools, we feel that 
 every scholar and teacher owes a debt of gratitude to Mrs. Willard. Miss 
 Robins has done for English History, what Mrs. Willard has now done for 
 American, and we trust these two works will be followed by others of as high or 
 higher character. We recommend Mrs. Willard’s work as better than any we 
 know of on the same subject ; not excepting Bancroft’s abridgment. This work, 
 followed by the careful reading of Mr Bancroft’s full work, is all that would be 
 needed up to the point where Bancroft stops ; from that point, Pitkin and Mar- 
 shall imperfectly supply the place, which Bancroft and Sparks will soon fUL 
 
 From the United States Gazette. 
 
 Mrs. Willard is well known throughout the country as a lady of high attain 
 ments, who has distinguished herself as the Principal of Female Academies, that 
 have sent abroad some of the most accomplished females of the land. 
 
 The plan of the authoress is to divide the time into periods, of which the be- 
 ginning and the end are marked by some important event, and then care has 
 been taken to make plain the events of intermediate periods. The style is clear, 
 and there appears no confusion in the narrative. In looking through the work, 
 we do not discover that the author has any early prejudices to gratify. The 
 book, therefore, so far as we have been able to judge, may be safely recom- 
 mended as one of g r eat merit, and the maps and marginal notes, and series of 
 questions, give additional value to the work. 
 
 From the Vr u-buryport Watchman. 
 
 An Abridged History of the United States : By Emma Willard. — We 
 think we are warranted in saying, that it is better adapted to meet the wants of 
 our schools and academies in which history is pursued, than any other work of 
 the kind now before the public. 
 
 The style is perspicuous and flowing, and the prominent points of our history are 
 presented in such a manner as to make a deep and lasting impression on the mind. 
 
 We could conscientiously say much more in praise of this book, but inust content 
 ourselves by heartily commending it to the attention of those who are anxious 
 to find a good text-book of American history for the use of schools. 
 
 From the Albany Evening Journal . 
 
 Wu lard’s United States. — This work is well printed on strong white paper, 
 and is bound in a plain substantial manner — all-important requisites in a school- 
 book. The text is prepared with equal skill and judgment. The memory of the 
 youthful student is aided by a number of spirited illustrations — by no means un- 
 important auxiliaries — while to lighten the labors of the teacher, a series of ques- 
 tions is adapted to each chapter. Nor is its usefulness limited to the school-room 
 As a book of reference for editors, lawyers, politicians, and others, where dates and 
 facts connected with every important event in American History may be readily 
 found, this little book is truly valuable- 
 
 91 
 
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