BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF flew«rs ^< Sage 189X A..A.AM.S.c>./i. jr^. /.a/al....... 9963 Oomall University Library arV18564 UelMre-notee on the ttiMi^^^ 3 1924 031 216 272 olin,anx Cornell University Library 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/cu31924031216272 LECTURE-NOTES ON THE THEORY OF ELECTRICAL MEASUREMENTS. PREPARED FOR THE THIRD-YEAR CLASSES OF THE COOPER UNION^ ' NIGHT-SCHOOL OF SCIENC^}^ WILLIAM A. ANTHONY, liate Professor of Physics, Cooper Union. THIRD EDITION, REVISED BY ALBERT BALL, Assistant Professor of Physics and Applied Electricity, Cooper Union. NEW YORK : JOHN WILEY & SONS. London: CHAPMAN & HALL, Limited. 1908. 33 Copyright, 1S98, BY WILLIAM A. ANTHONY. Copyright, 1908, BT ALBERT BALL. HSiii 0(tinttfic Vrma Itofanrt Brutnninnll anil (Sonqiang KnoQnirk REVISER'S PREFACE. By the courtesy of the publishers and under the advice of the author, the revision of these Notes was undertaken in order that the book might more fully meet the needs of the Cooper Union students. To this end numerous problems have been added. These have been selected with great care in order that their proper solution may indicate the application of the principles discussed in the text. A few of the principles have been more fully elaborated. Paragraphs upon capacity and its measure- ment have been incorporated. Among other minor changes the symbol for current has been changed to /, reserving the symbol C for capacity. Much credit is due to Professor F. M. Hartmann for valuable suggestions. Albert Ball. Cooper Union, N.Y. 1908. PREFACE. It is the purpose of these Notes to furnish the student the topics treated in the lectures ; to give in full such facts, data, and courses of reasoning as are not readily mastered by the student in the course of the lecture; in short, to aid the student in those matters which he is likely to find most difficult, or which he may fail at the moment to fully grasp. It is not, however, intended to relieve the student of the necessity of taking his own notes of the lectures as they are delivered, and every student is expected to take such notes, especially as to the experiments and the lessons which they teach. Unless the student writes short-hand, the notes he can take during a lecture must necessarily be brief, and he should aim to record suggestive phrases to be afterward more fully elaborated. The student is advised of the great importance, as soon as possible after the lecture, of going over the ground and filling in his notes, thereby clearing up PREFA CE. V subjects that may have appeared obscure, and fixing his knowledge of the topics treated. On no account should the student fail to make this review before the time for the next lecture. It is the purpose of this course of lectures to teach the fundamental principles of all electrical measure- ments, rather than to describe in detail methods em- ployed in particular cases. To this end the definitions and relations of electrical quantities have been dis- cussed at considerable length, and the derivation of the electrical units has been fully treated. It is believed that, with this thorough foundation in the theory of electrical measurements, and a knowledge of typical methods such as are treated in these lec- tures, the student will be better equipped for practical work than he could possibly be by the most extended instruction in special empirical methods without such foundation. W. A. Anthony. CONTENTS. The C. G. S. System of Units Page i Arbitrary and Derived Units; Basis of C. G. S. System; Fundamental Units; Characteristics of Matter; Motion; Units of Velocity and of Acceleration; Force; Work and Energy; Practical Units; Gravitation Unitg; Heat Units; Re- lations betvireen the Various Units. The Magnetic Field , Page 12 General Character of Magnets; Lines of Magnetic Force; Strength of Magnetic Poles; Unit Magnetic Pole; Intensity of Magnetic Fields; Graphical Representation of Magnetic Fields; The Earth's Magnetic Field; Measurement of Field Intensity. The Electric Current Page 22 Origin and Effect of Currents; Magnetic Field due to Currents; The Tangent Galvanometer; Current-measuring Instruments Employing Artificial Fields; Electrical Dyna- mometers and Electric Balances. Potential and Electromotive Force Page 32 Potential ajid Difference of Potential in General; Electrical Difference of Potential; Measurement of Difference of Poten- tial; Unit Difference of Potential; Electromotive Force; Ex- amples of Electromotive Force; Capacity. Resistance and Ohm^'s Law Page 42 Specific Resistance; Unit Resistance; Conductivity; Resist- ance and Temperature; Power Consumed by Resistance; Di- vided Circuits. Viii CONTENTS. Practical Measurements of Electrical Quanti- ties Page so The International Units; Definitions of the International Units by the International Congress. Measurement of Resistance Page 52 Instruments; Methods of Measurement; Measurement of Insulation Resistance; Measurement of very Small Resist- ances; Measurement of Resistance of Electrolytes; Resistance of Batteries. Measurement of Current Page 62 Measurement by the Tangent Galvanometer; By Direct- reading Instruments; By Fall of Potential. Measurement of Potential Page 64 By Electrostatic Forces; By Comparison with a Known Potential Difference; By the Current Produced in a Circuit of Known Resistance; By the Ballistic Galvanometer, Testing and Calibrating Instruments Page 67 Tests of Resistance Sets; JThe Divided-meter Bridge; Cali- bration of the Bridge Wire; Tests of Current Instruments; Tests of Instruments for Measuring Potential. Measurement of Capacity Page 71 Heating Effects of the Current Page 81 Temperature of a Conductor Carrying Current. Incandescent Lighting Page 83 The Incandescent Lamp; High Temperature Required for Economy; Incandescent Lamps of Different Candle-power. Arc Lighting Page 85 Source of the Light; Power Consumed. Chemical Effects of the Current Page 89 Decomposition of Salts; Definitions of Terms; Faraday's Laws; Applications of Electrolysis; Energy Required. CONTENTS. IX Electromagnetic Induction Page 95 Direction of Current; Law of Lenz; Electromotive Force Developed. Electromagnetism Page 98 The Magnetic Circuit; Magnetic Reluctance and Permea- bility; The Electromagnet; Measurements of Permeabil ty. NOTES UPON ELECTRICAL MEASUREMENTS. THE C.G.S. SYSTEM OF UNITS. To measure any quantity is to compare it with another quantity of the same kind that has been chosen as a unit. It was the practice originally to choose units arbi- trarily, without regard to the relation they might bear to other units already chosen. Thus the gallon, a unit of capacity, is 231 cubic inches. It would have been far more convenient if it had been 100 or 1000 cubic inches. When electrical science had reached the stage where units of measurement were necessary, units were at first arbitrarily chosen, but it was very early recognized that such a course would lead to a multi- tude of troublesome factors for reducing to other 2 NOTES UPON ELECTRICAL MEASUREMENTS. units already liili and, fortunately, the matter was taken up and a consistent system of units devised before the arbitrary units had acquired a strong foot^ hold. The system so devised is known as the centimetre- gramme-second, or the c.g.s., system of units. In order that it may be fully understood, it will be necessary to consider briefly the basis upon which the system rests. It has been said that all physical phenomena are the result of matter and motion. Any physical measurement may, therefore, be effected by measur- ing the mass of matter, and the motion involved. But motion implies two elements — space or length, and time. The measurement of any physical phe- nomenon, therefore, involves the measurement of three independent quantities, and for the measure^ ment of these quantities three independent units must be arbitrarily chosen. These are called funda- mental units, and from them all other units may be derived. Fundamental Units. — The fundamental units of the c.g.s. system are: for the unit of length, the centimetre, which is the one-hundredth part of the length of a certain platinum bar deposited in the archives of France and declared by government enact- ment to be a metre; for the unit of mass the gramme, which is the one-thousandth part of a cube of platinum THE C.G.S. SYSTEM OF UAT/TS. 3 deposited in the archives of France and declared by government enactment to be a kilogramme; for the unit of time, the second, which is the 86400th part of the mean solar day. Characteristics of Matter. — The distinctive char- acteristic of matter is its persistence in whatever state of rest or motion it may happen to have, and the resistance which it offers to any attempt to change that state. This property is called inertia. The resistance which a body offers to change of state of rest or motion is, other things being equal, propor- tional to its mass. Anything that changes the state of a body with respect to rest or motion is called force. Motion. — Motion may be uniform or varied. Rate of motion is called velocity. In a uniform motion, velocity is measured by the space passed over in unit time. In varied motion, the velocity at any instant of time is measured by the space which the body would pass over in the next second if, from that instant, the velocity were uniform. The unit velocity is the velocity of a body which, moving with a uniform motion in a straight line, describes unit space in unit time. Rate of change of velocity is called acceleration. Acceleration may be constant or varied. When constant, it is measured by the change in velocity which occurs in unit time. When varied, its waliip at anv instant is measured by the change in 4 NOTES UPON ELECTRICAL MEASUREMENTS. velocity that would occur in unit time if, from that instant, the acceleration were constant. Unit acceleration is the acceleration of a body whose velocity, changing at a constant rate, changes by the amount of one unit velocity in the unit time. A constant velocity is expressed by the ratio space to time : - = 7 (^) This expression is also true for the instantaneous velocity at a given instant of time in varied motion, if s represent a space described at that instant in a time t so short that during that time the velocity may be considered constant. In the same way, a constant acceleration is ex- pressed by the ratio velocity to time : V 1' '^ = - (2) V representing the change of velocity in the time /. If V and t be taken small enough, formula (2) gives the instantaneous acceleration when acceleration is variable, just as (i) gives the instantaneous velocity in varied motion. Uniformly Varied Motion, or Motion in which Acceleration is Constant. — Let v^ represent the initial velocity. Then velocity at end of time t is v=v,->i-at (3) THE C.G.S. SYSTEM OF UNITS. 5 Since the velocities in this case form a series in arithmetical progression, the mean velocity is the half- sum of the initial and final velocities, or v^-\- V v^-Yv^-\- at at 2 2 " ' 2 ' and the space described in time / is or s = vJ-\-\ai' (5) Substitute in (4) the value of t from (3) : s^^"^^^ (6) 2a ' If the motion start from rest, w, = o, and the above formulae become v — at; (7) s = \vt; (8) s = \af; (9) s = — (10) 2a Force. — Since force is the assumed cause of change of motion, it is proper to take the change produced 6 NOTES UPON ELECTRICAL MEASUREMENl^S. in unit mass in unit time, that is, the rate of change of motion, or acceleration, as a measure of the force producing it. But the force required to. produce a given change is proportional to the mass. Hence the force required to produce a given acceleration in any mass is proportional to the product of the mass by acceleration. Since we are free to choose a unit of fqrce, we may make the force F-= ma, (ii) m being any mass, and a the acceleration produced in that mass by the force F. We may now define the' c.g.s. unit force as that force which may produce in a mass of one gramme the c.g.s. unit acceleration. It is called a dyne. Work and Energy. — The physical idea of work is resistance overcome through space. Assuming a force to produce motion in its own direction, work is meas- ured by the product of that force by the space through which it acts. Hence the following equation: W^Fs (12) The c.g.s. unit work is the work performed by a force of one dyne acting through a space of one cen- timetre in the direction of the force. It is called an erg. When the resistance overcome is inertia, the force THE C.G.S. SYSTEM OF UNITS. 7 overcoming it equals ma\ see (11). If the force con- tinue to act until the velocity suffers a change equal to V, then the space through which it acts is (10), I/' s = — . Substituting these values of i^ and s in (12), W=\mv' (13) That is, the work which must be done to impart to the mass tn the velocity v equals half the product of the mass by the square of its velocity. Conversely, if a mass m, moving with a velocity v, be brought to rest, it will do work represented by the same product. Energy is capacity for doing work. Thus the mass of the last paragraph has a capacity for doing work equal to \ini^. This is the energy it possesses because of its motion. A body may also possess energy because of its position of advantage with respect to some force. The energy which a body possesses because of its motion is called kinetic energy. That which it possesses because of its position is called potential energy. Energy is measured in the same units as work. In describing the measurement of work it was assumed that the displacement of the body was in the line of direction of the force, but this may not be the case. The body may be constrained to move in a path whose direction makes an angle with the line of direc- tion of the forx;e. In this case, to obtain the effective 8 NOTES UPON ELECTRICAL MEASUREMENTS. force along the path, the force must be resolved into two components, one in, and the other at right angles to, the path. Evidently the component lying in the path is the only component having any effect to pro- duce motion along the path, and the work done is measured by the product of this component into the space through which the point of application of force moves. The component along the path is the projec- tion of the force upon the path. If a be the angle between the path and the line of direction of the force, the effective component along the path is F cos a. Practical Units. — The erg is a very small amount of work. For practical purposes a larger unit, equal to ten million (lo') ergs, is employed, and is called z. joule. The watt is a unit rate of working. It is work performed at the rate of one joule per second. Gravitation Units. — Before the adoption of the simply relatecf units of the c.g.s. system certain arbi- trary units of force and work were in use, and are still largely used in engineering practice. Those most in Use are: a force equal to the weight of a pound of matter, called also a pound, and a force equal to the weight of a kilogramme at Paris, called also a kilo- gramme. It is unfortunate that the name pound should have been used for two such totally distinct quantities. From these units of force are derived the units of THE C.G.S. SYSTEM OF UNITS. g work, the foot-pound, being the work done by a force of one pound acting through a space of one foot, and the Mlogramme-metre, being the work done by a force of one kilogramme acting through a space of one metre; also the units rate of working, the horse-power, being work performed at the rate of 550 foot-pounds per second, and the cheval-vapeur, work performed at the rate of 75 kilogramme-metres per second. Heat Units. — Since heat is a form of energy, it is important to define here the heat units and their relation to the other units of work and energy. The British thermal unit is the heat required to raise the temperature of one pound of water from 32° to 33" Fahrenheit. The pound-degree centigrade is the heat required to raise the temperature of one pound of water from zero to i" centigrade. The calorie is the heat required to raise the tem- perature of one kilogramme of water from zero to 1° centigrade. The gramme calorie is the heat required to raise the temperature of one gramme of water from zero to i" centigrade. Below are given the relations between these various units. UNITS OF FORCE. Kilogramme = 981 000 dynes. Pound = 444972 " 10 NOTES UPON ELECTRICAL MEASUREMENTS. UNITS OF WORK OR ENERGY. Kilogramme-metre =9.81 X 10' ergs. " =9.81 joules. Foot-pound = 1.356X 10' ergs. " = I -356 joules. UNITS RATE OF WORKING. Cheval-vapeur = 736 watts. Horse-power = 746 " UNITS OF HEAT. Calorie = 426 kgm. -metres. " = 4160 joules. British thermal unit = 778 foot-pounds. " " " = 1055 joules. Pound-degree centigrade = 1400 foot-pounds. = 1898 joules. Joule = .00024 calorie = .000948 B. T. U. = .000527 pound-deg. C. PROBLEMS. (1) A body is projected upward with a velocity of 5000 cm. How high will it rise ? (2) A rifle-barrel is 75 cm. long. A rifle-ball of 1 5 grms. leaves the rifle with a velocity of 60000 cm. per second. Assuming a uniform acceleration, for how 7'HE C.G.S. SYSTEM OF UNJTS. II long a time was the bullet in the rifle ? What was the force of the powder in dynes ? in pounds ? (3) If the bullet of the last example were stopped in a space of 10 cm. by a uniform resistance, what is that resistance ? (4) What energy — ergs, joules, foot-pounds — did the bullet possess on leaving the rifle ? (5) How much heat — calories, B.T.U. — can be generated in one hour by one horse-power ? (6) A loo-ton locomotive running at 60 miles per hour is stopped in 10 minutes. Required: Average acceleration in ft. per sec. per second ? Retarding force in pounds (assuming it uniform) ? Energy expended in foot-pounds? Heat generated in B.T.U. ? (7) Express all of the quantities referred to in problem (6) in c.g.s. units. (8) A locomotive exerting a pull of 1000 pounds main- tains a speed of 50 miles per hour. What H.P. is ex- pended ? How many watts ? (9) A constant force acting upon a mass of 3 kg. for 20 seconds causes it to move from rest a distance of 15 meters. Required: The force in grams? The velocity at the end of 20 seconds ? The distance traversed during the 15th second ? 12 NOTES UPON ELECTRICAL MEASUREMENTS. THE MAGNETIC FIELD. Definition of a magnet. Natural and artificial magnets. Bar magnets, horseshoe magnets. Distribution of magnetic force. Ends where force is manifested called poles. The two poles are not alike. Any magnet suspended so as to be free to swing in a horizontal plane settles with one pole toward the north and the other toward the south. One pole cannot exist without the other. Pole pointing north is in English writings called the north pole. Mutual action of poles. Force extends all around the magnet and tp a great distance. Space around a magnet where its forces are mani- fested is called the magnetic field. Direction and intensity of forces in different parts of the field vary greatly. A curved line so drawn in the field that at each THE MAGNETIC FIELD. 1 3 point of this line the line of direction of the magnetic force at that point is tangent to it, is called a line of force. The direction of the force along the line is assumed to be the direction in which a free north pole would move in obedience to that force. Lines of force indicated by iron-filings and by a small needle. Lines of force can never cross each other, for,' if they did, that would mean two directions of the mag- netic force at the point of crossing. This is iiTipossi- ble. Strength of Magnetic Poles.— Forces exerted by different poles vary greatly. Force exerted by the same pole at different dis- tances varies greatly. Theory indicates and careful measurements demon- strate that the magnetic force exerted by one mag- netic pole upon another varies inversely as the square of the distance. The strength of a magnetic pole is assumed, other things being equal, to be proportional to the force exerted by it. Unit Magnetic Pole. — Since the action between two magnetic poles is mutual, the force exerted by one pole upon another must be proportional to the product of the two pole strengths. Hence, as we are 14 NOTES UPON ELECTRICAL MEASUREMENTS. free to choose the unit strength of pole, we may put ^ = f (H) The c.g.s. unit strength of pole is, then, a pole of such strength that it actuates another equal pole at a distance of one centimetre with a force of one dynp. Intensity of Magnetic Field. — It is often con- venient to express magnetic forces in terms of the intensity of the magnetic field. The intensity of the magnetic field at any point is assumed to be propor- tional to the force exerted upon a pole of given strength placed at that point. Hence we may put F=Hp, (15) where H is the intensity of the field. The c.g.s. unit intensity of field is now a field of such intensity that in it unit pole is actuated by a force of one dyne. Since unit pole is also actuated by a force of one dyne at a distance of one centimetre from another unit pole, it follows that unit intensity of field is found at a distance of one centimetre from the unit pole. These definitions have been given as though one pole alone could act to produce a magnetic field, but this is a condition that cannot be realized in practice. THE MAGNETIC FIELD. 15 It has already been stated that one pole could not exist alone. It is also true that each pole affects to a greater or less extent the intensity and direction of the lines of force in the magnetic field. Graphical Representation of Mag^netic Field. — Lines of force may not only be used to indicate the direction of the forces in the magnetic field, but they may be so drawn as to indicate the intensity also. For this purpose they are so drawn that the number of lines passing through a square centimetre at any point is equal to the number of units expressing the field intensity at that point, the surface upon which the square centimeter is measured being perpendicular to the Knes of force. It follows that from the unit pole as defined there must emanate i,Tt lines of force. The Earth's Magnetic Field. — The lines of force of the earth's field in this region lie in a vertical plane about 7° west of the geographical meridian, and are inclined at an angle of some 75° with the horizon. The deviation from the true north is called the declination of the magnetic needle, and the deviation from the horizontal is called the inclination or dip. Since magnetic needles are usually free to swing only in a horizontal plane, they are affected only by the horizontal component of the earth's magnetic intensity. This is called the horizontal intensity of the earth's 1 6 NOTES UPON ELECTRICAL MEASUREMENTS. magnetic field, and is pepreseftfeed by the symbol H. If a be the angle of dip, then H = total intensity X cos a. Measurement of Field Intensity. — Suppose it is required to determine the horizontal intensity of the earth's magnetic field. A magriipli# needle is sus- pended by a fibre of silk so as to be free to swing in a horizontal plane. If it be deviated slightly from the magnetic meridian and then left to itself, it will vibrate back and forth in a time which will be less the greater the force, and greater the greater the resist- ance offered by its inertia. The resistance offered by the inertia of a body to a force producing rotary motion depends not only upon the mass of the body, but also upon the distribution of that mass with respect to the axis of rotation; that is, upon a factor of the body which is called the moment of inertia. This is a factor that may be determined by computation for some bodies of regular form, but for irregular bodies it must be determined by experiment. We will represent it by the symbol K. Let NS in the figure represent the magnetic me- ridian, and A a magnetic needle deflected from the meridian plane. A force at each end of the needle, equal to Hp, constitutes a couple which causes the needle to vibrate. The effect of this couple to pro- THE MAGNETIC FIELD. 17 duce rotation is measured by the product of one of the forces by the distance between them, which, when the needle is at right angles to the meridian, is the length of the needle, hence by Hpl, where / is the length of the needle. //, represented by the symbol Fig. I. M, is called the magnetic moment of the needle. Then it can be shown that the time of a single vibra- tion or oscillation is = n^. K HM' (16) [See Appendix.] If t and K are determined, HM may be found from formula (16). But the quantity sought is H, and the above ex- periment gives the product HM. To find H it is necessary to make another measure- ment to determine the ratio of H to M. IS NOTES UPON ELECTRICAL MEASUREMENTS. Let the magnet A of Fig. i be placed an in Fig. 2, at some distance to the east or west of a small needle Fig. 2. JB whose deflection can be accurately measured. A is so placed that its axis .prolonged passes through the centre of B. Then if r be the distance between the centres, and 6 the deflection of B produced hy A, it can be shown that M H = ir' tan 6. ' ■ (17) [See App.] From (16) and (17) both .fi^and J/ may be found. The method here described for determining /T is similar to that employed for determining the intensity of gravity by means of the pendulum. Horizontal intensity of the earth's field in New York is about ,17 c.g.s, units. THE MAGNETIC FIELD. 1 9 It has been suggested to adopt as a practical unit of field intensity the intensity of a uniform field in which there are lo' c.g.s. lines per cm.'. This unit has been called a gauss. A field of loooo c.g.s. units would be -^ milligauss. PROBLEMS. (10) A magnetic needle vibrates 15 times per minute in the earth's magnetic field in New York. The same needle vibrates 16 times per minute in another location. What is the value of H in the second loca- tion ? (11) Two needles identical in dimensions and mass make, at the same place, one 50, the other 30 vibra- tions per minute. How do their strengths compare? (12) If two needles known to be of the same strength make, at the same place, one 50, the other 30 vibra- tions, how is this accounted for? Explain the relation between the two. (13) The needle A of Fig. 2 causes B to be deflected 15°. Another needle substituted for A causes a de- flection of 20°. Required the relative strengths of the two needles. (14) If in Fig. 2 the distance AB is 50 cm. and the needle B is deflected 15°, what is the rehtion between the magnetic moment of A and the field in which B is placed ? 20 NOTES UPON ELECTRICAL MEASUREMENTS. (15) Two poles of equal strength are 20 cm. apart and the force of mutual attraction between them is 2,25 dynes. Find the strength of the poles. (16) What is the force with which a pole of strength 10 c.g.s. units is actuated when placed in a magnetic field that would be represented by 5 lines per sq. cm. ? (17) What is the total intensity of the earth's magnetic field at a point where the angle of dip is 75^ and the horizontal intensity is .17 c.g.s. units? (18) If a bar magnet whose magnetic moment is 1000 c.g.s. units be suspended in a magnetic field whose inten- sity is .2 c.g.s. units, what work in ergs must be done in turning the magnet from its equilibrium position through an angle of 30° ? 45" ? 90° ? (19) What will be the moment of the couple which would hold the magnet in problem (18) in each of the deflected positions? (20) What will be the intensity of a niagnetic field in which a couple whose moment is 5 gram-centimeters acting upon the magnet of problem (18) maintains a deflection of 45°? (21) If the moment of inertia of a bar magnet be 5000 gram-cm.2 and its magnetic moment 2000 c.g.s. units, what wiU be its time of vibration if suspended in a horizontal position by a torsionless fiber in a field whose horizontal intensity is .17 c.g.s.? (See equation 16.) THE MAGNETIC FIELD. 2 1 (22) If the poles of the magnet in problem (21) are 20 cm. apart, what is its pole strength ? (23) What strength of field will be produced by the magnet of problem (22) at a point 20 cm. from either pole? At a point 20 cm. from one pole on a line per- pendicular to the magnet? 22 NOTES UPON ELECTRICAL MEASUREMENTS. THE ELECTRIC CURRENT. When the two terminals of an electric generator are joined by a conductor, something takes place which is called an electric flow. The conductor is said to carry an electric current. This current is known only by its effects. It heats the conductor. It affects a magnetic needle near which the con- ductor may be placed. This shows that the current develops a magnetic field. Field due to Current. — Direction. — Studying the effect of the current upon a needle, it is seen that the lines of force are concentric circles of which the wire is the axis. Can be shown by means of iron-filings sprinkled on a glass plate. The direction of the force in these lines may be determined from the following rule : Suppose the cur- rent flowing from you. The lines then have the direc- tion of the movement of the hands of a watch whose dial faces you. Intensity. — Let AB, Fig. 3, represent the direction of the horizontal component of the earth's magnetism. THE ELECTRIC CURRENT. 23 Let a conductor carrying a current be placed parallel to AB and over or under the magnetic needle NS. B S fl,p The lines of force due to the current are at right angles to AB, and forces in opposite directions, consti- tuting a couple, will act upon the opposite poles of the needle. These will cause a deflection which is opposed by tittiS force of the earth's magnetism, and it is evident that the needle will be in .equilibrium when its direc- tion is that of the resultants of the two pairs of forces, 24 NOTES UPON ELECTRICAL MEASUREMENTS. as represented in the figure. The force due to the earth's magnetism acting upon each pole of the needle is Hp. That due to the current is H^p at right angles to Hp. If a be the angle of deflection, it is plain from the figurfe that or H^p = Hp tan a, H^= H tan a. . (18) If the conductor, instead of remaining in the mag- netic meridian, is turned with the needle and kept parallel to it, the deflecting force will always be, at Fig. 4. right angles to the needle as in Fig. 4, where only one force of each pair is shown. Here we have H^p = Hp sin a, THE ELECTRIC CURRENT. 2^ or Hi=H sin a (19) It may be assumed as self-evident that if all parts of a conductor were at equal distances from a needle, the force exerted would be proportional to the length of the conductor. It is shown experimentally that, other things being equal, the force exerted by a current upon a needle is proportional to the inverse square of the distance,* It is assumed that, other things being equal, strength of current is proportional to the force it exerts upon a magnetic pole. Hence we may put ^=^ (-) where I is the strength of current, L its length, d its distance from the pole whose strength is /. We may now define the c.g.s. unit current as a current of such strength' that, flowing in a conductor I cm. long, bent into an arc of a circle of i cm. radius, it will exert upon the c.g.s. unit magnetic pole at the centre of the circle a force of one dyne. The c.g.s. unit current has no name. The unit used in practice is one tenth of the c.g.s. unit, and is called the ampere.. It is impossible practically to realize the conditions stated in the definition of the unit current, because * All parts of the conductor being at, the same distance from the needle. 26 NOTES UPON ELECTRICAL MEASUREMENTS. the conductors by which the current is brought to and carried away from the arc of unit length would themselves have some influence upon the needle. But if the conductor be bent into a complete circle of unit radius, the conductors leading to and from the circle may then be twisted together so that the cur- rents flowing in them in opposite directions neutralize each other, and the effect procfuced is that of the circle alone. The length of such a circle being 2r, the field produced at the centre by unit current flow- ing in the conductor will be 2n. A conductor forming a circle of radius r will, there- fore, produce at its centre a magnetic field : ■n, — — 5— = — /. Tangent Galvanometer. — If the plane of such a circle coincide with the plane of the earth's magnetic meridian, and a short magnetic needle free to swing in a horizontal plane be placed at its centre, it will be in eqijilibrium (see (18)), when —I=H\.zxi. a (21) Hence /= tan « (2i\ If the conductor make n turns, ^ Hr 1 = - — tan « (2i\ THE ELECTRIC CURRENT. 27 Note that the result is independent of the strength of the needle. An instrument constructed to realize these condi- tions is called a tangent galvanometer because the current is proportional to the tangent of the angle of deflection. The quantity - — is the constant of the galvan- ometer. Helmholtz" s Form of Tangent Galvanometer. — In this instrument there are two equal coils placed at a distance apart equal to their radius, and the needle is on the common axis midway between them. The constant of this instrument is Hr , ^ .222 — (24) n ^ ^' [bee Appendix.] All the above expressions give / in c.g.s. units. To give / in amperes multiply by 10. Current-measuring Instruments employing Arti- ficial Fields. — The tangent galvanometer, depending for its indications upon the intensity of the earth's magnetic field, can only be used where this intensity is constant, or at least free from local disturbances. Furthermore, large currents cannot be accurately measured by this instrument because the fields pro- duced by such currents are very large in comparison with the field of the earth. Instruments are therefore 28 NOTES UPON ELECTRICAL MEASUREMENTS. constructed in which a strong artificial field produced by a permanent magnet is employed to direct the needle. Such instruments must be calibrated by direct comparison with some standard instrument. Other Current-measuring Instruments. — Instead of employing a magnetic field as the directive force to oppose the force of the current, a spring may be employed. Instead of making the magnetic needle movable, this may be fixed and the coil made the movable element, e.g., D'Arsonval galvanometers. Current- measuring instruments may be so graduated 'as to indi- cate the current directly in amperes. They are then called ammeters. Force upon Conductors Carrying Currents in a Magnetic Field. — From the rule given on page. 21 it is plain that if A (Fig. 5^) represents the cross-section Fig. s. of a conductor carrying a current away .from the ob- server a positive pole placed at P will be urged toward TB.E ELECTRIC CURRENT. 29 the left. Since for every such action there is always an equal and opposite reaction the conductor will be urged to the right with an equal force. This mutual action is of course due to the reaction of the two magnetic fields, each of which tends to distort the other. If we consider the relative directions of the current, the field in which the conductor is placed, and the force acting upon the conductor (see Fig. 56), we may arrive at the following rule: Place the thumb and the first two fingers of the left hand mutually at right angles. Point with the index finger in the direction of the field, with the second, finger in the direction of the current, the thumb will then point in the direction of the force acting upon the conductor. The above rule applies whatever be the source of the field. It follows that there must be a mutual action between any two ciurents placed near each other. The following rules appl3nng to this mutual action are special cases of forces upon conductors carrying current, in a magnetic field. Parallel currents flowing in the same direction attract, flowing in opposite directions they repel. Currents making an angle tend to become parallel and to flow in the same direction. Currents may be measured by means of their mutual action. For this purpose two coils are so connected that the same ciirrent traverses both and 30 NOTES UPON ELECTRICAL MEASUREMENTS. the force due to their mutual action is measured. Evidently this force is proportional to the square of the current. Electrodynamometers. Electric balances. / Electrical Quantity. — It is sometimes necessarylto consider the total quantity of electricity employed during a period of time. It is assumed that the unit current conveys the unit quantity per second. Hence the quantity conveyed in t seconds is Q=Ii (25) The practical unit quantity is the coulomb, which is the quantity conveyed by the ampere in one second. PROBLEMS. (24) Where H = .I'j, what is the constant of a tangent galvanometer having a coil of fifty turns 50 cm. diameter ? (25) If the needle of such an instrument is deflected 30°, what is the current in amperes ? What quantity of electricity per hour is conveyed by such a current ? (26) If it be required to measure a current approxi- mating 100 amperes, how large a coil of one turn would be required, the allowable deflection being 60°? (27) What field intensity exists at the centre of a THE ELECTRIC CURRENT. 31 circular coil of one turn one metre in diameter, carry- ing 1000 amperes? (28) A tangent galvanometer has two ceils, one 80 cm. diameter, ten turns, the other 100 cm. diameter, eight turns. Currents measured by the two coils' re- spectively produce the same deflection. What is the relation between those currents? (29) What must be the diameter of the coil of a tan- gent galvanometer of five turns so that a current of 2 amperes shall produce a deflection of 45° at a place where iT is .2 c.g.s. units? What is the value of the constant of the above galvanometer? (30) If the galvanometer of problem (24) is so con- structed that the c&il may be rotated about a vertical axis so that the needle shall always lie in the plane of- the coil, with what current in the coil will it be neces- sary to rotate it through 30° from the meridian? What is the value of the constant of the galvanometer when so used? What is the maximum current that can be measured with it in this way ? 32 NOTES UPON ELECTRICAL MEASUREMENTS. POTENTIAL ELECTROMOTIVE FORCE. Potential is a concept that was introduced into mechanics for the purpose of simplifying the study of the effects produced in a field of force. The charac- teristics of a field are known when we know the direction and intensity of the forces exerted at various points in it. It must be remembered that no force exists in a field except when there is present in it some body or agent peculiar to that field. For example, in a gravi- tation field no force exists except where matter is present. In a magnetic field no force exists except where a magnetic pole is present. The intensity of a field at any point is measured by the force which would act upon a test unit of the kind to which the force is due, if such a unit were present. The actual force exerted is the product of the field intensity by the number of such units present. Now in studying the effects of such forces where their directions and intensities vary from point to POTENTIAL AND ELECTROMOTIVE FORCE. 33; point within the field, the problem becomes very complicated if we attempt to solve it by taking into account the forces themselves. But every movement in a field, of a body acted upon by the forces, involves work, and problems relating to the effects of such movements are much simplified if we express the characteristics of the field in terms of the work done in moving a body from one point to another in it, instead of in terms, of the direction and intensity of the forces. DifTerence of Potential. — We define the difference of potential between two points in a field of force to be a difference of condition between the two points which is measured by the work which would be done by the forces in the field in moving a test unit from one point to the other. The work done in this case is independent of the path over which the body is moved. For it is self-evident that if work is done by the forces in moving a body from the point A to the point ^ in a field of force, exactly the same work must be done against the forces in moving the body back by the same path from B to A. Now if more work can be done by the forces of the field by moving the body over one path than by moving it over another, the body might be made to move frotn A to B by the path giving the greater work, and back to A by the path requiring the lesser work, and so v/ork could be continually done by simply allowing a body 34 NOTES UPON ELECTRICAL MEASUREMENTS. to go from one point to another by one path, and back to the first point by another. But this is in- consistent with the principle of the conservation of energy. If V and V, represent the potentials at the points A and B respectively, and s the distance between them, it is plain that the average force that is exerted upon a test unit as it moves from one point to the other is V— V F= ', and if the points are taken very near together F will be the force at the middle point between them. But -' is the rate of change of potential with respect to space. Hence the intensity of the field at any point is the rate of fall of potential at that point. Electrical Difference of Potential.— Electricity, which, flowing in a conductor, constitutes an electric cur- rent, may be collected in small amounts upon insulated bodies. When so collected it constitutes an electric charge, and a body receiving it is said to be positively . charged. In order that a charge may be put upon one body the same amount of charge must be taken from some other body, which is in consequence said to be negatively charged or to possess a negative charge. (This assumes both bodies originally in a state of elec- trical equilibrium.) A rapidly moving body possessing POTENTIAL AND ELECTROMOTIVE FORCE. 35 a positive charge produces magnetic effects precisely similar to those of an electric current in the same direction. If the moving body possess a negative charge, the effects are the same as of a current in the opposite direction. Whenever a difference of condition exists between two points, such that a positive charge tends of itself, without the aid of any other agency, to pass from one point to the other, a difference of electrical potential is said to exist between these points, and the former is said to have a higher potential than the latter. If an electric charge passes from one point to another of lower potential, work is done by it, just as work is done by the weight of a clock in running down. If the charge be carried by some outside agency from a point of lower to one of higher potential, work must be done upon it, just as work must be done upon the clock weight in wind- ing it up. The forces which cause the charge to move in the former case and against which it is moved in the latter case are called electrostatic forces, and the space in which such forces are manifest is called an electro- static field. Measurement of Potential Difference. — The amount of work necessary to carry a unit quantity of electricity from one point to another is a measure of their potential difference. It follows that the amount of work done in carrying any quantity of electricity from one point to another is proportional to the quantity carried and to the potential difference between the points. jG NOTES UPON ELECTRICAL MEASUREMENTS. If two points having a difference of potential be connected by a conductor, electricity will flow from the point of higher to that of lower potential. This flow, constituting an electric current, tends to restore the electric equilibrium and continues only until the two points are brought to the same potential. If a difference of potential between the two points be maintained by an electric generator, a continuous current flows through the conductor and the work done is proportional to the quantity of electricity transferred and to the difference of potential between the two points. Since we are free to choose a unit of potential difference, we may write W=EQ, (26) where W is the work done, E the potential difference, and Q the quantity. The c.g.s. imit potential difference may now be de- fined as that potential difference which, in transferring the c.g.s. imit quantity of electricity, performs work equal to one erg. The practical unit potential differ- ence is the voli = 108 c.g.s. units. The rate of working or power expended is t~ t ' or, since -7=/, P=EI (27) POTENTIAL AND ELECTROMOTIVE FORCE. 37 Since the volt is lo^ c.g.s. units and the ampere is ib~i c.g.s. units, one ampere flowing with a fall of poten- tial of one volt gives 10''' ergs per second, or one watt. The test of electrical difference of potential is the current produced when the bodies are coiinected by a conductor, the force exerted upon charged bodies between them, or the fact that the two bodies are themselves urged together by the electrostatic forces. Gold-leaf electrometer. Quadrant electrometer. Electromotive Force may be defined as anything that produces or tends to produce an electrical flow. Under this definition, potential difference is an electro- motive force, but electromotive force, E.M.F., is a much broader term than difference of potential. It includes all agencies that tend to produce an electric flow. The term electromotive force is usually applied to such agencies as tend to disturb the electrical equilibrium and bring about difference of potential. When a glass rod is rubbed with silk an electromotive force is developed which transfers electricity from the silk to the rod and develops a difference of potential. Difference of potential is always due to a disturb- ance of electrical equilibrium by -an electromotive force. Electricity, like water, seeks its own level, and left to itself, difference of potential would sooner or later disappear. ' 38 NOTES UPON ELECTRICAL MEASUREMENTS. E.M.F. is measured by the difference of potential it can produce. Examples of E.M.F. — When copper and zinc plates are immersed in dilute sulphuric acid the copper becomes positive in relation to the zinc. An E.M.F. exists, tending to carry electricity -from the metal to the liquid, but this is greater for zinc than for copper. This E.M.F. is independent of the size of the plates. When the junction of two metals is heated, an E.M.F. is in general developed which carries elec- tricity from one metal to the other, producing a difference of potential between them. When a conductor is moved across a magnetic field, an E.M.F. in general exists, causing a transfer of electricity from one end toward the other, so developing a difference of potential between the two ends. When the difference of potential so developed is equal to the E.M.F. producing it, there will be nc further transfer of electricity except to make up for any leakage to surrounding bodies. Capacity. — The amount of electricity that must be stored upon a conductor to change its potential by any given amount is found to depend upon the size and shape of the conductor, its proximity to other conductors, and upon the nature of the surrounding dielectric. Other things remaining the same, the ratio of the quantity of POTENTIAL AND ELECTROMOTIVE FORCE. 39 electricity put upon a conductor to the change of poten- tial produced is found to be a constant. This ratio is therefore a measure of the capacity of the conductor. And since we are free to choose a unit of capacity we may write C=QIE '. . (28) Hence a conductor has c.g.s. unit capacity if its poten- tial is changed by one c.g.s. unit when charged with one cg.s. unit quantity of electricity. It has a practical unit capacity, called a farad,, if its potential is changed by one volt when charged with one coulomb. , I coulomb io~ 1 „ I farad = r;^ — = 5- = 10 '• c.g.s. units. I volt lO^ " The combination of two conductors close together but insulated from each other is called a condenser. As ordinarily used the two conductors are connected re- pectively to the two terminals of a battery or other generator. When so used the capacity of the condenser is equal to the ratio of the charge upon one of its plates to the difference of potential between them. If, after being charged to any difference of potential E, the terminals of a condenser be disconnected from the charging source and joined by a conductor, the total quantity of electricity that will pass through the con- ductor during the discharge is Q=EC, where C is the capacity of the condenser. 40 NOTES UPON ELECTRICAL MEASUREMENTS. If two condensers whose capacities are Ci and C2 respectively be connected in multiple (Fig. 6a) to a charging source, their plates have the same difference of 1 1 Hi ■ 1 c-3 1 H Ci C2 (a) m Fig. 6. potential E and the two charges are respectively C\E and C2E and the total charge is (Ci+C2)£. If C be the capacity of the two combined and Q the combined charge, then, Q (Ci + C2)£ (29) Hence the capacity of two condensers in multiple is the sum of their separate capacities. If the two condensers be connected in series (Fig. 66) and then disconnected and discharged separately, it will be found that the same quantity will be discharged by each, and the same also as would be discharged by the two if discharged in series. It can also be seen that the difference of potential E between the extreme plates is the sum of the potential differences £1 and £2 of the individual condensers. If C represent the capacity and Q the charge for the series combination, POTENTI AL AND ELECTROMOTIVE FORCE. <3= Qi = Q2 and E=Ei-\-E2', • ^~E ) .-. E Q. c £1=77-; £2= t'l Q2 C2 . 2_ •■ C "Ci ^C2 111 Hence c=c[+c. • • 41 (30) Equations (29) and (30) can be easily extended to the combination of three or more condensers. The capacities of ordinary conductors being only a very small part of a farad are usually expressed in micro- farads (millionths of a farad). The capacity of a Leyden' jar is a small fraction of a microfarad. PROBLEMS. (31) A potential difference of 200 volts exists be- tween two bodies 10 cm. apart. What is the mean force acting upon a small body charged with one cou- lomb to carry it across from one body to the other ? (32) A i6-candle incandescent lamp consumes about .5 ampere at no volts. How many watts? How many horse-power to operate 500 such lamps? (33) How much heat per hour may be developed by a current of 6 amperes at 240 volts? (34) What quantity of electricity is conveyed in one hour by a current of 10 amperes ? (35) A body charged with 50 coulombs is discharged in 10 seconds. What is the mean current? 42 NOTES UPON ELECTRICAL MEASUREMENTS. RESISTANCE AND OHM'S LAW. There is no such thing as a perfect conductor of electricity. That the best conductors oiJer resistance to the flow of electricity in them is shown by the fact that whenever a current flows there is always a fall of potential along the conductor. Resistance is proportional to the length of the con- ductor and inversely proportional to its cross-section. Specific Resistance. — Different materials forming conductors of same length and cross-section vary greatly in resistance. The specific resistance of a substance may be defined as the ratio of the resist- ance of a conductor of that substance to the resist- ance of a conductor of same length and cross-section of some other substance, taken as a standard. Or, the absolute specific resistance of a substance is the resistance of a centimetre cube of that sub- stance taken between opposite faces. Hence the resistance R of any conductor is equal to its absolute specific resistance multiplied by its length RESISTANCE AND OHM'S LAW. 43 L in centimeters and divided by its cross-sectional area A in square centimeters or R=kL/A, where k is the absolute specific resistance of the material. In order to facilitate the computation of resistances of cylindrical wires whose dimensions are measured in English units, tables have been prepared which give for various materials the resistance of a cylindrical wire one foot long and one mil ( = .001 inch) in diameter. This is called the resistance per mil-foot. Since the sectional areas of cylindrical wires are proportional to the squares of their diameters, we have R=k'L/D2, where k' is the resistance per mil-foot, L the length in feet, and D the diameter in mils. Copper and silver have the least specific resistance. Other metals have varying specific resistances. Iron has about six times and mercury about sixty times the specific resistance of silver. Liquids have much higher resistances. The resist- ance of the liquids used in galvanic batteries is from one to ten million times that of copper. Ohm's Law states that the current ilowing in a conductor is directly proportional to the potential difference, and inversely proportional to the resist- 44 NOTES UPON ELECTRICAL MEASUREMENTS. ance, or, since we have yet to choose a unit of resist- ance, we may put ^=1 (31) Unit Resistance. — The c.g.s. unit resistance may now be defined as that resistance through which the c.g.s. difference of potential will carry the c.g.s. unit current. The practical unit resistance is the oAm =.lo' c.g.s. units. volts Hence amperes = —, . '^ ohms The megohm = a million ohms, and the microhm = one millionth ohm, are units often used. Conductivity measures the capacity of a conduc- tor to carry current. It is the reciprocal of resistance. Insulation Resistance. — No substance is 2, perfect insulator. Gutta percha, one of the best insulators, has a resistance 85 X 10" times the resistance of copper. The insulation of telegraph lines and cables, and of insulated wires generally, is given in megohms per mile. Resistance and Temperature. — The resistance of most materials is altered by a change in temperature. The ratio of the change in resistance per degree (Centi- grade) change in temperature, to the resistance at 0° C. RESISTANCE AND OHM'S LAW. 45 is called the temperature coefficient of resistance. In pure metals the resistance increases when the tempera- ture rises,, the temperature coefficient being about .4 per cent. The temperature coefficient of alloys varies greatly with the composition and with the temperature. For carbon and electrolytes and for some alloys the tem- perature coefficient is negative. Power Consumed by Resistance. — Combining equations (27) and (31), we have P-i'R; (32) P=R (33) This means that in a given conductor the electrical power consumed is proportional to the square of the current, or to the square of the fall of potential along that conductor. Since the electrical energy expended in a conductor develops heat, the heating effect of a current in a given conductor is proportional to the square of the current. Divided Circuits. — When the terminals of an elec- tric generator or any two bodies between which a difference of potential is maintained are joined by two or more conductors, current flows through each of them in accordance with Ohm's law. Conductors so connected are said to be joined in 46 NOTES UPON ELECTRICAL MEASUREMENTS. multiple or in parallel. Figs. 7 and 8 are typical repre- sentatious of such an arrangement. TERMINAL TERMINAU qenerAtor Fig. 7. If £ be the difference of potential between the two bodies to which the conductors are joined, and r,, r^^, If IT IT generator Fig. 8. r^,,, etc., are the resistances, respectively, of the several conductors, the currents flowing will be //= E ///= E ////= E :tc. etc. RESISTANCE AND OHM'S LAW. 47 Evidently the total current is ^=-+- + — + etc. =-5-, . . (34) '/ '// '/// ^ where R is the equivalent resistance of the several conductors. From (34) R can be calculated when r^, r^, etc., are known. For example, (34) gives for three conductors r.^r^^r,,, R^ whence (^y ^n + ''z '"//z + '■/z r,,)R = r, r,, r^,^ ; R= liliilm . . . (35) When two conductors are connected in multiple, the fall of potential is the same along both. Evi- dently for every point on one there must be a point on the other having the same potential. If two such points be connected by a wire, no current will flow through that wire. In Fig. 9 let ABD, ACD, be two conductors joining the terminals of the generator 5. The point C on ACD, which has the same potential as B on ABD, may be found by connecting B to one terminal of a delicate current-indicator G, to the other ter- minal of which a wire is connected which may be slid 1! mg ACD. When G indicates no current, the point C is found. 48 NOTES UPON ELECTRICAL MEASUREMENTS. Let r, r^, r^^, r^^^, be the resistances of the several sections of the conductors as marked on the figure. s Fig. 9. Let e be the fall of potential from A to B and from A to C. Let e^ be the fall of potential from B to D and from C to D. Then, since the same current flows through AB and BD, e e, r=r, (36) For a similar reason € € V^T' (37) Dividing (37) by (36), r r. r = ir 08) // ' /// which shows the relation between the four resistances. PROBLEMS. (36) Two conductors in multiple arc have resist- ances of 24 and 30 ohms respectively. What is the RESISTANCE AND OHM'S LAW. 49 equivalent resistance ? A current of 8 amperes flows in the circuit. What is tlie potential difference between the ends of the conductors ? What current flows through each ? (37) Four conductors, of i, 2, 3, 4 ohms respectively, are in multiple. What is the equivalent resistance ? (38) A galvanometer has a resistance of 4500 ohms; it is desired to place in parallel with it a resistance that shall shunt away from it ^ the current. What must be that resistance ? (39) What is the equivalent resistance of 500 in- candescent lamps in parallel, each lamp having a resistance of 200 ohms ? (40) What current will the lamps of the last prob- lem consume at a potential difference of 1 10 volts ? Suppose the leads from the generator to the lamps have a resistance of 0.01 ohm. What must be the potential difference at the generator to maintain no volts at the lamps ? (41) If the incandescent lamps of problem (39) are connected five in series and these groups connected in multiple, what is the equivalent resistance ? What current will be consumed if each lamp carries the same as before ? What potential difference between the supply leads will be necessary ? 50 NOTES UPON ELECTRICAL MEASUREMENTS. PRACTICAL MEASUREMENTS OF ELEC- TRICAL QUANTITIES. In the preceding lectures the relations between the several electrical quantities have been brought out, and the bases upon which the several units of meas- urement have been defined and established have been fully discussed. It is, o£ course, possible to measure these electrical quantities by methods based upon those relations and definitions. Measurements by such methods are called absolute measurements. When treating of electric currents it was shown how the value of a current could be determined in abso- lute measure by means of the tangent galvanometer. The methods for the absolute measurement of poten- tial and resistance are, however, too tedious and com- plicated to be made use of for general measurements, and are only resorted to for the purpose of construct- ing standards with which the quantities to be meas- ured are thereafter compared. In the measurement of currents, even, the absolute methods are unsuitable for general work, and standards have been devised which render unnecessary the absolute determination of any current. After comparing the results of the MEASUREMLNTS OF ELECTRICAL QUANTITIES. 51 most accurate absolute determinations the Electrical Congress held in Chicago in 1893 fixed upon the fol- lowing as the physical representatives of the electrical units: " As the Unit of Current, the International Am- pere, which is one tenth of the unit current of the c.g.s. system of electromagnetic units, and which is represented sufificiently well for practical use by the unvarying current which when passed through a solu- tion of nitrate of silver in water and in accordance with the accompanying specification deposits silver at the rate of 0.001118 grammes per second." Similarly the International Volt is declared to be represented sufficiently well " by xf^ of the E.M.F. between the poles or electrodes of the voltaic cell known as Clark's cell at a temperature of 15° C, and prepared in the manner described in the accompany- ing specification." And the International Ohm is declared to be " represented by the resistance offered to an unvary- ing electric current by a column of mercury at the temperature of melting ice, 14.4521 grammes in mass, of a constant cross-sectional area, and of the length of 106.3 centimetres." The cross-sectional area of such a mass of mercury 106.3 cm. in length, is one square millimetre. But it is not convenient in ordinary measurements to make use of these official representatives of the 52 NOTES UPON, ELECTRICAL MEASUREMENTS. units. For practical use instruments are constructed by which the electrical quantities may be measured much as we measure length by the foot-rule or tape- measure, or mass by the balance and weights. Ordi- narily we accept the accuracy of such instruments as we accept the accuracy of the weights of the balance, upon the reputation of the manufacturer; but it must be remembered that the electrical instruments, espe- cially those for measurement of potential and current, are likely to change with time, and all are liable to accidental derangements, and it is not safe to trust to their accuracy as we trust to the accuracy of the foot- rule or tape-measure for an indefinite period. For all important measurements the instruments employed should be carefully tested by comparison witli stand- ards of known accuracy. MEASUREMENTS OF RESISTANCE. Instruments. — Certified standard resistances. Resistance sets. These are sets of resistance coils so arranged that any resistance from that of the smallest coil to the sum of all the resistances in the instrument may be employed at pleasure. There are two principal arrangements: coils of i, 2, 2, 5, lo, 20, 20, so, etc., ohms, or ten unit coils, ten lo-ohm coils, etc., are arranged in series, with pro- vision for cutting in or out of circuit any desired portion. MEASUREMENTS OF ELECTRICAL QUANTITIES. 53 Methods of Measurement. — Firsi. By direct com- parison with known resistances : {a) By substitution. This consists in noting the deflection of a galvanometer when connected in cir- cuit with the unknown resistance, then substituting for the unknown resistance known adjustable resist- ances, and adjusting these until the same deflection is obtained. The known resistance is then equal to the unknown. (3) By the differential galvanometer. The differen- tial galvanometer is an instrument having two coils of equal resistance, so adjusted as to have exactly the same influence upon the needle. With equal currents flowing in opposite directions in these two coils the needle would be undisturbed. To use the' instru- ment, the unknown resistance is connected in circuit with one coil, and adjustable known resistances in circuit with the other, the two circuits being con- nected in multiple arc between the terminals of some electric source. When the known resistances are so adjusted that the galvanometer needle suffers no deflection, the known and unknown resistances are equal. Second. By fait of potential. This is a method especially applicable to the measurement of small resistances. The resistance to be measured is con- nected in circuit with a galvanometer which will measure the current flowing. The difference of po- 54 NOTES UPON ELECTRICAL MEASUREMENTS. tential between the two ends of the resistance is then measured by means of some instrument for measuring potential differences. If I be the current and e the difference of potential, then, from Ohm's law, ^=f The figure below illustrates the arrangement. R is the resistance to be measured, G the galvanometer, and V the potential instrument. Third. By Wheaf stone s bridge. This is an appa- ratus utilizing the principle illustrated in Fig. 9. Fig. 10. Suppose any one of the resistances of Fig. 9 to be unknown; it can be determined from equation (38). As the instrument is usually constructed, two of ■ the resistances, as r, fn, have a simple ratio, as 1:1, 1 : 10, 1 : 100. A third resistance, r„ is known and adjustable. The unknown resistance is then con- MEASUREMENTS OF ELECTRICAL QUANTITIES. 55 nected as r,,,. The instrument is often called Wheat- stone's balance; r and r^^ are called the arms of the balance. The manipulation consists in varying the resistance r, until the needle G is undisturbed by the closing of the circuit. Measurement of Insulation Resistance. — Insula- tion resistances up to ten megohms may be measured by means of the Wheatstone's bridge, but for the measurement of very high insulation resistances it is customary to use a delicate galvanometer which will give a deflection equal to one scale division for a difference of potential of one volt through a deter- mined resistance of several megohms. This galva- nometer is merely put in circuit with the insulation resistance to be measured, and the deflection for a given potential difference noted. Measurement of Very Small Resistances. — For such measurements methods must be employed by which the resistances of the connections and contacts by which the resistance to be measured is connected to the apparatus are eliminated. The fall of poten- tial method illustrated in Fig. 10 permits this. The connections a, S, to the potential instrument V are so made as not to include the contact resist- ances by which the battery is connected to the resist- ance R. The method as before described necessitates the accurate observation of current and potential. The 56 NOTES UPON ELECTRICAL MEASUREMENTS. arrangement shown in Fig. 11 does away with the necessity of observing either of these quantities, but permits, instead, the direct comparison of the resistance to be measured with a known adjustable resistance. A is the unknown resistance, R a known FiG.ri. resistance, such as a graduated wire. P is a delicate galvanometer, the value of whose indications heed not be known. The operation consists in sliding the con- tacts cd along R until P shows the same deflection whether connected with R or A. The resistance between a and 6 is then the resistance between c and d. If the deflections of the galvanometer are proportional to the diflferences of potential between its terminals, a fixed resistance R may be used in place of the calibrated wire. If di be the deflection observed when the galvan- ometer is connected to R and dz that when connected to A, then di : dz :: R : A. The 'galvanometer used must take so small a current that the difference of potential MEASUREMENTS OF ELECTRICAL QUANTITIES. 57 between a and 6 or c and d will not be appreciably altered by connecting the galvanometer. A modification of the Wheatstone bridge, known as the Thomson double bridge, is well adapted to the measure- ment of small resistances. Two pairs of ratio arms, ri and r2, a calibrated wire CD, and the resistance AB to be measured are connected as shown (Fig. 12). The iili lall HP in M ' ^.|N II | I MI|M.I ^ Fig. 12. resistances ri and r2 of the branch AC are equal re- spectively to fi and r2 of the branch BD, and these are arranged for adjustment to some simple ratio as 10 : 10, 10 : 100, etc. The operation consists in adjusting ri and r2 in both branches to a convenient ratio and moving the contacts C and D along the claibrated wire until the galvanometer shows no deflection. This shows that the points E and F are at the same potential, i.e., that the fall of potential from 4 to £ is the same as that from A io F\ also that the fall of potential from £ to C is the same as that from F to C Denoting the current in. AC by 1 1, in AB and CD by 1 2, and in BD by /s, the re- sistance AB hy X and CD by R, and remembering that the fall of potential in any resistance is, by Ohm's law, 58 NOTES UPON ELECTRICAL MEASUREMENTS. equal to the product of the resistance multiplied by the current in it, we have hn^hX+hn or ri(7i-73)=7Y and Iirz^hrz+IiR or r2{h—l3)==l2Ri from which ~~—^- ^2 R The advantage of this form of bridge over the ordinary Wheatstone, in the measurement of small resistances, comes from the fact that the contact resistances are thrown in with Ji and ^2 which are themselves of such high resistance that the error caused by the addition of a small contact resistance is negligible (see problem (62)). Measurement of Resistance of Electrolytes. — When an electric current flows through an electrolyte it not only does work in overcoming the true resist- ance, but it also does work in decomposing the elec- trolyte. This latter work is done in overcoming what is called the counter-electromotive force of the liquid. This is an apparent resistance which is independent of the dimensions of the liquid column, and depends only upon the nature of the liquid, assuming the liquid to have no action upon the electrodes. Means by which this apparent resistance may be eliminated must be employed for measuring the true resistance.' MEASUREMENT FOR ELECTRICAL QUANTITIES. $9 Fig. 13 shows one method. a6 is a U tube contain- ing the electrolyte, G is a. battery, and R an adjust- able resistance; c and d are platinum plates nearly filling the tube. Let R be adjusted until the galva- G II 1° ^ Fig. 13. nometer gives a convenient deflection. Now let one of the platinum plates be lowered a measured dis- tance — to e, say. Now adjust R until the galva- nometer shows the same deflection as before. The increase in R is the resistance of the column of liquid ce. If a column of an electrolyte is traversed by a rapidly alternating current, no permanent decomposi- tion occurs, and no work is done except in overcom- ing the true resistance. The resistance may then be measured by any of the methods before described for 6o NOTES UPON ELECTRICAL MEASUREMENTS. measuring the resistance of ordinary conductors, but, instead of the galvanometer, an electrodynamometer or some instrument affected by alternating currents must be used. If a Wheatstone's bridge is employed with alternating currents for measuring the resistance of an electrolyte, a telephone may conveniently be used in place of the galvanometer to indicate when a balance is obtained. The resistance of an electrolyte varies greatly with temperature and, if a solution, with the degree of concentration. Measurements are of no value unless these conditions are noted. Resistance of Batteries. — The measurement of the resistance of battery-cells presents some diiificul-, ties on account of the electromotive force. The following are some of the methods employed : (a) Two similar cells are connected by two like poles so that their electromotive forces are opposed. Their joint resistance may then be measured as in the case of ordinary conductors. (b) By Application of Ohm's Law. — As stiated on page 37, Ohm's law refers to a part of a circuit not con- taining an E.M.F. An equation of precisely the same form as (31) may also be written for a complete circuit, where E is the total E.M.F., i.e., the algebraic sum of all the E.M.F.'s in the circuit, R the resistance of the whole circuit and / the current. We may now deduce a form for Ohm's law for part of a circuit con- MEASUREMENTS OF ELECTRICAL QUANTITIES. 6l If R is- the resistance of the battery (Fig. 14) and E its electromotive force, i.e., E is the difference of potential between the terminals C and D when there is no current r^VWW^ O Fig. 14. flowing (key open), and e the difference of potential between the battery terminals when the circuit is closed through the external resistance r, and / the current flow- ing. Then /= E From which and subtracting which gives R+r r' IR+Ir^E Ir=e; IR==E-e, i? = E- and /= E-e (39) I R ' • ■ It will be noted that equation (39) refers to a part of a circuit (C-D) containing an E.M.F. and that the cur- rent here referred to is in the direction of the E.M.F. If in any circuit the current flows in the opposite direc- tion to an E,M.F., as in charging a storage battery, then e is larger than E and the direction of the current is indi- 62 NOTES UPON ELECTRICAL MEASUREMENTS. cated by the negative sign. Evidently the expression for the current in the direction of the potential diflference is e-E I=- — - in which case E is called a counter-electromotive force. This method of measuring the resistance of a battery consists in determining the values of E, e, and / by means of proper instruments and substituting them in the first of equations (39). The current measuring instrument may be dispensed with if the whole external resistance r be known. Sub- stituting in (39) for / its value e/r, we obtain „ E-e R= r. e If e=£;/2, then Hence we may observe the potential of the cell on open circuit, then close the circuit through a resistance which is so adjusted as to reduce the potential to one half. The known resistance in circuit is then equal to the resistance of the cell. This method assumes that the E.M.F. of the cell remains constant during the measurements. This is not necessarily true. MEASTTREMENT OF CURRENT. Measurements of current by means of the tangent galvanometer have already been fully explained. Other current-measuring instruments have been briefly MEASUREMENTS OF ELECTRICAL QUANTITIES. 63 described. These are usually adjusted by the man-u- facturers to read directly in amperes, and it is only necessary to connect the instrument in the circuit where the current is to be measured, and note the reading. It is important in the use of all such instru- ments to place them where they will be uninfluenced by outside magnetic forces. < Current Measured by Fall of Potential. — In a conductor carrying a current there is always a fall of potential between its ends. This fall for the same conductor is proportional to the current, hence may be taken as a measure of the current. Fig. 15 shows nrfm Fig. is. diagrammatically the arrangement of an instrument designed to utilize this method of measuring currents. Ji is the fixed resistance and A an instrument whose indications are proportional to the potential differ- ences between its terminals. It is not necessary to know the resistarice R. The instrument may be cali- brated by direct comparison with some standard current-measuring instrument. Examples of such instruments. 64 NOTES UPON ELECTRICAL MEASUREMENTS MEASUREMENT OF POTENTIAL. By Electrostatic Forces. — This consists essen- tially in the measurement of the electrostatic forces existing between two bodies charged to the difference of potential to be measured. Instruments designed for such measurements may be so constructed that the potential difference may be computed from their dimensions and the forces observed. This is an absolute measurement, but is applicable only to the measurement of large potential differences. The Quadrant Electrometer. The Attracted-disk Electrometer. By Comparison with a Known Potential Differ- ence. — Fig. i6 illustrates this method. ab is a Fig. i6. graduated resistance, such as a long wire or a series of resistance coils. G is a generator capable of main- MEASUREMENTS OF ELECTRICAL QUANTITIES. 65 taining a constant potential difference between a and l>, which must be known. C is a battery-cell whose E.M.F. is to be measured, -so connected in the branch aCd that its E.M.F. is opposed to the E.M.F. acting along that branch in consequence of the fall of potential along ad. Now the point of contact d is moved along the resistance ad until the galvanometer / is undeflected. The potential difference between a and d now balances the E.M.F. of the cell C. If £ be the potential difference between a and i, and E^ the E.M.F. of the cell C, we have res. ai> E res. ad ~ E^ An instrument so constructed as to provide for the convenient application of the above method is called a potentiometer. Different forms of potentiometer. By the Current produced in Circuit of Given Re- sistance. — It follows from Ohm's law that E.M.F. is proportional to the current it develops in a given resistance. Hence the readings of any galvanometer are proportional to the potential difference between its terminals. If a galvanometer of high resistance be connected between two points differing in poten- tial, its indications will be proportional to that poten- tial difference, and the instrument may be graduated 66 NOTES UPON ELECTRICAL MEASUREMENTS. to give the potential difference directly in volts. It is then called a voltmeter. Different forms of voltmeter shown and described. Since closing a circuit between two points may alter the potential difference between those points, the use of such voltmeters as are described above is inadmissible, except where the generating source is such as to maintain that potential difference notwith- standing the current consumed by the voltmeter.* By the Ballistic Galvanometer. — If two bodies, as the two coatings of a Leyden jar or other condenser, be connected to two points of an electric circuit, those bodies will be charged to whatever potential differ- ence may exist between those points. If they are afterward connected through a suitable galvanometer, they will be discharged, and the discharge-current flowing through the galvanometer coil will give the needle a sudden impulse, causing it to swing off a certain distance depending upon the quantity of elec- tricity discharged, and this again is proportional to the potential difference and to the capacity of the condenser receiving the charge. In this way potential differences may be measured by means of the galvanometer without actually form- ing a circuit and taking current from the source. A galvanometer suitable for this purpose is one whose needle swings freely, with the smallest possible retarding influence, so that its needle once disturbed * See PrnlilATn a e MEASUREMENTS OF ELECTRICAL QUANTITIES. 67 will swing for a long time before coming to rest. It should also have a slow rate of vibration. Such an instrument is called a ballistic galvanometer. [See Appendix]. TESTING AND CALIBRATING INSTRUMENTS. Electrical instruments are liable to derangement and must be frequently tested to determine whether changes have occurred. This is especially true of instruments for the measurement of current and potential. Where a high degree of accuracy is re- quired, instruments must be compared with accredited standards, their errors determined, and the necessary corrections applied when the instruments are used for measurements. Tests of Resistance Sets. — It is seldom required to reproduce the mercury standard ohm for purposes of comparison. A certified standard one-ohm coil may be used instead. The one-ohm coil of the set is compared with the standard. Then this one-ohm coil plus the standard is compared with the two-ohm coil of the set, and so on until all are compared. In a decade set each one-ohm coil would be compared with the standard, then the ten one-ohm coils in series with each ten-ohm coil, etc. Method of Comparison. — A form of Wheatstone's bridge known as the divided-metre bridge is usually employed for comparing resistances. Fig. 17 shows the arrangement. AB is a wire of as nearly as possi- 68 NOTES UPON ELECTRICAL MEASUREMENTS. ble uniform cross-section. G, G^, etc., are heavy copper strips. E and F are two nearly equal resist- ances, which, to give the greatest sensibility, should be about the value of the resistances to be compared, which are connected in the two gaps C, D. I is now moved along the wire AB until the galvanometer is undeflected by closing the circuit. The resistances at C and D are now interchanged. It is plain that, if they are equal, the galvanometer will still be un- c ol IK. Ih 6 m G, f m "ci s r vs' Fig. 17. deflected by closing the circuit. If C and D are not equal, / will have to be moved in order to obtain a balance after the interchange. It is easy to show that the resistance of the bridge-wire between the two positions of / equals the difference between the resistances of the two coils that are being compared. The bridge-wire AB in the standard form of this apparatus is one metre in length, and under it is a scale divided into millimetres; hence the name. If the resistance of one millimetre of the bridge-wire is known, the difference in fractions of an ohm between two coils under comparison is at once given. MEASUREMENTS OF ELECTRICAL QUANTITIES. 69 Calibration of the Bridge-wire. — It is rarely the case that the resistance of the bridge-wire is uniform. To determine its resistance in different parts of its length it must be calibrated. To effect the calibra- tion the resistances E and F are removed, and the points m and n are connected by a wire as shown by the dotted line. The galvanometer connection K is now made on the wire mn by a movable contact-piece. Place at C a standard one-ohm Coil, and at i? a i.oi- ohm standard ; then effect a balance by moving either / or K. Now interchange C and D and balance again by moving /. Evidently the resistance of the wire between the two positions of lis .01 ohm. Return C and D to their former positions, and, without mov- ing /, balance by sliding K along mn. Again inter- change C and D and balance by moving /. This will give another .oi-ohm section of AB. Continuing this process step by step, the whole wire may be sub- divided into .01 -ohm sections, from which the resist- ance between any two points may be obtained. In making such tests as those described, arrange- ments must be made for maintaining a constant tem- perature, and the connections at C and D must be so made that their resistances are extremely small and are invariable during all the interchanges. Tests of Current Instruments. — First. Compari- son with a standard. The instrument is connected in circuit with a si'ver voltameter and the test conducted 70 NOTES UPON ELECTRICAL MEASUREMENTS. as directed on page io6 of ''Physical Units" by Professor Magnus Maclean. This gives the true value of the reading for one point of the scale. Second. Comparison of different scale-readings. Having found the value of the scale-reading for one point, the instrument is connected in circuit with a variable resistance whose values can be accurately determined, and a source of electricity giving a con- stant difference of potential. The constancy of the potential may be determined by the use of any potential indicator. It is not necessary that its value should be known. The test consists in varying the current by means of the variable resistance, and noting the resistance and corresponding readings of the instrument. Tests of Instruments for Measuring Potential. — Voltmeters may be tested by means of the poten- tiometer and the standard Clark cell. Referring to Fig. i6, ab is the potentiometer resistance, which should be as much as 10,000 ohms. V is the volt- meter to be tested, and C the standard cell. The generator G should have an E.M.F. greater than the highest reading of the voltmeter, and it will be con- venient if its E.M.F. is adjustable. If this is not the case, the potential difference between a and b may be varied by shunting a part of the current away from ab. The test consists in varying the potential difference MEASUREMENTS OF ELECTRICAL QUANTITIES. 71 between a and b until the voltmeter gives a conven- ient reading. Then move the connection d until lis undeflected. We then have value of volt- ) res. ad ^ ,, ^ , ^. , J. y= — y X E.M.F. of Clark cell. meter readmg ) res. aa The E.M.F. of a Clark cell for any temperature t is 1.434 -■COl2{t ~ 15), Clark cells are themselves liable to derangement. It is best to have several of them, and compare them with each other by means of the potentiometer. If two or three of them agree at a given tempferature, it is safe to assume that their E.M.F. at 15° C. is- 1.434 volts. When using a Clark cell it is necessary to place in series with it a protecting resistance of several thou- sand ohms to prevent passing through it too large a current. This resistance may be shunted for the pur- pose of obtaining a higher sensitiveness when the potentials are nearly balanced. MEASUREMENT OF CAPACITY. (i) By charging to known difference of potential and discharging through a calibrated ballistic galvanometer. (See Appendix page 114). (2) By comparing with a standard condenser. (a) By charging both to known potential differences 72 NOTES UPON ELECTRICAL MEASUREMENTS. and discharging separately through a ballistic galvan- ometer, the difference of potential being so adjusted that the deflection is the same for each. (b) By the bridge method in which the condensers whose capacities are to be compared are connected, as shown in Fig. i8. The measurement consists in Fio. i8. adjusting the resistances ri and r2 until the sensitive galvanometer G shows no deflection on opening or closing the key. When this condition is obtained it is evident that the charges in the two condensers are equal and the differences of potential to which they are re- spectively charged are proportional to the resistances to which they are connected. Hence from which c =c^-r^-^ 'E^. MEASUREMENTS OF ELECTRICAL QUANTITIES. 73 PROBLEMS. (42) Four conductors whose resistances are i, 2, 3, and 4 ohms respectively are Joined in multiple to a source maintaining a P.D. of 12 volts. Find the current in each, the total current, the equivalent resistance of the four conductors, the total power consumed, and the power consumed in each. (43) If the resistance of the moving coil of an ammeter is 10 ohms, and if a current of .01 ampere is sufficient to cause a deflection across the full length of the scale, what must be the resistance of a lo-ampere shunt for the instrument? A 25-ampere shunt? A 5o-3mpere shunt? (By a lo-ampere shunt is meant a conductor such that when connected in multiple with the moving coil the latter will give a deflection equal to the full length of the scale when the total current in the line is 10 amperes.) (44) What resistance must be put in series with the moving coil of the instrument of problem (43) so that it will give full scale deflection when connected to two points whose P.D. is kept at 150 volts? 15 volts? (45) Ten coils having each a resistance of 10,000 ohms are joined in series to two points whose P.D. is main- tained at 100 volts. What wiU be the P.D. between the terminals of each coil? What will be the reading of a voltmeter of 20,000 ohms when connected in multiple with one of the 10,000 ohm coils? If coimected across the whole set of ten coils ? 74 NOTES UPON ELECTRICAL MEASUREMENTS. (46) A galvanometer whose resistance is to be found is connected in series with a megohm and a source main- taining a constant P.D. and the deflection noted. The megohm is then replaced by ^ megohm and a variable resistance connected, as a shunt across the galvanometer. When the resistance of the shunt is 2172 ohms the deflec- tion of the galvanometer is the same as before. Find the resistance of the galvanometer and give proof for the method used. (47) If the resistance of a galvanometer is 2000 ohms, what is the resistance of its i/io shunt? Of its i/ioo shimt? (A i/io shunt beiiig such as will permit i/io of the total current in the line to pass through the galvanometer.) (48) What resistance must be put in series with the shunted galvanometer of the previous problem when the i/io shunt is used so that the current in the circuit will be the same as when the galvanometer is used without a shunt? (49) If in Fig. 9 the resistance of the galvanometer is 25 ohms and the resistances r, r,, r,,, and r,,/ are 5, 10, 15, and 20 ohms respectively, find the current in the galvanometer if the difference of potential between A and Z? is 2 volts. (50) Two dynamos having each a P.D. of 120 volts are connected as shown. The wires a, 6, and c have a resistance of 2 ohms each. Current in a is 15 amperes MEASUREMENTS OF ELECTRICAL QUANTITIES. 75 and in c 10 amperes. Find the P.D. between the middle wire and each outside wire at the lamps. (51) If the lamps between a and b of problem (50) have a resistance of 12 ohms and those between b and c 20 ohms, find the current in each of the three wires. (52) From the data of problem (50) find the power furnished by the dynamos and the power used in the lamps. (53) Seven cars a mile apart oh a trolley line six miles long take 15 amperes apiece. If the resistance of the trolley wire is .52 ohms per mile and the rail return ,04 ohm per mile, what is the P.D. between the wire and the rail at each car, when the power-station at the end of the line maintains a P.D. of 550 volts ? (54) Solve problem (53) assuming the power-station at the middle of the line. (55) 5°° incandescent lamps having a resistance of 220 ohms each are connected in multiple. Current is supplied to the lamps from a generator 1000 feet distant by copper leads J inch in diameter. (Resistance of copper 10.5 ohms per mil-foot.) -What P.D. at the generator terminals will give no volts at the lamps ? 76 NOTES UPON ELECTRICAL MEASUREMENTS. (56) If in problem (55) the resistance of the generator armature is .1 ohm, what must be the E.M.F. ? (57) Current is to be furnished to a heating coil from a 120 volt source by two leads of ,5 ohm each. What must be the resistance of the coil so that it will use 200 watts ? (58) A voltmeter whose resistance is 15,000 ohms and a resistance to be measured are connected in series to a source whose P.D. is 240 volts. The reading of the voltmeter is 12 volts. What is the value of the unknown resistance ? (59) A galvanometer whose resistance is 4995 ohms and whose deflections are proportional to the current in it, a 5-ohm shunt, a megohm coil, and a resistance R to be measured are connected to a source of constant r<2y- U.\J i Meg-unm VVWWWVVVV B •- -VSAAMAMA- K-H- E.M.F., as shown in the accompanying figure. When the double pole double-throw switch S is turned to A and K turned to D the deflection is 20 scale divisions. When S is turned to B and if to C the deflection is 10 scale divisions. Compute R in megohms. MEASUREMENTS OF ELECTRICAL QUANTITIES. 77 (60) A small resistance X and a standard i/io-ohm coil are joined in series to a source of constant cxirrent. A galvanometer whose deflections are proportional to the current in it and whose resistance is 2000 ohms, having in series with it 8000 ohms, gives a deflection of 20 scale divisions when connected in multiple with the i/io ohm, and 25 scale divisions when in multiple with X. Find the value of X in ohms. What resistance must be put ia series with the galvanometer when it it in multiple with X so that the deflection will be 20 scale divisions for it also ? (61) If AB (Fig. 12) is a round wire 20 cm. long and 2.5 mm. in diameter, r\ and rz being 10 and 1000 ohms respectively, und if the bridge is balanced when the resistance included between C and D . is .0645 ohm, what is the absolute specific resistance of the material of which AB is made ? (62) What per cent error will be introduced in the result for problem (61) if the four contacts A, B, C, and D have each a resistance which may be as much as .01 ohm? If the same resistance were measured by an ordinary Wheatstone bridge, what per cent error would be intro- duced by .01 ohm contacts? (63) Three small storage cells whose E.M.F.'s are 2 volts each and whose resistances are i/io ohm each are being charged in series by a generator whose terminal P.D. is 120 volts. A resistance of 22.5 ohms is con- nected in series with the cells. Compute the current in 78 NOTES UPON ELECTRICAL MEASUREMENTS. amperes, and the P.D. at the battery terminals. If the resistance of the generator be .5 ohm, what E.M.F. must it have? (64) A galvanometer of high resistance whose deflec- tions are proportional to the current sent through it, when connected to the terminals of a battery gives a deflection of 25 scale divisions. When a wire of 10 ohms resistance is connected in multiple with the galvanometer the deflection is 20 scale divisions. What is the resist- ance of the battery? (65) A storage battery consisting of twelve cells in series, whose E.M.F. is 2.1 volts per cell and whose resistance is .05 ohm per cell, is to be charged from a generator having a terminal P.D. of 120 volts. What resistance must be put in series with the battery so that the charging current may be 10 amperes? What will be the P.D. across the terminals of the battery? What will be the total power consumed? The power consumed in the battery ? Explain the difference between the results for power computations obtained from the formulae PR and IE in the above. (66) If a uniform wire 9 meters long is connected to the terminals of a dynamo, and if when the terminals of of cell whose E.M.F. is 1.35 volts is connected to two points on the wire 10 cm. apart, the galvanometer shows no deflection, what is the difference of potential between the dynamo terminals? (67) In calibrating an ammeter by mean« of a poten- MEASUREMENTS OF ELECTRICAL QUANTITIES. 79 tiameter and a standard cadmium cell whose E.M.F. is 1.0185, the potentiameter current is so adjusted that the E.M.F. of this cell is balanced when shunted across 10,185 ohms of the potentiameter wire. The ammeter is connected in series with a standard .01 ohm to a source of current. The fall of potential across the .01 ohm is balanced by the fall of potential in 2550 ohms of the potentiameter wire. If the ammeter reading is 25 amperes, what is its error ? (68) A uniform wire 100 feet long joins two points whose P.D. is 100 volts. The terminals of a condenser having a capacity of 10 microfarads are connected to two points on this wire 20 feet apart. What charge is given to the condenser ? (69) (a) If the condenser of problem (68) be dis- charged through a ballistic galvanometer and give a deflection of 20 scale divisions, what is the capacity of a condenser which gives the same deflection of the galvan- ometer after being charged by being connected across 65 feet of the wire. (6) If the deflection of the galvanometer is propor- tional to the "quantity" discharged through it, what would have been the deflection of the galvanometer if the condenser of problem (69a) had been charged to the same P.D. as the condenser, of problem (68)? (70) Four condensers whose capacities are .5, .2, .2 and .1 microfarads respectively, are joined in series to a 8o NOTES UPON ELECTRICAL MEASUREMENTS. charging source having a P.D. of 120 volts. What will be the total quantity discharged if they are discharged in series? What quantity will be discharged by each if after charging they be disconnected and discharged separately? HEATING EFFECTS OF THE CURRENT. 8l HEATING EFFECTS OF THE CURRENT. When a current flows through a homogeneous con- ductor, that conductor is always heated. Equation (32) shows that the energy spent in such a conductor per second is PR — directly proportional to the resistance, and to the square of the current. 7 being given in amperes and R in ohms, the heat generated is .00024/2/2 calories per second =.000948/22? British ther- mal units per second. A 1 6-candle incandescent lamp consumes about 0.5 ampere at no volts. Its resistance is, therefore, 220 ohms. The energy expended in it is no X -5 = 220 X .5' = 55 watts = 55 X .00024 = -0132 calorie per second = .074 H. P. Temperature of a Conductor carrying. Current. — ^The temperature to which a conductor is raised by the current depends not only upon the rate of development of heat in it, but upon the rate at which heat escapes. The temperature becomes permanent when heat escapes as fast as it is generated. For a round wire of given length the resistance is proportional to the. inverse square of the diameter, while the radiating surface is directly proportional to 82 NOTES UPON ELECTRICAL MEASUREMENTS. the first power of the diameter. The heat generated by the same current in a wire whose diameter is d, as compared to that generated in a wire whose diameter is unity, is, therefore, -j,, while the surface from which d heat escapes is — times as great. The heat which must escape from unit surface of the larger wire is, therefore, -7-, of that which must escape from unit surface of the smaller wire. If heat escaping per unit surface is proportional to the difference of tempera- ture between the wire and its surroundings, the larger wire will rise in temperature only -r, as much as the smaller. Equation (33) shows that the heat developed in a wire is proportional to -n-. This means that for the same difference of potential the heat generated in conductors of different resist- ances is inversely proportional to the resistance, and, since resistance for wires of the same length is pro- portional to the inverse square of the diameter, the heat generated in such wires when subjected to the same potential difference {■s, proportional to the square of the diameter directly. Hence if two wires, diam- eter unity and diameter d, are connected in multiple between tjie terminals of an electric generator, d"" HEATING EFFECTS OF THE CURRENT. 83 times as much heat will be generated in the wire whose diameter is d. But its surface is only d times as great, hence d times as much heat must escape from unit surface, which requires that it rise in tem- perature d times as much. It follows that a coarse wire will be heated to a higher temperature than a fine one of the same length when connected across a circuit where the difference of potential is the same. INCANDESCENT LIGHTING. Description of the incandescent lamp. Incandescent lamps are usually connected in multi- ple arc across a circuit from a generator capable of maintaining a constant difference of potential, whether lamps in use are few or many. Fig. 8, on page 46, may be taken as a diagrammatic illustration of such a system. Economy requires High Temperature. — Econ- omy in incandescent lighting requires that the carbon filament shall be maintained at as high a temperature as it will bear without a too-rapid deterioration, for the reason that the ratio of light emitted to energy consumed increases Very rapidly as the temperature increases. At the best, only about 5 per cent of the energy expended in the lamp appears as light; the remaining 95 per cent is dark heat, useless for illumi- nation, and therefore wasted. 84 MOTES UPON ELECTRICAL MEASUREMENTS. Incandescent Lamps of Different Candle-power. — Since potential is constant, the power expended in an incandescent lamp is inversely proportional to its resistance (see equation (33) ). Let it be required to construct a 32-candle lamp, that is, a lamp of twice the usual illuminating power. This requires that twice the power be expended; hence that the resistance be reduced to one half. Since the temperature must remain constant, the radiating surface must be doubled. 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A Manual for Steel-users. , i2mo, 2 00 Patton's Practical Treatise on Fbundations , Svo, s 00 Sice's Concrete Block Manufacture Svo, 2 00 Richardson's Modern Asphalt Pavements Svo, 3 00 Richey's Handbook for Superintendents of Construction — .... i6mo, mor., 4 00 * Rles's Clays: Their Occurrence, Properties, and Uses Svo, s/00 Sabin's Industrial and Artistic Technology of Paints and Varnish Svo, 300 *Schwarz'sLongleafPinein Virgin Forest i2mo, i 25 Snow's Principal Species of Wood Svo, 3 So Spalding's Hydraulic Cement lamo, 2 00 Text-book on Roads and Pavements i2mo, 2 00 Taylor and Thompson's Treatise on Concrete, Plain and Reinforced Svo, S 00 Thurston's Materials of Engineering. In Three Parts Svo, 8 00 Part I. Non-metallic Materials of Engineering and Metallurgy Svo, 2 00 Part n. Iron and Steel Svo, 3 so Part nX. 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Butt's Civil Engineer's Field-book i6mo, mor. 2 50 Crandall's Railway and Other Earthwork Tables 8vo, i 50 Transition Curve i6mo, mor. i 50 * Crockett's Methods for Earthwork Computations Svo, i 50 Dawson's "Engineering" and Electric Traction Pocket-book. 1... . iSmo, mor. 5 00 Dredge's History of the Pennsylvania Raiteoad: (1S79) : , . . .Paper, 5 00 Fisher's Table of Cubic Yards Cardboard, 23 Godwin's Railroad Engineers' Field-book and Explorer^' Guide. ,. . i6mo, mor. 2 50 Hudson's Tables for Calculating the Cubic Contents of Excavations .and Em- bankments Svo, I oo Ives and Hilts's Problems in Surveying, Railroad Surveying and .Geodesy i6mo, mor. i' go'. . Mulitor and Beard's Manual for Resident Engineers idmo, i 00 ITagle's. Field Manual for Railroad Engineefsi > .» i6mo, mor. 3 00 Philbrick's Field Manual for Engineers i6mo, mor. 3 00 Raymond's Railioad Engineering. 3. volumes. . Vol. . I. Railroad Field Geometry. (In Preparation.) Vol. II. Elements of Railroad Engineering. Svo, 3 50 Vol, III. Railroad Engineer's Field Book. (In Preparation,}, Searles's Field Engineering. ... i6mo, mor. 3 00 Railroad Spiral i6mo, mor. i 50 . Taylor's. ^irismoidal Formulae and Earthwork.:. .8vo, i go *Trantwine's Field Practice of Laying Out Circular Curves for Railroads. i2mo. mor, 2 go * Method of Calculating the Cubic Contents of Excavations, and Embank- ments by the Aid of Diagrams Svo, 2 00 Webb's Economics of Railroad Construction Large z2mo, 2 50 Railroad Construction. , i6mo,'mor. 5 oo Wellington's Economic Theory of the Location of Railways Small Svo, 5 00 DRAWING, Barr's Kinematics of Machinery Svo, 2 go * Bartlett's Mechanical Drawing Svo, 3 00 * " " " Abridged Ed Svo, 150 Coolidge's Manual-of Drawing Svo, paper, x 00 Goolidge and Freeman's Elements ot General Drafting for Mechanical Bngir, neers Oblong 4to, 2 50 -Durley's Kinematics of- Machined Svo, 4 00 Emch's Introduction to Projective Geometry and its Applications Svo, 2 So Hill's Text-book on Shades and Shadows, and Perspective. Svo, 2 00 Jamison's Advanced Mechanical Drawing. . - Svo, 2 00 Elements of Mechanical Drawing i Svo, 3 50 Jones's Machine Design: Part I. Kinematics of Machinery. Svo, z 50 Part n. Form, Strength, and Proportions of Parts .- Svo, 3 00 MacCord's Elements of Descriptive Geometry, Svo, 3 00 Kinematics; or. Practical Mechanism g^o, g 00 Mechanical Drawing 4to, Velocity Diagrams. ,• i 8to_ McLeod's Descriptive Geometry, -. Large ismo, * Mahan's Descriptive Geometry and Stonercutting, 8vo, i so Industrial Drawing, .(Thompson.) ' 4 00 I 50 SO Moyer's Descriptive Geometry 8to, Reed's Topographical Drawing and Slcetcliing 4to, Reid's Course in Mechanical Drawing 8vo, Text-book of Mechanical Drawing and Elementary Machine Design, 8vo, Robinson's Principles of Mechanism ; 8vo, Schwamb and Merrill's Elements of Mechanism 8vo, Smith's (R. S.) Manual of Topographical Drawing. (McMillan.) 8vo, Smith (A. W.) and Marx's Machine Design. . \ 8vo, * Titsworth's Elements of Mechanical Drawing Oblong 8vo, 'Varren's Drafting Instruments and Operations i2mo. Elements of Descriptive Geometry, Shadows, and Perspective 8vo, Elements of Machine Construction and Drawing. 8vo, Elements of Plane and Solid Free-hand Geometrical Drawing. . . i .2mo, General Problems'of Shades and Shadows 8vo, Manual of Elementary Problems in the Linear Perspective of Form and Shadow '. i2mo. Manual of Elementary Projection Drawing i2mo, Plane Problems in Elementary Geometry. i2mo. Problems, Theorems, and Examples in Descriptive Geometry 8vo, Weisbach's KJjoetei^tics i and Power of Transmission. (Hermann and Klein.) 8vo, Wilson's the Study of Electrical Engineering 8vo, 2 50 * Parshall and Hobart's Electric Machine Design 4to, half morocco, 12 50 Reagan's Locomotives: Simple, Compound, and Electric. New Edition. Large i2mo, 3 30 * Rosenberg's Electrical Engineering. (Haldane Gee — Kinzbrunner.). ..8vo, 2 00 Ryan, Iforris, and Hozie's Electrical Machinery. Vol. 1 8vo, 2 so S^happer's Laboratory Guide for Students in Physical Chemistry i2mo, i 00 Thurston's Stationary Steam-engines Svo, 2 ^g * Tillman's Elementary Lessons in Heat Svo, i 50 Tory and Pitcher's Manual of Laboratory Physics Large i2mo, 2 00 Ulke's Modern Electrolytic Copper Refining. Svo, 3 00 LAW. * Davis's Elements of Law Svo, 2 50 * Treatise on the MiUtary Law of United States. Svo, 7 00 * Sheep, •} so * Dudley's Military Law and the Procedure of Courts-martial . . . .Large i2mo, 2 s<> Manual for Courts-martial i6mo, mor. i so Wait's Engineering and Architectural Jurisprudence Svo, 6 00 Sheep, 6 50 Law of Contracts Svo, 3 oo Law of Operations Preliminary to Construction in Engineering and Archi- tecture Svo s 00 Sheep, 5 50 MATHEMATICS. Baker's Elliptic Functions Svo, i So Briggs's Ele|n^n4^ of Plane Analytic Geometry. 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(Truscott and Emory. )'i2mo, a oo * Ludlow and Bass's Elements of Trigonometry and Logarithmic and Other Tables ' 8vo, 3 00 Trigonometry and Tables published separately Each, 2 00 * Ludlow's Logarithmic and Trigonometric Tables 8vo, i 00 Macfarlane's Vector Analysis and Quaternions 8vo, i 00 HcMahon's Hyperbolic Functions Svo, i 00 Manning's IrrationalNumbers and their Representation bySequences and Series i2mo, I 25 Mathematical Monographs. Edited by Mansfield Merriman and Robert S. Woodward Octavo, each i 00 No. I. History of Modern Mathematics, by David Eugene Smith. No. a. Synthetic Projective Geometry, by George Bruce Halsted. No. 3. Determinants, by Laenas Glfford Weld. No. 4. Hyper- bolic Functions, by James McMahon. Ko. s. Harmonic Func- tions, by William E. Byerly. No. 6. Grassmann's Space Analysis, by Edward W. Hyde. No. 7. Probability and Theory of Errors, by Robert S. Woodward. No. 8. Vector Analysis and Quaternions, by Alexander Macfarlane. No. 9. 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Bacon's Forge Practice. i2mo, i 50 Baldwin's Steam Heating for Buildings i2mo, 2 50 Bair's Kinematics of Machinery gyo, 2 50 '* Bartlett's Mechanical Drawing Svo, 3 00 * " " " Abridged Ed Svo, 150 fienjamin's Wrinkles and Recipes ..i2mo, 2 00 * Burr's Ancient and Modern Engineering and the Isthmian Canal Svo, 3 so Carpenter's Experimental Engii^ering Sxo, 6 00 Heating and Ventilating Buildings Svo, 4 00 Clerk's Gas and Oil Engine , Large i2mo, ^4 00 Compton's First Lessons in Metal Working i2mo, i so Compton and De Groodt's Speed Lathe 12mo, 1 50 Coolidge's Manual of Drawing. Svo, paper, i 00 Coolidge and Freeman's Elements of General Drafting for Mechanical En- gineer, Oblong 4to, 2 50 Cromwell's Treatise on Belts and Pulleys i2mo, i so Treatise on Toothed Gearing i2mo, i 50 Durley's Kinematics of Machines Svo, 4 00 13 Flather's Dynamometers and the Measurement of Power i2mo. Rope Driving. i2mo> Gill's Gas and Fuel Analysis for Engineers i2mo, Goss's Locomotive Sparks : . ,, 8vo, Hall's Car Lubrication i2mo, Hering's Ready Reference Tables (Conversion, Factors) i6mo, mor., Hobart and Elus's High Speed Dynamo Electric Machinery. (In Press.) Button's Gas Engine , 8to, Jamison's Advanced Mechanical Drawing. 8vo, Elements of Mechanical Drawing 8vo, Jones's Machine Design: Part 1. Kinematics of Machinery. ,,,.,. 8vo, Part n. Form, Strength, and Propoj'tions of Parts 8vo, Kent's Mechanical Engineers' Pocket-book i6mo, mor , Kerr's Power and Power. Transmission 8vo, Leonard's Machine Shpp Tools and Methods 8vo, * Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.) . . 8va, MacCord's Kinematics; or. Practical .Mechanism. 8vo, Mechanical Drawing ,. , 4to, Velocity Diagrams , 8vo, MacFarland's Standard Reduction Factors for Gases. Svo, Mahan's Indiistrial Drawing. , (Thompson.). . ,. ,. Svo, * Parshall and Hobart's Electric Machine Design Small 4to, half leather, Peele's Compressed Air Plant' for Mines. (In Press.), Poole's Calorific Power of Fuels , ^ Svo, * Porter's Engineering Reminiscences, 1855 to 1882 Svo, Reid's Course in Mechanical Drawing. Svo, Text-book of Mechanical Drawing and Elementary Machine Design. Svo, Richard's Compressefd Air i2mo, Robinson's Principles of Mechanism, ..,, ; Svo, .Schwamb and Merrill's Elements of Mechanism Svo, Smith's (O.) Press-working of Metals. ,:..,. 1 .Svo, Smith (A. W.) and Marx's Machine Design .Svo, Sotel'sCarbuietingandXkjmbustionJiiAlcDhol Engines. (Woodwardand Pieston). Large i2mo, Thurston's Animal as a Machine and Prime Motor, and the Laws of Energetics. i2mo. Treatise on Friction and Lost Work in Machinery and Mill Work... Svo, Tillson's Complete Automobile Instructor i6mo, inor., * Titsworth's, Ele;ments of Mechanical Drawing,.' .j, Oblong Svo, Warren's Elements, of Machine Construction and Drawing.- Svo, * Waterbury's Vest Pocket Hand Book of Mathematics for Engineers. 2j X'sl inches, mor., Weisback's Kinematics and the Power of Transmission. * (Herrmann — Klein.) Svo, Machinery of Transmission and Governors. (Herrmaim — Klein.). .8vo, Wolff's Windmill as a Prime Mover , , .'Svo, Wood's Turbines Svo, MATERIALS OF ENGINEERING. * Bovey's Strength of Materials and Theory of Structures. Svo, Burr's Skisticity and Resistance of the MateriUs of Engineering Svo, Church's Mechanics of Engineering gvo, * Greene's Structural Mechanics .Svo, HoUey and Ladd's Analysis of Mixed Paints; Color Pigments, and Varnishes. Large i2'mo, Johnson's Materials of Construction '. . . Svo, ' Keep's Cast Iron 8vo, ' Lanza's Applied Mechanics. ;............,.,,-,. s..,. 3 oo 2 0» I 25 2 o» I oo- 2 so 5 oo 2 00 2 so I so 3 oo 5 oo 2 oo 4 oo 4 oo S oo 4 oo I so I so 3 so 12 so 3 oo 3 oo 2 oo 3 oo I so 3 oo 3 oo 3 oo 3 oo 3 oo I oo 3 oo I so 2 oo I 2S 7 so 1 oo S oo 5 oo 3 oo 2 so 7 so 7 SO 6 oo 2 so 2 so 6 00 2 so Kaire's Modern Pigments and their Vehicles izmo, 2 00 Uartens's Handbook on Testing Materials. (Henning.) 8vo, 7 50 JUaurer's Technical Mechanics 8vo, 4 00 Merriman's Mechanics of Materials 8vo, 5 00 * Strength of Materials i2nio, i, 00 Metcalf's Steel. A Manual for Steel-users i2mo, 2 00 Sabin's Industrial and Artistic Technology of Paints and Varnish 8tO, 3 00 Smith's Materials of Machines i2mo, i 00 Thurston's Materials of Engineering .3 vols., 8vo, 8 00 Fart I. Non-metallic Materials of Engineering, see Civil Engineering, sage 9. , Pai:t II. Iron and Steel v 8vo, 3 5B Part III. A Treatise on Brasses, Bronzes, and Other Alloyp. and their Constituents : Svo, X 50 Wood's (De V.) Elements of Analytical Mechanics. Svo, 3 00 Treatise on the Resistance of Materials and an Appendix on the Preservation of Timber .8vo, a 00 Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and Steel '. .8vo, 4 00 STEAM-ENGINES AND BOILERS. Berry's Temperature-entropy Diagram. izmo, i 25 Camot's Reflections on the Motive Power of Heat (Thurston.) i2mo, i 50 Chase'.s Art of Pattern Making i2mo, 2 50 Creighton's Steam-engine and other Heat-motors , Svo, 5 00 Dawson's "Engineering" and Electric Traction Pocket-book. ,. .i6mo, mor., 5 00 ford's Boiler Making for Boiler Makers .iSmo, i 00 Goss's Locomotive Performance .■ . , ; 8vo/ s 00 Hemenway's Indicator Practice and Steam-engine Economy. i2mo, 2 00 Hutton's Heat and Heat-engines :8vo, 5 00 Mechanical Engineering of Power Plants. n,, 8V0i 5 00 Kent's Steam boiler Economy. Svo, 4 00 Kneass's Practice and Theory of the Injector Svo, i 50 MacCord's Slide-valves Svo, 2 00 Meyer's Modern Locomotive Construction;. ■ . . . : .'. 4to, 10 oa Moyer's Steam Turbines. (Tn Press.) Peabody'S' Manual of the Steam-engine Indicator i2mo. x 50 Tables of the Properties of Saturated Steam and Other Vapors. .Svq, i oo Thermodynamics of the Steam-engine' and Other Heat-engines.. . .8vo, 5 00 Valve-gears for Steam-engines , ,. Svo, 250 .Peaibody and Miller's Steam-boilers .Svo, 4 00 Pray's Twenty Years with the Indicator Large Svo, 2 50 Pupin's Th^modynamics of Reversible Cycles in Gases and Saturated Vapors. (Osterberg.). .i2mo, i ag R.eagan'S Locomotives: Simple, Compound, and Electric, ^ew Edition. ' ; ' ,j. . Largp limo, 3,5? Sinclair's Locomotive Engine Running and Management.' .,...'..'..'... i2mp, 2 0.0 Smart's Handbook of Engineering Laboratory Practice ..'.i2mbi 2 50 Snow's Steam-boilei; Practice. . . . : .■ .................'.....;. .Svo, 3 oo Spangler's Notes on Thermodynamics .'..'....,: .i2mo, i.oo. Valve-gears. .Svo, 2 so Spaagler, Greene, and Marshall's Elements of Steam-engineering ■S'^°j 3 00 Thomas's Steam-turbines. ... 1 ......... . ... ...;.... ..v. .;'. . ....... .8v6, 4' 00 Thurston's Handbook of E^ngihe and Boiler Trials, and the XTse of ' thi Indi- cator and tSS Prony Brake ...:'...'.:....... .'. . '. . .'; ; . . .Svo, s 00 Handy Tables 8vo, i SQ Manual of Steam-boilers, their Designs, Construction, and Operation..8vo, 5 00 15 Xhureton's Manual of the Bteam-engine 2 vols., 8vo, 10 00 Part I. History, Structure, and Theory. — 8to, 6 00 . Part II. Design, Construction, and Operation. 8vo, 6 crnC Stationary Steam-engines 8vo, 2 .^(£ Steam-boiler Explosions in Theory and in Practice 12mo, i so Wehrenfenning'sAnalysisandSofteningof Boiler Feed-water (Patterson) 8to, 4 00 'Weisbach's Heat, Steam, and Steam-engines. (Du Bois..) 8vo, 5 00, Whitham's Steam-engine Design 8vo, s 00 Wood's Thermodynamics, Heat Motors, and Refrigerating Machines. . .Sto, 4 00 MECHANICS PURE AND APPLIED, Church's Mechanics of Engineering. 8vo, 6 00 Notes and Examples in Vedhanics 8vo, 2 00 Dana's Text-book of Elementary Mechanics for Colleges and Schools '. . I2mo, i 50 Du Bois's Elementary Principles of Mechanics: Vol. I. Kinematics Miro, 3 SS' Vol. II. Statics .8vo, 4 00 Mechanics of Engineering. Vol. I Small 4to, 7 ^0 Vol. II Small 4to, 10 00 * Greene's Structural Mechanics 8vo, z 50 ' James's Kinematics of a Point and the Rational Mechanics of a Particle. ' Large''12mo, 2 00 * Johnson's (W. W.) Theoretical Mechanics 12mo, 3. 00 Lanza's Applied Mechanics ;'. . ,8vo,' f W' * Martin's Text Book on Mechanics, Vol. I, Statics ./.IZmo, i 23' * V(d. 2, Kinematics and Kinetics . .I2ma, 1 50° Maurer's Technical Mechanics 8vo, 4 00 * Merriman's Elements of Mechanics 12mo, i 00 Mechanics of Materials 8vo, 'poo * Michie's Elements of Analytical Mechanics Svo, V 00 Robinson's Principles of Mechanism 8vo, 3 00 Sanborn's Mefchantcs Problems Large 12mo, i 50' Schwamb and Merrill's Elements of Mechanism 8to, 3 00 Wood's Elements of Analytical Mechanics 8vo, 3 00 Principles of Elementary Mechanics 12mo, i 25 MEDICAL. Abderhalden's Physiological Chemistry in Thirty Lectures. (Hall and Defren) (In Press). von Behring's Suppression of Tuberculosis. (Bolduan.) i2mo, i 00 * Bolduan's Immune Sera lamo, i so Dave'nport's Statistical Methods with Special Reference to Biological Varia- tions i6mo, mor., i 30 Ehrlich's Collected Studies on Immunity. (Bolduan.) .Svo, 6 00 * Fischer's Physiology of Alimentation Large i2mo, doth, 2 00 de Fursac's Manual of Psychiatry. (Rosanofi and Collins.) Large z2mo, ^ go Eammarsten's Text-book on Physiological Chemistry. (Mandel.). Svo, 4 00 Jackson's Directions for Laboratory Work in Physiological Chemistry . . .8vo, i 25, Lassar-Cohn's Practical Urinary Analysis. (Lorenz.) izmo i 00 Mandel's Hand Book for the Bio-Chemical Laboratory izmo, i so * Pauli's Physical Chemistry in the Service of Medicine. (Fischer.), .. .izmo, 1 25 * Pozzi-Escot's Toxins and Venoms and their Antibodies. (Cohn.) izmo, i 00 Rostoski's Serum Diagnosis. (Bolduan.) Izmo i 00 Ruddiman's Incompatibilities in Prescriptions " 8vo, 2 00 Whys in Pharmacy i2mo', i 00 Salkowski's Physiological and Pathological Chemistry. (Orndorfi.) Svo, 2 50 * Satterlee's Outlines of Human Embryology izmo, 1 25 Smith's Lecture Notes on Chemistry for Dental StiiHontc steel's Treatise on the Diseases of the Dog 8to, 3 so • Whipple's Typhoid Fever Large ismo, 3 00 WoodhuU's Notes on Military Hygiene i6mo, i so * Personal Hygiene izmo, t oq Worcester and Atkinson's Small Hospitals Establishment and Maintenance, and Suggestions for Hospital Architecture, with Flans for a Small Hospital i2mo, z 2S METALLURGY. Betts's Lead Refining by Electrolysis 8vo. 4 00 Bolland's Encyclopedia of Founding and Dictionaiy of Foundiy Tenns Used in the Practice of Moulding l2mo, 3 00 Iron Founder 12mo. 2 50 " " Supplement l2mo, 2 so Douglas's TTntectanical Addresses on Technical Subjects l2mo, i oo Goesfel's Minerals and Metals: A Reference Book i6mo, mor. 3 00 * Iles's Lead-smelting 12mo, 2 50 Keep's Cast Iron ,...,..,... 8vo, 2 so Le Chatelier's High-temperature Measurements. (Boudouard — Burgess.) 12mo, 3 00 Metcalf's SteeL A Manual for Steel-users. . , : : IZmo, 2 00 Miller's Cyanide Process 12mo i 00 Minet's Production of Aluminum and its Industrial Use. (Waldo.) 12mo, 2 50 Robine and Lenglen's Cyanide Industry. (Le Clerc.) 8vo, 4 00 Ruer's Elements of Metallography. (Mathewson). (In Press.) Smith's Materials of Machines r 12mo, i 00 Thurston's Material of Engineering. In Three Parts Bvo, 8 00 Fart I. Non-metallic Materials Of Engineering, see Civil Engineering, page 9. .. . , i«j Part n. IronandSteel. .,,;... ..,...8vo, 3 '^■ Part HI. A Treaitiise on Brasses, Bronzes, and Other Alloys and their Constituents 8vo, 2 50 Ulke's Modem Electrolytic Copper Refining , 8vo, 3 00 West's American Foundiy Practice i2mo, 2 so Mouldeis Text Book 12mo, 2 50 Wilson's Chlodnation Process 12mo, i 50 ' Cyanide Processes , 12mo, 1 So MINERALOGY. Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2 so Boyd's Resources of [Ssul|west Virginia. Svo 3 00 Boyd's Map of Southwest Virginia Pocket-book form. 2 00 ♦Browning'slntroduction to the Rarer Elements; 8vo, i 50 Brush's Manual of Determinative Mineralogy. (Penfield.) Svo, 4 00 Butler's Pocket Hand-Book of Minerals 16mo, mor. 3 00 Chester's Catalogue of Minerals 8va, paper, i 00 Cloth, I 2S Crane's Gold and Silver. (In Press.) Dana's First Appendix to Dana's New " System of Mineralogy. ." . . Large Svo, i 00 Manual of Mineralogy and Petrography. i2mo 2 00 4 f- lEmerals and How to Study Them i2mo, i so ' s Sy,mca of Mineralogy Large Svo, half leather, 12 so Text-book of'Mineralogy. 8vo, 4 00 Douglas's UntechnScal Addresses on Technical Subjects.' i2mo, i 00 Eakle's Mineral Tables Svo, i 2S Stone and Giay Froducts Used in Engineering. (In Pt^Baration). 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