ar 7 17994 V THE Universal Metric System. ALFRED COLIN, M. E. §ohvt pttt;jj ®ftttt;pit(rM ^ mn u Cornell University Library ar y 17994 The universal metric system : ,. 3 1924 031 230 034 olin.anx The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031230034 THE UlilYERSAL METRIC SYSTEM PKEPAKEti ESPECIALLY FOE CANDIDATES FOK SCHOOLS OF SCIENCE, EMINEERS, and OTHERS. BT , ALFRED COLIN, M. E., PEIlfOIPAI. OF A PEEPAEATOET 8CIEHTIFI0 SCHOOL. NEW YORK : D. appleton and company, 549 & 551 BEOADWAT. 18V6. I!iiTEBra>, according to Act of Congress, In the year 18T6, By D. APPLETON & CO., In {he Office of the librarian of Congress, at IVaBhington. The following pages present a simple exposition of the Metric System, no attempt at any historical or critical sketch having been made. Numerous problems have been added — some containing valu- able data — and, after careful reading, it is hoped that no book employing the System will present the least difficulty, A. C. New Yobk, March, 18T6. THE UNIYERSAL METRIC SYSTEM. FoEMEELT every nation, and almost every village, had a particular set of measures, for the word System cannot be applied to units taken at random. Evi- dently commerce could only be a loser from such a diversity of methods of measurement, and, besides, no accuracy was possible. The originators of what is known as the French Metric System had in view the removal o± all these difficulties. The Metric System is called French because every system bears the name of the nation which introduced it, and until this system becomes Universal, or Inter- national, it will be styled French. Scarcely can any one unhesitatingly answer, accord- ing to the methods usually adopted, such questions con- cerning the reduction of quantities as the following : How many feet, yards, or poles, are there in 5 miles ? How many acres are there in 5 square miles ? To render such questions easy of solution, even to persons but little skilled in arithmetic, was the aim of 6 THE UNIVERSAL METRIC SYSTEM. the originators of the Universal Metric System, as they had not only France but the civilized world in view when framing their system. The units of this system are : 1. The Metee for the unit of measure of length. 2. " Squaee Metee and the Aee " surface. 3. " Cubic Metee and the Steeb " volume. 4. " Litee " capacity. 5. " Gramme " weight. Unfortunately, we cannot add here a sixth name for the unit of money, consequently all our commer- cial necessities but the last can be referred to these Jive units. However, as these may prove too small or too large, we have m,ultiples and suimultiples. (as well as their doubles and halves for the convenience of small traders), which are formed by prefixing the Jive above words with the following for their multiples : Deca, . . . . meaning 10. JSecto, . . . . " 100. Kilo, .... «. 1,000. Myria, .... « 10,000. These four names are taken from the Greek. And by prefixing them to the following words for their submultiples : Deci, . .. . meaning ^ = O'l. Centi, ... " ^ = 0-01. Milli, . , . « 3-jjL^ = 0-001. The last three are derived from the Latin. THE UNIVERSAL METRIC SYSTEM. 7 Consequently, only twelve words are necessary to express any quantity in this system. From the metre we obtain the following : Multiples. — Decametre, hectometre, kilometre, my- riametre. Submultiples.' — Decimetre, centimetre, millimetre. From the litre : Multiples. — Decalitre, hectolitre, kilolitre, myria- litre. Submultiples. — Decilitre, centilitre, millUitre. From the gramme : Multiples. — ^Decagramme, hectogramme, kilogram- me, myriagramme. Submultiples. — Decigramme, centigramme, milli- gramme. This system, based on our decimal system of nu- meration and notation, was adopted in France in 1799, but only became compulsory, to the exclusion of all others, since 1840 (and is sometimes for this reason called legal). Almost all the nations of the globe have adopted it. It was legalized in England in 1864, in the United States in 1866. It is employed in most scientific works, and to come into common use in this country requires but to be adopted by the Government in its official transactions. THE TTNTT OF LENGTH. The unit of length is the metre ([lerpov, measure), which is equivalent to the ten-millionth ( nnn r^nn, ) part of the distance from the pole to the equator. 8 THE UNIVERSAL METRIC SYSTEM. The distance from the pole to the equator is the quarter of the meridian. Hence, Metres. From the pole to the equator there are 10,000,000. From one pole to the other " 30,000,000. In a great circle or a meridian " 40,000,000. Here we meet with the only objection to the sys- tem. Is the distance from the pole to the equator ex- actly measured? No; and it cannot be, and, should it ever be, it would vary as taught by geology and astronomy. Then, why has such an unsatisfactory unit been chosen? Because nothing in the universe is everlasting, and the earth, notwithstanding its great changes, will outlive its inhabitants. Besides, pro- vided a unit be adopted and kept as a standard in the archives of nations, all the conditions are satisfied, and the beauty and simplicity of the fundamental princi- ples apply to it. One metre = : 39-3707904 English inchesi Hence the following table : Metres, Inches. Myriametre, or 10,000 = S9S,101-90i = 6-21 miles. Kilometre, 1,000 - S9,S10-1904: = 3,280 ft. 10 in. Hectometre, 100 = 3,93'7.0Y904 = 328 ft. 1 in. Decametre, 10 = S9Z-101904: =32-8 ft. Metbe, 1 = Zd-Slonoi = 3-28 ft., almost 40 in. Decimetre, O'l = S-gSTOVOO = almost 4 in. Centimetre, 0-01 = 0-39370'79 Millimetre, • 0-001 = 0-0393TO'7 THE UNIVERSAL METRIC SYSTEM. 9 The reduction to English measures is easy, when the English tables are known. The following table is self-explanatory : MiUimetras. Metbeb. 1 Centimetres. 10 1 Deci- metrea. 100 10 1 1,000 ' 100 10 1 Deca- metres. 10,000 1,000 100 10 1 Hecto- metres. 100,000 10,000 1,000 100 10 1 Kilo- metr.iB. 1,000,000 100,000 10,000 1,000 *100 10 1 Myria- metre. 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1 We find that 1 metre = 10 decimetres = 100 centimetres = 1,000 millimetres. " " 1 myriametre = lOkilometres = 100 hectometres = . . . . The Standard Metre, kept in the National Ar- chives in Paris, is a rod of platinum, which is only exact when at the temperature of 0° centigrade, the point at which ice melts. The materials of which metres are manufactured, as well as the care taken- in making them, depend on their destination. For measuring dry goods they are generally wooden 10 THE UNIVEESAL METEIC SYSTEM. rods, with only ten divisions answering to the deci- metres. By architects, engineers, draughtsmen, etc., only half a metre (50 centimetres), or rather a double deci- metre (20 centimetres), with the millimetres divided into two parts (corresponding to 0-0005 metre), is used, and this is made of brass, ivory, or box-wood. For the use of artisans and others, a folding metre of ten divisions, each fold corresponding to one deci- metre, is found convenient, and each decimetre is di- vided into centimetres and millimetres. This metre is made of box-wood, but more generally of brass, and sold at a trifling cost. By surveyors, tape-lines and chains of 10 metres in length are used. The decametre (10 metres) and the hectometre (100 metres) are only employed by surveyors in their cal- culations. It is more convenient to say 10, 20, 30 metres than 1, 3, 3 decametres, and 400, 500, 600 metres than 4, 5, 6 hectometres. The kilometre (1,000 metres) is used as the unit of distance, and along roads and railways there are Mlo- metric poles or stones. The m,yriametre (10,000 metres) is hardly ever used, it being inconveniently large (6'21 miles). The decimetre (O'l metre) is frequently used, but it is still more common to say 10, 30, 30 centimetres than 1, 3, 3 decimetres. The centimetre (O'Ol metre) is the most common submultiple of the metre. THE U-NIYERSAL METRIC SYSTEM. H The millimetre (O'OOl metre) is very generally made use of ; for delicate work like machinery it is the unit, and 654 -written on a drawing means 0'654 metre. Carpenters, masons, etc., employ the centimetre as their unit. There are no measures smaller than the millime- tre ; but we count by tenths, hundredths, thousandths, etc., of a millimetre, when precision requires It is not usual to write 0'012^ metre, but rather 0*012j metre. There is no need of giving rules for reading and writing lengths expressed in metres, as these rules are essentially the same as those of the decimal fractions and numiers. For instance, 13,345*675 metres may be read : 1 myriametre, 3 kilometres, 3 hectometres, 4 deca- metres, 5 metres, 6 decimetres, 7 centimetres, and 5 millimetres. Or, 13 kilometres, 345 metres, and 675 millimetres, or in any other way we may choose. The reduction of French to English measures, and conversely, is easily accomplished. , , ., ^ 39-37079 X 1,000 39,370-79 1 ^"""^'''^ = 13x3x5ix40 = -^peo- = 0-631383 mile. Conversely — 1 mile = ^^„,„„ = 1-6093149 kilometre. \J'<3ai.oo6 The same result is directly reached from — 13 THE UNIVERSAL METRIC SYSTEM. 13 X 3 X 5i X 40 39-37079 X 1,000 = 1-609 . . . kilometre. THE UNIT OF SURFACE. The unit of surface is the square metre ; it is the area contained within a square each of whose sides is one metre long. Its multiples and submultiples, as well as their sur- faces, are : Square myriametre = 10,000' = 100,000,000 sq. metres, kilometre = 1,000^" = 1,000,000 hectometre = 100' = 10,000 decametre — 10' = 100 METEE = 1' =r 1 decimetre = • 0-1' z= 01 centimetre = 0.01' = O'OOOl millimetre = O'OOl' = O-OOOOOl From which it appears that — 1. One square decametre contains 100 square me- tres, and not 10, as we might be tempted to believe. 3. One square decimetre is the -^^ part of the square metre, and not ^. In fact, every unit is equiva- lent to 100 of the next lower order. This must be kept well in view, and is better illus- trated by the following diagram representing : THE UNIVERSAL METRIC SYSTEM. 13 —\10 d 7 6 S 3 1 Str€^,a7'e J)ecin?£^e Coyvteun/7-i^ iOO Sff^are CeM^me^s or iO,000 AT^iOire ]\MIl[metres. Aectzon. ^ /O s^icare ee7t^7netn!S . SO', cm 'or 100 sn.Tn.Tn ^M Although 1,000 metres make 1 kilometre, 1,000 square metres make but 10 square decametres. To prove it, let us in the above diagram suppose that the millimetres (O'OOl metre) are metres. Then 100 square metres cover the square A^ and 10 such squares or 14 THE UNIVERSAL METRIC SYSTEM. (100 X 10 = ) 1,000 square metres give but an hori- zontal section, or rectangle 31 W. But 100 square metres make, as seen in the diagram, 1 square deca- metre A. Hence, the ■whole rectangle M N'is equiva- lent to 10 square decametres. Furthermore, the vrhole square containing 10 such rectangles is equivalent to 100 X 100 = 10,000 square metres. Let us remark also that its side being 100 metres long or 1 hectometre, 1 square hectometre con- tains 10,000 square metres. Here we must add that the numbers 10, 1,000, 100,000, 0"1, and 0"001, having no exact square roots (and, had they any, those roots would not he multiples or submultiples of ten), consequently these numbers are not ttiultiples or submultiples of the square metre. Hence, such a number as SS'^S square metres must be read 35 square metres 75 square decimetres. The 7 belongs certainly to an order ten times smaller than the units ; however, it does not represent 7 squares whose sides are a decimetre long, but 7 rectangles of 1 metre in length and 1 decimetre in width. And the 5, representing hundredth parts of the square metre, are squares whose sides are equal to 1 deci- metre. Now, such a number as 19,875,643'46,789 square metres must be read hy separating it into periods of two figures, and adding one zero to the decimal, if odd. Kilo. Hecto. Deca. HetrcB. Deci. Genti, Milli, 19, 87, 56, 43- 46, 78, 90. And is read : 19 sq. kilometres, 87 sq. hectometres, . . . THE UNIVERSAL METRIC SYSTEM. 15 Remark. — We say 19 square kilometres, meaning 19 equal squares whose sides are each 1 kilometre long; while the expression 19 Hlomelres square means a square whose sides are each 19 kilome- tres long, and whose area is consequently (19X19 = )361 square kilometres. For surveying, a larger unit than the square metre is necessary, and this is the Aee (Lat. area, surface), which is the area contained within a square whose sides are 10 metres long ; or, more simply, it is a square decametre. The demonstration of the square metre being un- derstood, the multiples and submultiples of the are present no difficulty. Let us state : 1. There are no such terms as Decare and JS^lare, because these expressions would be equivalent : Sq. MetreB. The decare, to 10 ares or 100 X 10 — 1,000. The kilare, to 1,000 " 100 X 1,000 = 100,000. And 1,000 and 100,000 have no exact square roots, and, should they have any, these would not be multiples of 10. 3. For the same reason Deciare and Milliare would also be equivalent : The deciare, to -— = —-- = 10 square metres. The milliare, to :r-^r^ = ^ = O'l square metre, which numbers have no exact square roots. We have, therefore : 16 THE UNIVERSAL METRIC SYSTEM. Myriare = 10,000 ares = 1,000,000 square. metres, or 1 square kilometre, for v'ljOOO.OOO = 1,000. Hectare = 100 ares = 10,000 square metres, or 1 square hectometre, for ^lOjOOO = 100. Aee = 1 are = 100 square metres, or 1 square decametre, for v'lOO = 10. Centiare = 0*01 are = 1 square metre, for \/l = 1. The following table explains itself, and shows that each unit is equivalent to 100 of the next lower order. ^ J' '4 1 II 100 1 hi 10,000 100 1 ll 1,000,000 10,000 100 1 PI 100,000,00.0 1,000,000 10,000 100 1 ill B it 10,000,000,000 100,000,000 1,000,000 10,000 100 1 i II !5 1,000,000,000,000 10,000,000,000 100,000,000 1,000,000 10,000 100 1 100 100,000,000,000,000 i,ooo,oog,ooo,ooo 10,000,000,000 100,000,000 1,000,000 10,000. The square myriametre is hardly ever employed, and then only to express the areas of countries or . APPLETON & CO., Pdblishers, 549 & 551 Broadway, N. Y. RECENT PUBLICATIONS. I>isease8 of modern Life. By Dr. B. W. Richardson, F. R, S. i vol,, izmo. Cloth. $2.00. 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His work is popularly written, and every page is replete with solid instruc- tion of a kind that is just now lamentably needed by multitudes of our people who are victimized by the grossest fallacies." — Popvlar Scie?ice Monthly^ " If Professor Jevons's book is read as extensively as it deserves to be, we shall have sounder views on the use and abuse of money, and more correct ideas on what a circulating mediimi really means." — Boston Saturday Evening Gazette, " Prof. Jevons writes In a sprightly but colorless style, without trace of either prejudice or mannerism, and shows no commitment to any theory. The time is not very far distant, we Jiope, when legislators will cease attempting to legislate upon money before they know what money is, and, as a possible help toward such a change. Prof. Jevons deserves the credit of having made a useful contribution to a depar't- toent of study long too much neglected, but of late yeaj-s, we are gratified to say, be- coming less so."— TAe Mnancier, New Tork. Weights, Measures, and Money, of all Nations, Compiled by F. "W. Clakkb, 8. B., Professor of Physics and Chemistry in the Uni- versity of Cincinnati. Price, $1.50. " This work will be found veiy useful to the merchant, economist, and banker, as the arrangement is highly convenient for reference, and in a form and classification never before presented to the public. It also contains a series of tables, arranged alpha- betically, showing the value of each unit as given both in the English and the metric standards. The metric system is used 'coextensively with the ordinary system, and ^ a characteristic feature of the book. "The contents, among* other things, contain the following usefUl and comprehen- sive tables, viz. : I. Measures of Length, in both the Enghsh or American feet or inches, and in French metres. II. Boad^Measures in English miles and French kilo- metres. III. Land-Measures. IT. Cubic Measures. T. Liquid Measures. TI. Dry Measures. TII. "Weights, and finally Money. This latter table is one of the most useful and valuable tables probably to be found, giving as it does the standards in dollars, fi^ncs, sterling, and marks, and alone is worth the cost of the book." — N. Y, Commercial and FinaTu^al Ohronicle. "We commend this carefully-prepared and convenient volume to all persons who wish to acquire information on the subject of which it treats." — Boston Globe. "The work necessary to the production of this little volume has been judiciously planned and skillfully executed.!'— CAicag'o Trldune, D. APPLETON & CO., Publishers, 549 & 551 Broadway, N. Y. THE GREAT ICE AGE, AND ITS RELATIONS TO THE ANTIQUITY OF MAN. By JAMES GEIKIE, F. R. S. E. ■With Maps, Charts, and numerous Illustrations. I vol., thick l2mo. . . . Price, $2.50. OPINIONS OF THE PRESS. ** Intelligent general readers, as well as students of geology, will find more infor- mation and reasonable speculation concerning the great glacial epocli of our globe in this volume than can be gathered firom a score of other sources. The author writes not only for the benefit of his * fellow-hammerers,* but also for non-specialists, and any one gifted with curiosity in respect ta the natural history of the earth will be de- lighted with the clear statements and ample illustrations of Mr.' Geikie's ' Great Ice Age.' " — Episcopal Register. " ' The Great Ice Age ' is a work of extraordinary interest and value. The subject is peculiarly attractive in the immensity of its scope, and exercises a fascination over the imagination so absorbing that it c^n scarcely find expression in words. It has all the charms of wonder-tales, and excites scientific and unscientific minds alike." — Boston Gazette. " Mr. Geikie has succeeded in writing one of the most charming volumes in the library of popularized science." — Utica Herald. " We cannot too heartily commend the style of this book, which is scientific and yet popular, and yet not so popular as to dispense with the necessity of the reader's putting his mind to work in order to follow out the author in his forcible yet lucid arguments. Nor can the attentive reader fail to leave the work with the same enthusiasm over the subject as is shown in every page by the talented anihoi."— Portland Press. "Although Mr. Geikie's position in the scientific world is such as to indicate that he is a pretty safe teacher, some of his views are decidedly original, and he does not make a point of sticking to the beaten f^ih.." —Springfield Union. "Prof. Geikie's book is one that may well engage thoughtful students other than geologists, beating as it does on the absorbing question of the unwritten history of our race. The closing chapter of his work, in which, reviewing his analytical method, he constructs the story of the checkered past of the last 200,000 years, can scarcely fail to give food for thought even to the indifferent."— .Sj{^& Courier. " Every step in the process is traced vrith admirable perspicuity and fullness by Mr. Geikie." — London Saturday Review. " It offers to the student of geology by far the completest account of the period yet published, and is characterized throughout by refreshing vigor of diction and originaUty •f thought."— G&i^iB Herald, D. APPLETON & CO., Publishers, 549 & SSI Broadway, N. Y. THE EXPANSE OF HEAVEN; A Series of Essays on the Wonders of the Firmament. By R. A. PROCTOR, B. A. I vol., i2mo. Cloth Price, $2.00. " It is Mr. Proctor's good fortune that not only is he one of the great- est of living astronomers, but Jhat he has a power of imparting knowl- edge that is not equaled by any living astronomer. His style is as lucid as the light with which he deals so largely, and the plainest of readers can go along with him with entire ease, and comprehend all that he says on the grandest subject ever discussed by mortal intelli- gence. Most scientific writers either cannot or will not so use the pen as to make themselves understood by the many ; not so with Mr. Proctor : he both can and does so write as to command the attention of the million, and this too without in the least derogating from the real dignity of his sublime theme. Few of us can study astronomy, because that implies a concentrated devotion to an inexhaustible matter, but we all can read astronomical works to our great advantage if astrono- mers who write will but write plainly ; and in that way, without having the slightest claim to be spoken of as " scientists," we can acquire no ordinary amount of knowledge concerning things that are of the loftiest nature, and the effect of which must be to elevate the mind. Such a book as ' The Expanse of Heaven ' cannot fail to be of immense use in forwarding the work of education even when it is read only for amusement, so forcible is the impression it makes on the mind from the importance of the subjects treated of, while the manner of treat- ment is so good." — Boston Traveller. "Since the appearance of Ennis's book on 'The Origin of the Stars,' we have not read a more attractive work on astronomy than this. It is' learned enough to be instructive, and light enough to be very entertaining." — Alta California. " It reads like a work of fiction, so smooth and consecutive is it ; but it inspires the worthiest thoughts and the highest aspirations." — Boston Commonwealth. " Perfectly adapted to their purposes, namely, to awaken a love for science, and at the same time to convey, in a pleasant manner, some elementary facts." — Church Herald. "This is not a technically scientific work, but an expression of a true scholar's conception of the vastness and grandeur of the heavens. There is no dry detail, but blended with the scholar's discoveries are the poet's thoughts, and a true recognition of the Almighty's power." — Troy Times. D. APPLETON & CO., PuUishers, 549 & 551 Broadway, N. Y. THE POPULAR SCIENCE MONTHLY. CONDUCTED BX This periodical was started (in 1872) to promote the dij^sion of valuable sci- mtMJki knowledge^ in a readable and attractive form, among all classes of the c