NRLF r REESE LIBRARY OF THK UNIVERSITY OF CALIFORN _-n_jT_ji, IA. A SYSTEMATIC TREATISE ON ELECTRICAL MEASUREMENTS BY HERSCHEL C. PARKER, PH. B., Tutor in Physics, Columbia University. Instructor in Electrical Measurements Associate Member of the American institute of Electrical Engineers. NEW YORK: SPON & CHAMBERLAIN, 12 CORTLANDT ST- LONDON : E. & F. N. SPON, LIMITED, m STRAND. 1897, Entered according to Act of Congress in the year 1897 by HERSCHEL C. PARKER, PH. B. in the office of the Librarian of Congress at Washington. Press of Mcllroy & Emmet. 36 Cortlandt St., N. Y. NOTK The present Treatise on Electrical Measurements recently appeared as a series of articles in an electrical monthly and has been bound in book form with but very little revision. It should, therefore, not be judged as a finished work. The method of classification here made use of has been found very satisfactory in several courses of lectures given by the writer to students in Electrical Engineering at Columbia University. CONTENTS. CHAPTER I. PAGE CLASSIFICATION OF ELECTRICAL MEASUREMENTS 3 CHAPTER II. GALVANOMETERS 8 CHAPTER III. Low RESISTANCE 19 CHAPTER IV. THE WHEATSTONE BRIDGE 28 CHAPTER V. SPECIFIC RESISTANCE AND GALVANOMETER RESISTANCE 38 CHAPTER VI. COMPARISON OF STANDARDS AND CALIBRATION OF BRIDGE WIRE AND RHEOSTAT 41 CHAPTER VII. HIGH RESISTANCE , 46 CHAPTER VIII. INSULATION 49 CHAPTER IX. RESISTANCE OF TELEGRAPH LINES, CABLES, ETC 55 CHAPTER X. LOCALIZATION OF FAULTS 58 CHAPTER XI. RESISTANCE OF BATTERIES AND ELECTROLYTES 63 CHAPTER XII. INCANDESCENT LAMPS, DYNAMO RESISTANCE, ETC 68 yi CONTENTS. CHAPTER XIII. DETERMINATION OF THE OHM, CONSTRUCTION OF STANDARDS, ETC 70 CHAPTER XIV. MEASUREMENT OF E. M. F. OF BATTERIES AND DIRECT CURRENTS 73 CHAPTER XV. E. M. F. OF ALTERNATING CURRENTS, VERY HIGH E. M. F. AND VERY Low E. M. F 81 CHAPTER XVI. CALIBRATION OF VOLTMETERS, AND STANDARDS OF E. M. F. 86 CHAPTER XVII. MEASUREMENT OF CURRENT 89 CHAPTER- XVIII. MEASUREMENT OF ENERGY AND QUANTITY. TOO CHAPTER XIX. MEASUREMENT OF CAPACITY 103 CHAPTER XX. INDUCTANCE 108 CHAPTER XXL MEASUREMENTS OF EFFICIENCY 112 CHAPTER XXII. MAGNETIC DETERMINATIONS 114 INDEX.. u8 INTRODUCTION. AN ACCURATE knowledge of electrical measurement, to the electrical engineer as well as the physicist, is of the first importance. It is a branch of science where engineering and physics meet. There appears, however, in many instances, to be a lack of uniformity in the methods employed. Indeed, it almost seems as if there were two schools of electrical measurement. But this is probably due, to some extent at least, to the lack of a proper co-ordination and classification of the subject. New methods of practice have rapidly developed, and im- proved instruments are constantly coming into use, so that it is not strange if there be a little confusion. Thus we may find a text-book that is almost perfect as far as resistance work is concerned, but deficient with regard to E.M.F. or current, describing at length obsolete methods and entirely omitting many of the best ones. So that often the student may be compelled to consult a great number of standard works and supplement this by long personal observation to obtain even a fair comprehension of the practical methods. The subject, it seems to the writer, should be attacked in the most systematic manner and the classification thoroughly worked out. Indeed, classification and knowledge are very nearly synonymous terms. What follows is offered as an example of such a method of treatment. It seemed advisable to make the classification fairly complete^ and then to clearly point out the most desirable methods or those applicable to any particular case. Of course, there are many omissions and possibly errors ; but i 2 INTRODUCTION. it is hoped that it will facilitate the acquirement of a working knowledge of the subject by students of electrical engineering. In the text of the treatise, free use has been made of the standard works, especially " Kempe's Hand-book of Electrical Testing," but it is also believed that a considerable amount of new material is presented. CHAPTER I. CLASSIFICATION OF ELECTRICAL MEASUREMENTS Low RESISTANCE. RESISTANCE. 1. Thomson's Double Bridge.* 2. Differential Galvanometer.* 3. Projection of Potentials. 4. Fall of Potential. 5. Potentiometer. 6. Carev Foster's Method. WHEATSTONE BRIDGE. SPECIFIC RESISTANCE MEDIUM RESISTANCE. Wire Bridge.. (Variable Ratio ) f Straight (Metre). J Circular (Kohlrausch). j Parallel (Poggendorff). [Direct Reading (Kirchhoff). o/ -j r / ( Five Arc (Cushman).* Sltde Cotl \ Quadruplex(Muirhead) (Variable Ratio.) | Duplex (Varley). ( P. O. Bridge.* ." "1 Conductivity Balance. COMPARISON OF STANDARDS j Carey Foster's Method.* . ( Substitution in the Bridge. CALIBRATION... Bridge Wire . . . ( Comparison with Rheostat (Po- tentiometer Method.) * -| Carey Foster's Method. | Double bridge. I Differential Galvanometer. Rheostat ] Substitution in the Bridge. GALVANOMETER RESISTANCE. P. O. Bridge.* Thomson's Method. y>> Deflection. HIGH RESISTANCE. Slide Coil Bridge.* Potentiometer Method. Deflection Method.* Loss of Charge. 3 INSULATION. ELECTRICAL MEASUREMENTS. i. Insulite." Specific Insulation." Short Lengths. ft 2. Insulated Wires. \ 3. Aerial Wires. r , , ( Single Core. ^ aDie> ( Multiple Core. j Loss of charge.* Joint Testing. \ Accumulation. ( Electrometer. RESISTANCE OF TELEGRAPH LINES, CABLES, ETC. LOCALIZATION OK FAULTS. 1. P.O. Bridge. 2. Loop Test | 3. Equilibrium. 4. Mance's Method. 5. Equal Deflection. 1. Complete Fault in Insulation. 2. Partial " " (Earth Resistance.) 3. Variable " " " (Polarization or Ca- ble Current.) 4. Fault plus E. M. F. (Earth Current.) 5. Fault in Conductor. 6. Faults of High Resistance. BATTERY RESIS- TANCE. RESISTANCE OF ELECTROLYTES. , Fall of Poten. ( ^ ttal * j Volt { 2. Added tance Resis- Voltmeter.* Tangent Galvanometer. *A Deflection. 3. Mance's Method. 4. Current and E. M. F* ( Constant Current. \ Alternating Current* INCANDESCENT LAMPS, " DYNAMO RESISTANCE," ETC. Fall of Potential. Current and E. M. F. Ohmmeter. DETERMINATION OF THE OHM. ELECTROMOTIVE FORCE. BATTERIES AND DIRECT CURRENTS. Resistance \ '* i Deflection and Resistance. Deflection. Resistance. Wheatstone's Method. Lums den's Condenser " * Potentiometer. * ... Five Arc (Cushman.) 8uadruplex (Muirhead.) uplex (Varley.) Current and Resistance. Electrometer. Voltmeter* CLASSIFICATION. ALTERNATING CURRENTS. Quadrant. , Multicellular.* Electrometer \ Electrostatic Volt- j Thomson's. meter.*/ Weston's. Low Reading. i Siemens' Weston's* (Alternating Current Voltmeter.) Caloric Voltmeter (Cardew's.)* Attraction Volt- j Evershed's. meters 1 Magnetic Vane, etc. ( Electrostatic Voltmeter. VERY HIGH E. M F. \ Absolute Electrometer. ( Striking Distance of Spark. ( Galvanometer* VERY Low E. M. F. \ Voltmeter* ( Capillary Electrometer (Lippmann's.) STANDARDS OF E .{ ? M F I Checking by Current and Resistance. CURRENT. DIRECT CURRENTS. * ** B j v* ( Di ,. M. P. and Ke- J Di stance .......... j Bri E. sistance Direct Method. Differential Method (Cardew's.) Bridge Method (Kempe's.) D n *,J r?,e,-c P. D. and Rests- tance .......... Direct Deflection Method. Equilibrium Method. potentiometer " Voltmeter "* Galvanometer "* Tangent Galvanometer. Ammeter.* f D C Dy Cu namometer. urrent Balance (Thomson's.) ALTERNATING^ ^ Attraction Am- ( Ever shed's, Schuckert's, etc. I meters ( \ Calorimetrtc Methods. CALIBRATION OF AMMETERS. ABSOLUTE DETERMINATION (Tangent Galvanometer.) ELECTRICAL MEASUREMENTS. Voltmeter and Ammeter. ( QUANTITY. ( Voltameter, r .. -J "Meters" ( Ballistic Ga Galvanometer. CAPACITY. Direct Deflect ton* Divided Charge M.... ABSOLUTE DETERMINATION (Ballistic Galvanometer.) INDUCTANCE. BRIDGE METHOD (Maxwell's.) SECOHMMETER j With Standard. METHOD. \ Withou' 4 ' CONDENSER j Deflection. METHOD. \ Zero. CALCULATION. [IMPEDANCE.] f Cells. \ Lamps. EFFICIENCY ^ Motors. Transformers. [ Dynamos. Field (OC) Intensity of Magnetization / & \ Permeability (p -- 1 MAGNETIC . \ 3C/ DETERMINATIONS, j / 3 \ Susceptibility Ir^j VJC/ I Hysteresis. \ Magneto-Motive Force. ^ Reluctance. CLASSIFICATION. 7 REMARKS. In the above classification it is not attempted to give the vari- ous methods in the order of their relative merit, but rather ac- cording to their logical sequence. What are believed to be the superior methods, or those especi- ally applicable in any given case, are indicated by stars. In the classification of resistance measurements it was thought advisable to give the different forms of the Wheatstone Bridge. It also seemed best to classify the different cases of " Insula- tion " and those that might occur in the " Localization of Faults." The determination of " Energy " and of u Quantity " so closely approximates the measurement of current that they appear to belong as sub-headings under that subject. " Impedance " is given as a special application of the meas- urement of " Inductance." Under " Efficiency " are given several special cases. To complete the subject, a number of Magnetic Determina- tions are added, for there certainly should be no fixed line drawn between electrical and magnetic measurements, considering the present state of electrical science. CHAPTER II. GALVANOMETERS. Tangent. Astatic. j Single Coil. MOVABLE MAGNET- J Thomson -j Duplex. ic SYSTEM. ] ( Quadruplex. Aperiodic. Differential. Ballistic. <\ Weston Pattern (Portable ) MOVABLE COIL Ayrton &* j Aperiodic. Mather Pattern.. \ Ballistic. Rowland ~~~** Electro-Magnet Pattern. GENERAL. Figure of Merit. By the "Figure of Merit" is meant the strength of current required to produce a deflection of one scale division, or the resistance that must be introduced into the cir- cuit to reduce the deflection to one scale division with a p. D. of one volt. All the conditions should be specified, such as the distance of the scale from the galvanometer, width of scale divisions * and time of vibration of galvanometer. ( Deflection = 250 scale divisions (joV^r shunt.) Example : < P. D. = 2.5 volts. ( Resistance = 100,000 ohms. Figure of Merit = I00>000 ^o x r>000 = ' X io- amperes. or i X i o 10 ohms, that is .0001 micro-amperes, qr 10,000 meg- ohms. Sensitiveness. This term may be employed to indicate the P. D. across the galvanometer terminals necessary to give a deflection of one scale division. Since E = C R, it may be obtained by * Unless otherwise specified it is assumed that a mm. scale is used at the distance of a metre from the galvanometer mirror. GALVANOMETERS. $ multiplying the figure of merit by the resistance of the galvan- ometer. Thus, if the galvanometer in the above example had a resist- ance of 10,000 ohms, its " Sensitiveness " would be .0001 micro- ampere X 10,000 = i micro- volt. In the measurement of low resistance it is, of course, desirable to have a galvanometer of the maximum " efficiency." Usually, galvanometers of low resistance have a greater efficiency than those of high resistance, but the figure of merit increases with the number of turns, and consequently high resistance galvan- ometers have a greater figure of merit. In the measurement of high resistance and insulation the galvanometer resistance has but little effect on the current, and hence it is best to employ a galvanometer with the maximum figure of merit. Shunts. In order to vary the sensitiveness of galvanometers, a portion of the current is deflected by a resistance in parallel with the galvanometer. The value of this shunt is given by the formula : e _ i O Lr X n i, where S = resistance of shunt, G = resistance of galvanometer, and 1 = the portion of the current received by the galvanome- n ter, (that is, the amount the galvanometer deflection is reduced to, where such deflection is proportional to the current.) Example : in.i = 1000 X 10 i In this case the resistance of a one-tenth shunt for a 1000 ohm galvanometer must be in.i ohms. When the resistance in the main circuit is comparatively low, the use of a shunt reduces the resistance of the entire circuit an appreciable amount and introduces a certain error in the meas- urement unless a compensating resistance is added. The formula cl ^ n i o (JT X gives the value of this resistance. In the above example it would be ooo ohms / f 10 (9 = '> co x -F Errors. With a reflecting galvanometer and a tangent scale, the beam of light is deflected through twice the angle that the mirror is turned. In an observation where two deflections are taken, the error in assuming that the ratio of the tangents of twice the angles is the same as the ratio of the tangents of the angles may amount to one per cent, or over where the ratio is greater than six to one. to ELECTRICAL MEASUREMENTS. The formula for the induction is : --/): c, : c z :: d, (V/ 8 + tf /) : 4 (V** + 4 where d^ d%, represent the two deflections; c ly c z , the ratios of the two currents, and /, the distance from the scale to the mirror in scale divisions. The error of observation where two deflections are taken, is increased the more widely the deflections differ. The formula is: T = X ioo m X (i +) T = percentage error of the determination, = error of observ- m ation in scale divisions, d = first deflection, n = ratio of first deflection to the second. Example : 250 From the above considerations and also on account of possible variations in the E. M. F. during experiment, it is apparent that zero methods are preferable. When deflection methods are employed it is often practicable to so vary the P. D. that the two deflections may be nearly equal. The ratio of the differences of potential is then used in the calculation. Angle of maximum sensitiveness. Where the strength of current and consequently the deflections are proportional to the tangents of the angles, the galvanometer has the greatest sensitiveness when the needle makes an angle of 45 with the coil. With a reflecting galvanometer, the angle of maximum sensitiveness is the largest angle that can be obtained, since the angle of deflec- tion is but a very few degrees and, therefore, the true maxknum angle can never be obtained. TANGENT GALVANOMETER. In this form of galvano- meter, a short magnetic needle is centrally placed within a coil of wire of large radius as shown in Fig. i. The needle may carry a pointer moving over a graduated circle, or the deflections can be read by means of a mirror and tele- scope and scale, or lamp and scale. FIG - * If the influence of the coil GALVANOMETERS. ii * C on the needle is the same whatever angle the needle makes with it, then the strength of the current circulating in the coil is di- rectly proportional to the tangent of the angle of deflection. Theoretically, to obtain this result, the magnet should be a mere point, but practically it is sufficient for the coil to be about ten times as large in diameter as the length of the needle. This instrument furnishes a most convenient means for the comparison of current strengths, and is of the greatest interest on account of its employment in the absolute measurement of cur- rent and consequently in the absolute determination of the ohm. The perfection of the ammeter, however, and the accuracy and facility with which current may be measured by determin- ing the P. D. across a shunt, render the tangent galvanometer of far less importance than formerly to the electrical engineer. ASTATIC GALVANOMETER. This instrument is of very simple construction and is quite sensitive. It is especially adapted for use with zero methods or may be employed as a sine galvanometer. It consists of an astatic pair of needles of any convenient length suspended by a fibre arranged as in Fig. 2 ; one needle turns within the coil while the other moves above it. If the coil is made to rotate and the angle of rotation meas- ured, then when a current is sent through the galvanometer if the coil be turned until it is parallel with the needles, that is, if the needles are again brought to zero, the current is propor- tional to the sine of the angle of rotation. This is independent of the size or shape of the coil or the length of the needles. THOMSON GALVANOMETER. The limits in the range of electrical measurement are usually fixed by the sensitiveness of the galvanometer. The highest figure of merit, and perhaps the greatest effi- ciency may be obtained with the Thomson galvanometer. The magnetic system is astatic and is formed of a number of small light magnets, usually pieces of watch-spring. One set of these magnets is attached to the back of a small mirror, while another set is fixed to a light aluminium vane (Fig. 3) ^/VVW I ' VWW FIG. 2. 12 ELECTRICAL MEASUREMENTS. The upper set of magnets moves in the 'centre of a large coil of wire of many turns, while the lower set is beneath the coil. This coil consists of two portions, and is hinged so that it may easily be opened and the magnetic system put in place. The high resistance galvanometers are usually furnished with two coils, and the more recent instruments with four coils. There is, of course, a set of magnets for each coil, and by this means the magnetic moment and number of turns may be greatly multiplied. (Fig. 4.) The entire magnetic system is suspended by means of the very finest fibre, either of silk or quartz. The galvanometer is also FIG. 3. % FIG. 4. provided with a field magnet. This magnet is used to neutral- ize the earth's field, and, being nearer the upper set of magnets than the others, it also acts as a directing or controlling magnet. The needles being very small, and each set being placed in GALVANOMETERS. 13 the axis of a large coil of wire which completely surrounds it, the tangents of the deflections are approximately directly pro- portional .to the strength of the currents producing them. Since the deflections are read by means of a reflected beam of light, the angle through which this beam of light turns will be twice the angle through which the mirror turns, and, conse- quently, the deflections will be proportional to the tangents of twice the angles. If, however, the deflections to be compared are both small, or if they do not differ greatly, these deflections may be taken as proportional to currents producing them. Considerable care is required in setting up the galvanometer. FIG. 5. FIG. 6. A position should be selected as free from vibrations and mag- netic disturbances as possible, and all torsion should be carefully removed from the fibre. The magnetic system is usually not quite astatic, and if the field magnet is removed, will set in the magnetic meridian. The field magnet should then be lowered until it just neutral- izes the earth's field. This is shown by the magnetic system being in unstable equilibrium. The control magnet is then raised slightly above this position. Two control magnets are sometimes employed to render the field more uniform. i 4 ELECTRICAL MEASUREMENTS. The scale should be placed parallel to the mirror. The high resistance galvanometers are wound with a resist- ance varying from 3,500 ohms to 100,000 ohms, and as great a figure of merit as 100,000 meg-ohms may be obtained. This form of instrument is extremely useful in insulation work. The low resistance galvanometers are extraordinarily sensitive but are also very easily affected by thermal currents, so that it is sometimes found advisable to use some form of D'Arsonval galvanometer for low resistance determinations. FIG. 7. APERIODIC GALVANOMETER. In this galvanometer a large bell magnet is employed. This magnet is enclosed between massive plates of copper, and hence when set in motion it induces powerful Foucault currents in the copper which quickly bring the magnet to rest. (Figs. 5 and 6.) Moreover, slight changes in the surrounding magnetic field seem to produce but little effect on this form of galvanometer, and a rather high figure of merit may easily be obtained even where no great care has been exercised in its construction. GALVANOMETERS. 15 DIFFERENTIAL GALVANOMETER. A galvanometer may be made differential by winding two wires on the same coil or by the use of two coils, and then send- ing the current through in opposite directions. It is adjusted by sending the same current through each coil and adding re- sistance to one of the coils until no deflection is produced. Where two coils are employed, a rough adjustment may be made by moving one of the coils. It is always better, however, to make the final adjustment by the addition of resistance. The coils of a Thomson galvanometer may be connected dif- ferentially. The differential galvanometer is useful in the measurement of low resistance. BALLISTIC GALVANOMETER. For certain determinations a galvanometer with a long period of vibration, a large moment of inertia, and with but very little decrement is required. One of the standard forms of this instrument is shown in the diagram. (Fig. 7.) Four bell magnets are employed, a coil of high resistance, a control magnet and a directing magnet. It is desired to give the moving magnetic system considerable weight and yet have the air resistance as little as possible. The mirror used should be very small, and the suspending fibre extremely fine and without torsion. This form of galvanometer is exceedingly sensitive to vibra- brations and changes in the magnetic field. The deflections are controlled by means of a check coil placed near the instrument. THE D'ARSONVAL GALVANOMETER. The radical difference between this form of galvanometer and those previously described, is that here the coil is movable and the magnets are fixed as shown in Fig. 8. A very intense field is obtained by the combination of several horse-shoe magnets having a soft iron core or a compound magnet placed between their poles. In this space moves the rectangular coil wound on a thin cop- per or silver frame. The Foucault currents induced in this frame render the galvanometer almost aperiodic. The resisting force is the torsion of the suspending wires. Consequently, assuming the field to be uniform, the currents flowing through the coil are directly proportional to the angular deflection. 16 ELECTRICAL MEASUREMENTS. WA/VW Hence, for accurate work in deflection methods, a circular scale should be employed or the tangential deflections reduced to the corresponding 1 angles. ' On account of the great strength of field, this galvanom- eter is scarcely effected by con- siderable magnetic changes, even in its immediate vicinity. The coil is usually wound to about 100 ohms, but a higher resistance may be used when desired. The figure of merit that may be obtained, expressed in megohms, is usually some- what less than the galvanometer resistance in ohms. For nearly the whole range of electrical measurement, this gal- vanometer is probably the most satisfactory one that can be em- ployed. When the metallic frame is not used, the decrement be- comes very small ; and since the weight of the coil is consider- able, the moment of inertia is large. That is, the conditions of a ballistic galvanometer are ful- filled. The moment of inertia may be still further increased by adding a weight to the coil. The coil may be brought to rest by means of a short circuiting key. Westcn Pattern. If the coil, instead of being suspended by a wire turns in jeweled bearings, the current being lead in by delicate watch-springs (Fig. 9) ; and if the horse-shoe magnet or magnets be placed horizontally, the coil having an oblique posi- tion between the poles, the gal- FIG. 9. GALVANOMETERS. 17 vanometer is then of the Weston pattern. This form of instru- ment is generally used in combination with a low shunt resistance or a high series resistance and then constitutes the well-known Weston ammeter or Weston voltmeter. Without these auxiliary resistances, however, it is one of the very best forms of D' Arson val galvanometer. The sensitiveness is almost as great, while it is far more compact and portable than the ordinary /wvv h FIG. IO. galvanometer. Besides this, the angular deflections are accur- ately proportional to the currents producing them. Ayrton and Mather. In this form of galvanometer (Fig. 10) a large number of circular magnets are placed horizontally, the poles being brought very near together. In this small space is suspended a long- narrow coil. The coil carries alight metallic i8 ELECTRICAL MEASUREMENTS. sheath where aperiodicity is desired, but is without the sheath when used ballistically. The coil may be wound to as high a resistance as 4,000 ohms, and a figure of merit of over i,coo meg-ohms may be obtained. This is probably the best form of ballistic galvanometer and may also be employed in ordinary insulation work. Rowland. The Rowland D' Arson val galvanometer has an el- liptically shaped permanent magnet enclosed between two faces of sheet brass, thus forming a closed space in which the coil swings. The coil is provided with a large mica vane for damp- ening its vibrations. The pole faces of the magnet are so shaped that the deflec- tions, as read with a telescope or lamp and scale, are said to be exactly proportional to the current passing. The coil may be given a resistance of 1,500 ohms and a figure of merit of 500 meg-ohms obtained. Electro- Magnet Pattern. The strength of field, and conse- quently the sensitiveness of the galvanometer may be increased by the use of electro-magnets. This, however, is only necessary in special cases of research work. Conclusions. From the above considerations it is evident that the Thomson galvanometer, having the highest figure of merit and the greatest sensitiveness is the most desirable for either very high or very low resistance determinations. In certain cases of low resistance work, however, on account of thermal currents, a D'Arsonval galvanometer may prove preferable. For all or- dinary measurements a D'Arsonval galvanometer is recom- mended. For the determination of high insulation it is best to employ a Thomson high resistance galvanometer. CHAPTER III. Low RESISTANCE. f Thomson's Double Bridge * Differential Galvanometer* \ Projection of Potentials. j Fall of Potential. \ Potentiometer [ Carey Foster's Method. Low resistance is, of course, a relative term ; but it is here used to indicate resistances too small to be accurately determined by the ordinary Wheatstone bridge methods. For most re- sistance measurements, an accuracy of about one per cent, is desirable. That is, if .01 ohm is to be measiired, it requires the determination to be made to .0001 ohm. But contact resistances are an unknown variable, and may easily introduce an error as great as the last named figure. Since the effect of these contact resistances can never be en- tirely eliminated with the Wheatstone Bridge, the upper limit of low resistance may be placed at about .01 ohm. It is true that there is a form of Wheatstone Bridge that reads to .00000 1 ohm, but measuring to a millionth of an ohm and reading to a millionth of an ohm are very different affairs. In most of the special methods described, the effect of contact resistance is practically eliminated. It should also be understood that when a measurement is made to, say, i x io~ 7 ohm, the entire resistance is not much more than i x io~* ohm. For it is hardly possible in low re- sistance work to measure better than . i per cent, under the most favorable conditions, on account of temperature coefficients and thermal effects. The measurement of such extremely low resistances is made E> possible by Ohm's law, C = - . R One of the limiting conditions is the sensitiveness of the galvanometer, and the galvanometer deflections are approxim- ately proportional to the current. The current, however, is in- versely proportional to the resistance. Hence, the lower the resistance, the greater the current for 20 ELECTRICAL MEASUREMENTS. any given p. D. That is, the smaller the resistance in circuit, the lower the limit of the measurement becomes. But, of course, there is a constant and limiting resistance due to the battery, conducting- wires, etc., no matter how small the resistance to be measured is. The case very roughly approximates that of a balance whose sensitiveness varies inversely as the weights to be determined. Thomson's Double Bridge. This is one of the most satisfactory and convenient methods for the measurement of low resistance. The arrangement of the experiment is shown by the diagram, Fig. ii. If the ratio coils A, A', are each made equal to 100 ohms, and the coils B, B', each equal to 10 ohms, then when R : x :: 100 : 10 FIG. II. there will be no deflection of the galvanometer on closing the circuit. R is the known variable resistance and x is the resistance to be determined. The principle is as follows : If there be no junction between R and x, that is, if r = a , and then if R and x are zero, we have the ordinary case of the Wheatstone Bridge, 100 : 10 :: ico : 10, and the potential at g, g', will be the same. If x is given a value, and R is changed until equal to 10 x, we have: . ioo : 10 :: ,00 + 10 x : 10 + x, or 2? = I0 (' + x ) = 5, 10 10 -f- X I which is again the condition of equal potential at^-and^'. That is, ioo : jo ;; R : x, when the galvanometer shows no deflection LOW RESISTANCE. 21 If now R and x be joined by any resistance r, if R be zero, we have : R I OO IO -_ = = , or ioo : 10 :: R : x. x 10 i But zero and oc are the limiting values for small R ; hence whatever the resistance of r, it does not effect the potential at g, g'. That is, it simply shunts off a portion of the current, leaving the potential at g, g' still the same. The resistance of the movable contacts a, a' , and /, b' t together with the wires leading to them, is added to that of the ratio coils. Hence the resistance of these coils should be so great that the above mentioned resistance may be negligible compared to them. The smaller coils ought not to be less than 10 ohms. FIG. 12. The contact points a y a\ and b, b\ must occupy the same rela- tive positions as shown in the diagram. If, for instance, they should be placed in the positions a, a', b' , b, it would be impos- sible to obtain a balance. Again, on first setting up the experiment, the terminals a, a\ should be joined to one point in the circuit, and the terminals b, b\ to some other point in the circuit. Then if, on closing the key, there is any deflection, a compensating resistance should be added to one of the coils until there is no deflection. Special coils may be used for the ratios, or a p. o. bridge and rheostat can be employed according to Fig. 12, A portable form of Thomson's bridge is manufactured by Siemens & Halske. The standard low resistance is a thick wire, 22 ELECTRICAL MEASUREMENTS. stretched around the instrument, and a movable contact is ar- ranged so as to include more or less of the wire. Peg resistances are arranged so that the resistance can be multiplied or divided, so that the range of the instrument is very large. A good method of procedure is the following : A metre of G. s. wire of about o. i ohm resistance is accurately measured on the P. o. bridge, and its resistance per mm. calculated. The wire is then stretched over a metre stick, and used as the known resistance in the double bridge to determine the resistance of a second metre of copper wire. This last wire is employed to measure the resistance of a still larger copper wire. FIG. 13. We then have three standard wires and make use of either one or the other, according to how low the resistance is that must be determined. The arrangement is best shown by the diagram. It is evident that the measurement is only limited by the sensitiveness of the galvanometer and the strength of current that may be employed. A D'Arsonval galvanometer or a Thomson high resistance galvanometer should be used. The Thomson low resistance galvanometer is too strongly effected by thermal currents, although it is far more sensitive. LOW RESISTANCE. 23 Using a copper wire with a resistance of about .000002 ohm per mm., two " Samson " cells in parallel, and a D'Arsonval galvanometer with a "sensitiveness " of only about 50 micro- volts, it is possible (if a telescope and scale be used to observe the galvanometer deflections) to make measurements to about .000001 ohm. Now it is easy to obtain galvanometers with a sensitiveness of i micro-volt, and twice the current strength may well be em- ployed. The measurement could then be made to .0000000 r ohm. That is, a millionth of an ohm may be measured with an accuracy of one per cent. We may place the limit of what seems at present the lowest FIG. 14. possible resistance measurement at about .ooocooooi ohm, or the one billionth of an ohm. Differential Galvanometer. A very similar method to the one just described is that where a differential galvanometer is em- ployed. In this case, it is possible that even considerably lower resistances may be determined than with Thomson's double bridge ; but a special form of galvanometer is required. If the coils d, d ', Fig. 14, have an equal and opposite effect on the galvanometer needle, then when the p. D. between a, a\ equals that between b, b' , there will be no deflection, and the resistance of R will equal x. R is a standard wire or bar with adjustable contacts a, a'. The resistance per scale division is accurately determined by the step-down method given for the double bridge. 24 ELECTRICAL MEASUREMENTS. When it is desired to have the ratio of R to x as 10 : i, a re- sistance, r, is added to the coil, such that r + d 10 d' y then there must be ten times the p. D. between a, a', that there is between b, b\ before the current through the coil VyAA^^ FIG. 25. indefinitely in either direction. The following conditions should be observed : The entire resistance of the last series of coils must be equal to the resistance of two coils in the preceeding series. If there be 10 coils in the last series, the others must contain n coils, or if 100, then 101, etc. The resistance of the coils in the last series should not be so low that they cannot be accurately adjusted. The principle may be shown by referring to Fig. 26. Since the P. D. is proportional to the resistance, the p. D. from A to B is the same as that across 10 ohms. Consequently the p. D. across FIG. 26. 20 ohms in either of the parallel branches i& the same as that across 10 ohms in the direct circuit. Therefore the p. D. across 2 ohms in one of the parallels is -fa the p. D. across 10 ohrhs in the direct circuit. Probably the best known form of slide coil bridge is the WHEATSTONE BRIDGE. 33 Thomson -Varley instrument. This employs 101 coils of 1,000 ohms, and 100 coils of 20 ohms, Fig 1 . 27. JOOO Ohms E.OLCK FIG. 27. 1.0 OKmt LacK. The entire resistance is 100,000 ohms, and it gives readings to ' rhr* or - 0001 - The coils are arranged in two dials. The Muirhead pattern has four series of coils, 3 of IT each and i of i o coils ; the coils are arranged in dials. The reading is : -fa X iV X jV X -j 1 ^, or YTJ" ooo* 10,000 ohm bridge is employed, the following would be the values of the resistances in the different series : First. 1,000 ohms (n coils). Second. 200 " " Third. 40 " Fourth. 8 " (10 coils). The Cushman five arc instru- ment, Fig. 28, possesses many ad- vantages. It employs : IT coils of 10,000 ohms each. II " " 2,000 " " ii " " 400 " " n " 80 " " 10 " " 16 " " The entire resistance is 100,000 ohms, while readings may be ob- tained to ^V X A X iV X A X A* <> r FIG. 28. By this means the range of the bridge is increased TO times 34 ELECTRICAL MEASUREMENTS. over that of the Varley Bridge, and but 54 coils are used instead of 201. With this instrument, resistances whose ratio is as great as ioco : i may be compared with an accuracy of about one per cent. When the resistances are equal^ of course, they may be compared to .002 per cent; but errors due to temperature co- efficients, contacts, adjustment of the coils, etc., would probably be much greater than this. Each series of coils is provided with binding posts, so that any of the higher series may be left out when a lower resistance bridge is desired. For quick work, the settings of the lower series may be omitted. The arrangement of the coils in arcs gives great ease and rapidity of adjustment. 000 100 100 1000 B I Z 3 * 5 5000 1000 1000 (000 FIG. 29. The slide coil bridges described above are generally known as " potentiometers " on account of their employment in the com- parison of potential differences. For most resistance work, the constant ratio form of Wheat- stone bridge is to be recommended. The two patterns of the P. O. bridge are shown in diagrams 29 and 30. A and B may be given several different values, such as 1000 : 10 etc. R can be adjusted from one ohm to 10,000 ohms. Resis- tances are inserted by, removing pegs. The ratio of A to B is determined by the resistance to be meas- ured. If x is very low, A should be as great a's possible and B as small as possible, thus : 1000 : 10 : : R : x. For higher resistances A and B should not be made so unequal that a change of one unit in the adjustment of R will not be shown by the galvanometer, WHEATSTONE BRIDGE. 35 If the galvanometer does not show a change of several units in R, A must be made equal to B and as nearly equal to x as pos- sible. Thus, suppose x is about 1,000 ohms, then we may have 1,000 : 1,000 : : R : x. If x be very great, say about 1,000,000 ohms, then we must have 10 : 1,000 : : R : x. Thus the range of these bridges is from .01 ohm to 1,000,000 ohms, though, of course, it may be increased by the use of addi- tional resistance coils in A and B or R. For accurate work in the measurement of low resistance, such as the determination of specific resistance, special manipulation is required. To the binding posts 1 1' Fig. 30, clips are added and the ends of the bridge are thus brought near together. The circuit is then FIG. 30. closed by inserting a wide, thick piece of copper between the clips. The oc peg is then removed and a piece of fine copper wire is joined to the posts s s'. The ratio of A to B is made i, coo : 10. The length of the auxiliary wire is then adjusted until there is no deflection on closing the circuit. The resistance of this wire compensates for the resistance of the peg row, contacts, clips etc. The copper plate between the clips is then removed and the resistance to be measured is joined to the clips. With a sensitive reflecting galvanometer, resistances far be- low .01 ohm may be determined by interpolation. The operation is as follows : Suppose, when R = 4 ohms, a deflection of 250 scale divisions to the left is obtained, and when 36 ELECTRICAL MEASUREMENTS. R = 5 ohms, a deflection of 150 divisions to the right is obtained. Then the exact value of R is 4} ohms = 4.625 ohms, and 1000 : 10 : : 4.265 : x, or x = .0427 ohm. At the beginning of the measurement, the galvanometer key k' should be closed ; if there is a deflection it is due to thermal currents. The battery key k is then closed, leaving the key k' open ; if there is a deflection, it is due to induction. These effects should be corrected for. Generally, it is better to connect the battery to the posts / , as indicated in Fig. 30. If the battery had a low internal re- sistance and were joined to the posts /' k', in the case where the compensating resistance is being adjusted or where x is a very r- -A- -B- i or S = R 2 r - If the battery resistance is appreciable compared to the gal- vanometer resistance, a correction should be made. A modification of this method would be to shunt the battery until the desired deflection is obtained, and then add a resistance R, such that the deflection is one-half. Then, g = R. CHAPTER VI. j Comparison of Standards. \ Calibration of Bridge Wire and Rheostat. In the comparison of standard ohms, an accuracy of from .01 per cent, to .coi per cent, is desirable. This means that the de- termination must be made to within at least .cooi ohm. Some special method must, therefore, be employed. The best is Carey Foster's Method. In the diagram, Fig. 34, A, B, is a large German silver wire whose resistance per metre has been accurately measured, and from this the resistance per mm. calculated before placing the wire in position on the bridge. R, R', should be approximately one ohm each. They are known as the ratio coils, s, s', are the stand- ard ohms to be compared. They are placed in water baths, and contact is made with the bridge by means of mercury cups. The galvanometer slider is adjusted on the wire A, B, until there is no deflection. The positions of s, s', are then reversed and a balance again obtained. The length of wire, r, included between the two po- sitions of the galvanometer slider is equal to the difference in resistance between s, and s'. The slider is moved toward the greater resistance. Example : Resistance of A, B, per mm. = .00005 ohm, r = 3 mm., slider moved toward s'. Then s' is greater than s by .00015 ohm or .015 per cent. The standards should be placed in the water baths a consid- erable time before commencing the measurement, and the tem- perature during the determination carefully noted. Several observations should be taken, and after some time another set obtained. If these last differ materially from the first, it is probably due to the standards not having arrived at a constant temperature. The temperature coefficient of the wire composing standard ohms may betaken at about .02 per cent, to .04 per cent, per degree C., so that a difference of ^ C. would have accounted for the difference of resistance in the above example. At the beginning of the measurement the galvanometer key 4 1 42 ELECTRICAL MEASUREMENTS. should be closed, the battery key remaining open. If there be a deflection caused by thermal currents, it is p'robably due to the ends of the bridge being at different temperatures. It is, therefore, well to cover the bridge ends with cotton or some other non-conducting material, if the apparatus is not used in a room of constant temperature. It should also be noted if there is any effect due to induction. This is observed by closing the battery key, leaving the galvan- ometer key open. Where great accuracy is required, the utmost care must be exercised throughout the determination. A special form of bridge, such as the Jenkin's bridge, is usu- ally employed. The instrument is extremely compact. A short standard wire is used, and copper blocks with mercury cups and commutator so arranged that the standard ohms to be compared - n\ a IOOOI.K 10 o OIK O_L 3 Ol S IO A. i . i iliii.it i 1 _i iS i i i B FIG. 34. may be placed very near together and their positions reversed by means of the commutator. The ratio resistances are wound on the same bobbin and thus identity of temperature is in- sured. Another method by which resistances may be compared with considerable accuracy is by " substitution in the bridge." In Fig. 35, A, B, is a German silver wire, preferably of about three or four ohms resistance. R is an auxiliary rheostat, i, an interpolation resistance that may be made .001, .01 or .1 ohm, and s, s\ the resistances to be compared. At the commencement of the de- termination, s and i are short-circuited, the one ohm peg is re- moved in the rheostat, R, and a balance against the standard resistance, s', is obtained by moving the galvanometer slider, g', until there is no deflection. An interpolation resistance of, say .001 ohm is then added and COMPARISON OF STANDARDS. 43 the galvanometer deflection observed. This resistance is then short-circuited and another observation made to see if the bal- ance remains unchanged. For interpolation, it is convenient to I 7T71 Ol R 10 C I IO O Ol 8 IO O Ol S a= ^ O - ^^ f ^ L I y _. *7k j i FIG. 35. have an interpolation box, and add the resistances by removing 1 pegs. If the balance is still perfect, s' is shunted by the short-circuit piece c', and the resistance, s, to be compared is shown in cir- cuit. The galvanometer deflection is then read and the differ- ence in resistance calculated. Example : Interpolation resistance = .001 ohm ; deflection = 1 60 (to the right) ; deflection when s is substituted for s' = 40 (to the left) ; then s is less than s' by T y^ of .001 ohm or .00025 ohm. The same precautions with regard to thermal currents, etc., should be taken as in the first method. For the comparison of standard ohms the Carey Foster me- thod should be employed ; but where the resistances in a rheo- stat are to be checked against a standard resistance, the method just described is particularly applicable. Calibration of a Bridge Wire. The most direct and convenient manner of checking a bridge wire is to determine the lengths of wire that corres- pond to the ratio of known resistances. Suppose R, R', Fig. 36, to be two rheostats each adjustable from 1,000 to 10,000 ohms. If it be desired to step off the bridge wire A, B, into 10 parts of equal resistance, R is first FIG. 36, 44 ELECTRICAL MEASUREMENTS. made i,oco ohms and R' 9,000 ohms, and g' adjusted to no de- flection. This point gives the first tenth. R is then made 2,000 and R' 8,000, and the second point on the bridge wire deter- mined, and so on for the other points. Of course, lower resistances for R, R', might be used if the leads were negligibly small compared to them. The resistances, R, R', are supposed to be as correct as the percentage of accuracy required in checking the bridge wire. It is important that the battery leads be connected directly to the ends of the bridge wire A, B. In that case the resistance of the leads from the rheostats is added to the large resistances R, R', and tends but slightly to disturb their ratio. In place of the two rheostats it is exceedingly convenient to employ a slide coil bridge (or potentiometer.) In Carey Foster's method, an auxiliary bridge wire A', B', Fig. 37, is made FIG. 37. use of. G is the " gauge " or a resistance equal to the resistance of certain length of A, B, according to the desired interval of calibration, c is a copper connecting piece. The operation is as follows : The "gauge " being in the posi- tion shown in the diagram, g' is placed very near the end of the bridge wire at B, and the other slider, g, of the galvanometer, is adjusted on the auxiliary wire A', B', to no deflection. The positions of G and c are then reversed and the slider g' adjusted to no deflection. G and c are replaced in their former positions, the slider g adjusted to no deflection, and so on. By this means the bridge wire A, B, is stepped off in portions of equal resistance. The resistance of the " gauge " determines, of course, the amount of displacement of g' at each reversal. With the double bridge, the wire may be calibrated by simply measuring any convenient resistance on different portions of the wire. CALIBRATION OF BRIDGE WIRES. 45 When the differential galvanometer is made use of, the bridge wire may be checked by determining some suitable resistance at different points along the wire. Calibration of a Rheostat. A rheostat may be calibrated by the method of " Substitution in the Bridge," previously described. The one ohm coil in the rheostat is compared to a standard ohm. Then the one ohm -{- the standard is balanced against two ohms in the auxiliary rheostat. An interpolation resistance is added and the deflection noted. This is then short-circuited and the two ohm coil in the rheostat to be calibrated substituted for the one coil plus the standard, the deflection noted and from this the difference in resistance calculated. The one ohm coil -|- the two ohm coil is next balanced against three ohms in the auxiliary rheostat, interpolation made, and the three ohm coil is then substituted for the two ohm coil + the one ohm coil, and the difference in resistance determined. By this means all of higher resistances in the rheostat may be compared with the sum of the next lower ones. When the resistance in the circuit is increased, the deflection of the galvanometer for any given change of resistance grow less, so that it is necessary to interpolate after each change of resistance. It is better to have several resistances for interpo- lation, such as o.i, o.oi and o.oor ohm. and when the deflections become small to use one of the higher resistances. Since this is a deflection method, thermal and inductive effects should be carefully corrected for. CHAPTER VII. HIGH RESISTANCE. f Slide Coil Bridge. \ Fall of Potential.* I Deflection Method. [ Loss of Charge. It is difficult to define any exact limit for the term " High Resistance." In a general way, any resistance above 100,000 ohms may be called a high resistance, though usually in insula- tion measurements the unit taken is a million ohms or a meg- ohm (//). Again, in certain cases of insulation such as that of a telegraph line, the insulation may be considerably less than a meg-ohm. The term " insulation " is applied to the resistance of dielectrics and materials that are not good conductors. Thus any "insulation " is usually a * high resistance," but any " high resistance " is not necessarily that of a dielectric or an " insulation." Just how great a resistance can be measured with the present methods it is hard to say, but theoretically by the deflection method, using 200 volts and a Thomson galvanometer whose figure of merit is 100,000 J2, resistances up to 20,000,000 ti might be determined. The imperfect insulation of the apparatus, however, is likely to produce considerable error before reaching resistances nearly so great as the above figure. The accuracy required in high resistance measurement is much less than for the lower resistance measurements, but in many cases of insulation the resistance of the dielectrics vary greatly according to circumstances, and it is therefore necessary to know the conditions of the experiment with great exact- ness. Slide Coil Bridge Method. Very great resistances could be measured on the Wheatstone Bridge if the other three arms could be made of such resistance that they would be somewhat near the magnitude of that to be determined. This require- *" Fall of Potential" should be substituted in place of ' Poientiometer " in the general classifi- cation. 46 HIGH RESISTANCE. 47 ment is fulfilled if the stand- ard resistance be at least ico,ooo ohms, and a slide coil bridge of say 100,000 ohms be used for the adjustable ratio. The connections are shown in Fig. 38. A rather high voltage should be used. By this method resistances of several meg-ohms may be determined with great accu- racy. FIG. 39. 38. Fall of Potential Another method is to join the known resistance in series with the battery and the resistance to be measured. The E. M. F. of the testing battery E having previously been determined with a voltmeter or by other suitable means, the p. D. across R (E') is measured. This is best accomplished by charg- ing a condenser across R, and discharging it through a high resistancegalvanometer. The value of the deflection so obtained may be found by afterwards charg- ing the condenser with a standard cell and noting the deflection. The resistance of x is found by the proportion : E : E' : : (R -f- x) : x* The P. D. across R can also be measured with an electrometer or a potentiometer and standard cell may be used ; in the latter case the conditions of the circuit are rather uncertain, and it is doubtful if the results obtained can be relied upon. Deflection Method. The standard method for nearly all insu- lation determinations is that of." direct deflection." Very great resistances can be measured by it, the conditions of experiment are completely under control and may be varied according to circumstances. A high resistance Thomson galvanometer is joined up in ser- ies with a known resistance and testing battery. The deflection is then read, the galvanometer being shunted, and fr6m this the " constant " is calculated. By the " constant " of the galvanometer is meant the resis- tance that must be introduced into the circuit to reduce the deflection to one scale division with any given battery. ELECTRICAL MEASUREMENTS. K O O FIG. 40. It will be seen that it de- pends upon the " Figure of merit " of the galvanometer and the E. M. F. used ; but since the same E. M. F. is em- ployed throughout the meas- urements, it is not brought into the calculation. After the " constant " is obtained, the resistance to be measured is substituted in place of the known resistance and the de- flection again read. This de- flection, multiplied by the shunt, if one be used, and divided into the "constant," gives the resistance desired. The connections are indicated by Fig. 40. Here a Kempe's reversing key is shown. Example : R = 100,000 ohms (o.i j?), deflection with R in cir- cuit = 250 divisions, when y^Vfr shunt is used ; then " constant " = o.i J2 X 250 X 1,000 = 25,000 Q ; deflection with x in circuit = 50 divisions, shunt = -f$. Then resistance of x = 25,000 Q -^ 50 X 10 = 50 J2. If the insulations to be measured are not very great, the Thomson galvanometer may be replaced by some form of D'Arsonval galvanometer. Loss of Charge Method. For very high insulations that cannot be conveniently measured by " direct deflection," this method may be employed. It is especially useful in testing joints of insulated wires. The connections for this determination are shown in Fig. 42. A condenser is charged and the discharge deflection, v, noted. The condenser is again charged using the same E. M. F. and insu- lated for T seconds with the resistancedto be measured between the poles ; it is then discharged and the deflection, v, noted. Then if F = capacity of condenser in micro-farads, R = re- sistance in meg-ohms between poles of condenser. T n ~ 2.303 F (log V log v.} The resistance of the condenser should first be determined before placing the resistance to be measured between the poles. The final result is, of course, the combination of the two resis- tances when placed in multiple. CHAPTER VIII. f Insulating Material " Specific Insulation." f Short Lengths. Cable j Single Core. ,. res J ( >le '-j Multiple Core. INSULATION. 4 Insulated Wires. ( Loss of charge* I Joint Testing, -j Accumulation. [ ( Electrometer. A erial Wires The requirements in the measurement of insulation are so varied that it seems best to make out a classification of the dif- ferent cases and then treat each separately. The resistance of dielectrics differs so greatly according to circumstances that a determination is of little value unless all of the conditions are given. The E. M. F. used is of great importance ; it should usually be from ioo to 200 volts. It is true that if the insulation is perfect it is independent of the E. M. F., but in a faulty insulation a high E. M F. may dis- cover faults that a low one will not, hence a determination made with a low E. M. F. may be valueless. The battery should be very constant, for if there is any ca- pacity in the circuit, slight variations of E. M. F. may produce considerable variations in the galvanometer deflections. Secondary batteries are the best. The silver chloride testing cells require careful handling to keep in good order and may get to have a very high internal resistance. Insulation resistance decreases with an increase of tempera- ture, and there is also a time lag. Hence, it should be kept at the same temperature for some time. The standard tempera- ture is 75 F. The resistance of dielectrics appears to increase by the con- tinued action of the current. This action is known as " electri- fication." It seems to be due to a sort of dielectric polarization. The deflection should, therefore, be read after some stated time usually after one minute " electrification." 49 50 ELECTRICAL MEASUREMENTS. It is much more marked at low than at high temperatures. It depends on the kind of material, being quicker in some kinds of gutta-percha than in others, and is smallest in the best qual- ity. In the case of gutta-percha the rate of fall between the first and second minute would average about 2 per cent, to 5 per cent. In india rubber it may be as much as 50 per cent, be tween the first and fifth minute. If the insulation is sound, the " electrification " should be reg- ular. An unsteady "electrification" is usually 'a sign of de- fective insulation. It may be caused, however, by a bad con- dition or insulation of the battery, imperfect insulation of the ends of leads or cable, or it may be due to currents induced in cables when they are coiled. There also seems to be a difference of effect in cable testing, whether the + or pole of the battery is put to the cable. When the battery is not reversed, the pole should be joined to the cable. The 4- pole seems to have the effect of sealing up a fault. When the current is reversed, a good insulation should give equal deflections. Specific Insulation. This should be determined by the deflec- tion method, substituting the insulating material in place of R in Fig. 40. The insulation of the apparatus and leads should first be carefully tested. It is best to use a rather large surface of the insulating material. The contact may be made in the following manner : On a well insulated support or table is placed the wire leading from the galvanometer ; next comes a piece of tinfoil the size of the area to be measured ; then a piece of wet felt or wet blotting paper of the same size, and upon this the insulite. The contact above is made in the same way with the addition of a cover upon which is placed a heavy weight. By this means good contact is secured over the surface to be measured. The deflection should be taken after one minute " electrifica- tion." This gives the " absolute " insulation. The "specific insulation " is the insulation of unit volume. It is obtained from the absolute insulation by multiplying by the area of the contacts and dividing by the thickness of the insulating material. Thus : Sp. Ins. = Ab. Ins. x area thickness The E. M. F. used should be stated and the temperature at time of experiment. Short Lengths of insulated Wire When short lengths of cable, such as y mile to one or two miles are to be tested during man- INSULATION. 51 ufacture to obtain the insulation per mile, the following method should be employed. The connections are shown in the diagram, Fig. 41. The cable is coiled and placed in a tank of water. One end is carefully insulated while the other end is joined to the circuit. Contact with the inner surface of the insulation is thus obtained by means of the conducting wire, while contact with the outer surface is secured through the water into which attached to a metal plate dips the wire from the other end of the circuit. Fig. 41 is a general diagram for cable testing and does not show this special arrangement. Q- c\ O J 1 FIG. 41. "'-. The galvanometer is provided with a commutator, c, and a short circuit key, g, the battery is joined to a key of 'the Rymer-Jones pattern. The cable is shown in position for test- ing. The manipulation is as follows : The battery key being closed, the short-circuit key, g, is opened and the deflections read at the end of one minute and two minutes ; g is then closed, the current reversed, the galvanometer commutated and the de- flections again read. The idea in commutating the galvanometer is to obtain the deflections on the same side of the scale. This is important when the deflections with first the and then -j- poles of the battery joined to the cable are compared. Of course, the " con- 52 ELECTRICAL MEASUREMENTS. stant " should also have been obtained from deflections on the same side of the scale. The short-circuit key must always be used in cable testing, for cables act like condensers, having a capacity of aboul y$ mf. per mile, and are charged and discharged every time the battery key is opened or closed. This charge and discharge would, of course, take place through the galvanometer were it not shori- circuited. In the report, the insulation after one minutes' " electrifica- tion " with the pole joined to the cable should be given. The percentage of " electrification " between the first and second minute should also be reported. It is better to keep the cable in the water for at least 24 hours before making the determination. The standard temperature for the water is 75 F.; at any rate, the temperature should be specified. The E. M. F. used should be stated. The " absolute " insulation divided by the length expressed in miles will give the insulation per mile. A good cable should have an insulation of from about 400 Q to 1,000 Q per mile. Cable Testing. This is the case where the cable is in position, either sub-marine or underground. The connections are the same as Fig. 41. The terminal, E, is " grounded," and one end of the cable is insulated. The resistance after one minutes' " electrification," the pole being joined to the cable, is re- ported and also the "electrification" between the ist and i5th minutes. In making careful tests on long cables, a rather complicated set of observations is required, and a report based upon these is made out. In cases of this kind it is advisable to consult " Kempe's Handbook of Electrical Testing." When submerged cables are tested, the "earth current" may render the readings unsteady. There is no method of elimina- ting these effects in single cored cables, but if the cable is mul- tiple cored, a second core may be joined to the battery in place of '* grounding " it and the total insulation divided by two. Joint Testing. Here the length of cable tested is very short and, consequently, the resistance is enormously great so that some more delicate method than " direct deflection " must be employed. One of the most convenient methods is that by " loss of charge." The connections are shown in Fig. 42. The condenser is first charged and the discharge deflection INSULATION. 53 taken. It is then charged and insulated with the joint to be tested submerged in water in well insulated vulcanite trough be- tween the poles. The deflec- tion, after a certain time, is again taken, and difference between this and the first de- flections shows the loss of charge for the given time. The rate of loss of charge through a perfect joint is first obtained for a fixed time, and afterwards the loss of charge for the same time through the joints tested is compared to this taken as a standard. Another method is to charge the condenser for a certain time through a perfect core FIG - 42. and note the deflection, and then charge it through the joints to be tested. An electrometer may also be used. The quadrants are charged through the joint and the deflection noted. This is then compared with a perfect core. Aerial Wires. In this case, the resistances to be measured are usually comparatively low, so that if the deflection method be employed less elaborate apparatus can be used, or the deter- mination may be made by the p. o. bridge. One end of the wire is joined to one of the bridge terminals, the other terminal being "grounded." The other end of the wire should be insulated. The measurement can then be made in the usual manner. When the deflection method is used, the constant should be obtained in ohms instead of meg-ohms. The standard insulation of the English Postal Telegraph De- partment is 200,000 ohms per mile. If the resistance is below this, the line is considered faulty. The insulation per mile is approximately equal to the total insulation multiplied by the length in miles. It may be ob- tained accurately by the formula : = Where i = insulation per mile, R^ = total resistance of line with one end insulated, R e = total resistance of line with further end grounded, y = the conductivity resistance of line per mile. 54 ELECTRICAL MEASUREMENTS. It is sometimes required to find the insulation resistance of two sections of one wire when it can only be tested from one end. Suppose A, c, to be the wire I x 1 which is required to be tested for insulation resistance from _ A in two sections, A B and B c. A, | C Let a be the insulation resis- tance of the section, A, B, and F1G - 43 - b that of B, c ; and suppose x to be the insulation resistance of the whole wire from A to c, then ab ~^+-j from which It is only necessary, therefore, in testing from A, to get the end c insulated and measure the insulation resistance, x. Then get the wire separated at B, the end of the section, A, B, insu- lated and measure the insulation resistance, a. From these two results b can be calculated. CHAPTER IX. RESISTANCE OF TELEGRAPH LINES, CABLES, ETC. f P. O. Bridge. I Loop Test. | f Equilibrium. Mance's Method. Equal Deflection. When the conductivity resistance of a wire is to be measured whose further end is not at hand, one end should be joined to one of the terminals of a p. o. bridge while the other bridge ter- minal is put to earth the other end of the wire is also put to earth, and the measurement is then made in the usual way. Whenever possible, however, it is better to measure without using a " ground," by looping two wires together at their further ends, the nearer ends being joined to the bridge terminals ; this gives the joint conductivity resistance of the two. Errors due to earth currents or a defective earth, etc., are thus avoided. The conductivity resistance of each wire separately cannot be obtained, however, by this means. If there be three wires at hand, however, then the conduc- tivity resistance of each wire may be obtained by making three measurements in the following manner : Let the three wires be numbered respectively i, 2 and 3. First loop wires i and 2 at their further ends, and let their re- sistance be R^ ; next loop wires T and 3, and let their resistance be R z ; finally, loop 2 and 3, and let their resistance be R z . In- dicating the resistances of i, 2 and 3 by r lt r z r z , we have r^ -f- r z = J? lt r^ + r z = R z , r z -f r 3 = J? s . From this, by adding the equations, we get 2 and r s = By a method very similar to the above, if there be only two wires at hand, the resistance of the " earths " at the ends of the lines may be measured and also the resistance of each wire, 55 ELECTRICAL MEASUREMENTS. Denote the resistances of the two wires by r r^ and the re- sistances of the " earths " by E. First loop the wires, then r + r z = ^i> next " ground " the first wire and measure the resistance, then r -j- E = R z ; finally, ground the second wire, then r z -f- E = fi s . From these we get: _ . then E = R R^ r x = R = R z , and r 2 = R R z . Such a test, however, although it eliminates errors due to de- fective earths, does not eliminate errors due to earth currents. When it is not possible to make use of the loop test and the conductivity, resistance of a line of telegraph must be obtained by " grounding " one end, the presence of earth currents and also currents due to the polarization of the earth plates, renders the Wheatstone bridge formula A : B : : R : x, when equilibrium is produced, incorrect. To obtain the true value of the wire resistance different methods and formulae are necessary. Equilibrium Method. Fig. 44 shows the Wheatstone bridge arrangement, where x = re- sistance of wire to be deter- mined, E = E. M. F. due to earth currents, etc., and r = resis- tance of the battery circuit. R is first adjusted to no de- flection ; call this resistance R-L. The current is then re- versed and R readjusted to no deflection ; call this resistance R z . Then by applying KirchhofFs laws, X = ' k) - k\ where = \ r ( i + Mances Method. Here the current is not reversed but the values of A and B are changed and R is again adjusted to no deflection. Call these values A^ B^ R^ and A 2 , B z , R%. In practice, A^ = B^ and A z = B z ; where x __ R (2 r + A 2 ) R z (2 r -f- A^ (R, + A,} - (^ + A,) Equal Deflection Method. This is the same as Mance's method for the measurement of battery resistance except that a battery LINES AND CABLES. 57 is included in the circuit joining the ends of the bridge. The connections are shown in Fig. 44. If there be an earth current the galvanometer is permanently deflected if the galvanometer key is kept closed. R is adjusted until on closing the battery key no change in deflection is produced. Then, A : B : : R : x. In practice, it would be necessary to short-circuit the galvan- ometer at the moment when the battery key is closed or opened, otherwise a violent deflection of the needle would be produced by the static discharge from the cable. CHAPTER X. LOCALIZATION OF FAULTS. The conditions met with in testing for the location of faults are so varied and complex that it is hardly possible to give any general method of procedure. The best way is to consider each of the several cases separately. Faults may be of the following descriptions : t . Complete Fault in Insulation. 2. Partial Fault in Insulation (Earth Resistance). , 5. Variable Fault in Insulation (Polarization or Cable Current]. * 4. Faults plus E. M. F. (Earth Current). 5. Fault in Conductor. 6. Faults of High Resistance. (1) The simplest kind of fault to localize is a complete frac- ture where the fault offers no resistance. Its position is easily determined by dividing the conductivity resistance to the fault by the conductivity resistance per mile of the line. (2) When the fault has a resistance, the localization becomes more difficult. The following are two theoretical methods that may be em- ployed. Blavier's Method. Let A B, Fig. 45, be the line which has a fault/ at c, A being the testing station. The end B is first insulated and the resistance from A to the fault measured ; call this /. The end B is then put to earth, and the resis- tance from A again measured; call this A . Then if the con- ductivity resistance of the line be Z, and the resistance from A to c is denoted by , it may be shown that 58 LOCALIZATION OF FAULTS. 59 Dividing a by the resistance of the line per mile would, of course, give the position of the fault. Overlap Method. In this method two measurements are made, one from station A when B is insulated, and the other from B when A is insulated. Calling the first resistance /, the second / 2 , resistance of line L, and the resistance from A to the fault a, then 2 (3) The practical application of the above methods, however, presents considerable difficulty. This is owing to the variation of the resistance of the fault when the testing current is put to the cable, due to electrolytic action at the fault which may in- crease the resistance and also set up a polarization current in the opposite direction to the testing current. This is especially true in the case of sub-marine cables. To make a proper measurement, then, it is necessary to so manipulate the testing apparatus and battery as to get rid of the polarization and resistance set up. In Lumsden's method, the further end of the cable being in- sulated, the conductor is cleaned at the fault by applying a zinc current from 100 cells for 10 or 12 hours, the current being occasionally reversed for a few minutes. This followed by other special manipulation. In Fahie's method, the cable current is tested by an auxiliary galvanometer. This current is then neutralized with a battery. If the cable current is negative, a positive current should be used in measuring the resistance. (4) The principal difficulty in testing for faults is the presence of earth currents, especially in the case of long cables. These earth currents are seldom constant either in strength or direc- tion for any length of time. Mance's Method has for its object the elimination of the effects of an earth current in a cable when making a resistance test. The general principle of this method is the same as that pre- viously described for the measurement of the resistance of a telegraph line. The bridge arms A and B are made equal, and then given two different values, corresponding adjustments be- ing made for R. In the Deflection Method, the Wheatstone bridge is not made use of. A Thomson galvanometer with a reversing switch and shunt and a battery with reversing key are joined in series with the cable and earth. The testing current is reversed, the galvano- 6o ELECTRICAL MEASUREMENTS. meter being also reversed so that the deflections may be in the same direction. Since in one case the battery current is in the same direction as the earth current, and in the other case it is opposing it, the two deflections will differ. Call these deflections d v and 4- A rheostat is then substituted for the cable, and the resistances adjusted until the same deflections are produced. Call these resistances R v and R% , and X the resistance to be measured ; then, x ^i -^i H- 4 ^2 4 + 4 This method, of course, requires careful manipulation. When possible, the " Loop Test," described below, should be made use of. (5) When the conductor is broken inside the insulating sheath- ing of a cable, a battery joined to the end of the cable will charge the latter up as far as the fault only. Consequently, if the discharge be measured and compared with the discharge from a condenser of known capacity charged fry the same bat- tery, the capacity of the cable up to the fault will be obtained. This capacity divided by the capacity per mile of the cable will give the distance of the fault. (6) In the previous methods described for localizing faults, it was assumed that the insulation resistances of the portions of cable on either side of the fault were infinitely great, compared with the resistances of the conductor. This assumption is practically true when the cable under test is short, and also if the resistance of the fault is small ; but in the case of long cables having faults of high resistance, the formulae given above are no longer correct. The latter case requires the use of very complicated formulae. Whenever possible, however, the loop test, with corrections, should be employed. For a complete discussion of the subject of localization of faults, Kempe's " Handbook of Electrical Testing " should be consulted. The Loop Test. When a faulty cable is lying in the tanks at a factory, so that both ends of it are at hand, or when a sub- merged cable can be looped at the end farthest from the testing station, with either a second wire, if it contains more than one wire, or with a second cable which may be lying parallel with it, then the simplest and most accurate test for localizing the posi- tion of the fault is the loop test. This test is independent (within certain limits) of the resis- tance of the fault. LOCALIZATION OF FAULTS. 6l There are two ways of making this test with the P. o. bridge. Murray's Method. (The connections are shown in Fig. 46.) / is the point where the two wires or cables are looped together, / being the fault. Let x be the resistance from one end of the bridge to the fault, y the resistance from the other end of the bridge to the fault. Then the arm B being plugged up, A and R are adjusted until equilibrium is produced. Then, A x y = R X x. Let L be the total conduc- tivity resistance of the whole loop ; then, x + y L 5 L Mfc. substituting, E KIG. 46. therefore, y = L x ; A (L x) = R X x, from which x = L - . A -}- R Z may be determined in the usual manner for measuring re- sistance. A should be given a rather high value, say 1,000 ohms, in order that the range in adjustment of R may be increased. The zinc current should be put to the cable (through the bridge). The value of x divided by the conductivity resistance of the cable per mile or foot, as the case may be, gives the position of the fault. Farley's Method. (Fig. 47 shows the arrangement of this method.) A and B are fixed resistances, and R is adjusted until equilibrium is produced. Then, B (R -f x) = A 7, and y L x ; therefore, B (R + x) = A (L x), from o i B o-. '_A H'I'H which x = A L B R A + B If |- then A = B, x = L R FIG. 47. The conditions for making this test with accuracy are not quite so simple as in Murray's 62 ELECTRICAL MEASUREMENTS. method. In this case they are almost precisely similar to what they are in the ordinary Wheatstone bridge measure- ment. CHAPTER XI. RESISTANCE OF BATTERIES AND ELECTROLYTES. f ( Condenser. Fall of Potential* \ Hi^h Resistance. Voltmeter.* BATTERY RESISTANCE. Added Resistance, Mance's Method. Current and E. M. F.* The resistance of a battery is not a perfectly fixed quantity. It may vary somewhat according to the strength of current that is flowing and the time that the current has been maintained. The resistance varies also with the temperature of the battery. It is therefore desirable in an accurate determination to know the conditions of the circuit, especially the value of the external resistance. The best method is probably that by Fall of Potential. This measurement may be carried out in several ways. Condenser Method. The cell or battery x is joined in series with a known resistance R and a key b. Across the terminals of the cell are connected a con- denser, galvanometer and dis- charge key, shown in the diagram, Fig. 48. The condenser is first charged by closing the key #, the key b remaining open. The con- denser is then discharged through the galvanometer. The deflection thus obtained, ;/!, is proportional to the E.M.F. of the cell. The key b is then closed and the condenser again charged and discharged. This deflection, d% , is proportional to the P. D. across R. Therefore ^ d z is proportional to the p. D. across x. Then : d l d* : d* , : : x : R. FIG. 48. 64 ELECTRICAL MEASUREMENTS. If R be varied until 4 = *, then R = x. 2 R may be given different values, and the corresponding 1 values of x determined, or x may be measured after the current has been flowing for different lengths of time. This method is especially applicable when the efficiency of any particular cell is to be investigated. High Resistance Method. A galvanometer and high resistance may be substituted in place of the condenser. The high resis- tance is joined in series with the galvanometer, and readings are taken across the terminals of the cell similar to those in the above method. The calculation is the same. Voltmeter Method. A low reading voltmeter, such as the Weston voltmeter, that can be read directly to ^ volt and estimated to ^^^ volt, may be used to take the deflections across the cell. Readings are made with the key open and with the key closed, in the same manner as in the condenser method, and the same calculation is used. If R is adjusted until the de- flection with the key closed FIG> 49> is one-half of the deflection with the key open, then R is equal to the resistance of the cell. This method is to be recommended for all ordinary deter- minations of cell resistance. It is, of course, inapplicable in the case where the resistance of a battery is appreciably great compared to the resistance of the voltmeter. Tangent Galvanometer Method. If a low resistance tangent galvanometer be at hand, the determination can be made in the following manner : Take the deflection with the cell and galva- nometer in series, call this deflection 4 , and the resistance of the circuit x. Then add a known resistance, R, preferably such that will about halve the deflection, call this 4- Then : x : x + R : : tan 4 ' tan d lt and x galvanometer resistance = the cell resistance, assuming the resistance of the leads to be negligible. This method may sometimes be found convenient for a labor- atory determination where the cell is fairly constant. If a low resistance reflecting galvanometer be used and the resistance neglected, and such a resistance, R, added, that d = 1 , then R = the battery resistance. BATTERY RESISTANCE. 65 If the battery has a fairly high resistance and the galvano- meter resistance, G, is not neglible, then the following method may be used : The galvanometer, battery and a rheostat are joined in series. The resistance, R X , is adjusted until some con- venient deflection is obtained. Then the resistance is increased until the deflection is halved ; call this second resistance R 2 . Then: R = R 2 (2 RI + G), where R is the resistance of the battery. Mance's Method. In this method, the cell is joined to the terminals of a Wheatstone bridge, in place of the unknown re- sistance, the ends of the bridge being connected by a wire fur- nished with a key. The connections are the same as those shown in Fig. 44, except that no testing battery need be em- ployed. The position of the cell is indicated by x. The galvanometer key is closed and the steady deflection pro- duced by the cell is reduced to some convenient amount either by lowering the magnet, if the Thomson galvanometer is used, or by the addition of an extra resistance to the galvanometer circuit. R is then adjusted until no change is produced in the deflection on closing the key joining the ends of the bridge. The manipulation in this method is sometimes rather difficult, and it is hardly to be recommended when fall of potential me- thods can be employed. Current and E. M. F. In some instances, where the internal resistance of a cell is very low, the P. D. across an external re- sistance subtracted from the E. M. F. of the cell gives such a small difference, that measurements cannot be made accurately by fall of potential methods. In this case, it is best to measure the current with an ammeter and the E. M. F. with a voltmeter ; then the resistance can be E> calculated from the formulae R = . R E S,ST AN CE OF E.BCTKO..VTE, { %%%?,. When the resistance of a fluid, which is decomposed by the current, is to be measured, account must be taken of the oppos- ing E. M. F. of polarization. The simplest method is that of substitution. The fluid is placed in a U tube provided with platinum elec- trodes, one arm of the tube being calibrated. The fluid thus contained is included in a simple circuit with a rheostat, a galvanometer and a galvanic cell. 66 ELECTRICAL MEASUREMENTS. FIG. 50. The arrangement is shown in Fig. 50. The position of the needle is then observed when so much of the column of fluid is included that the deflection is a conveni- ent amount ; then one electrode is approached to the other by the length /, and such an amount R of rheostat resistance thrown into the circuit that the same deflection is produced- The resistance -R is then equal to that of the fluid between the two positions of the movable electrode, assuming the polar- ization to be the same in both cases. It is well to use spirals of platinum wire or platinum gauze for the electrodes. Since the conductivity of fluids varies greatly with their tem- perature, this should be observed, and be kept constant by placing the tube in a water-bath provided with a thermometer. The influence of polarization may be avoided, and the resis- tance of an electrolyte measured directly, just as that of a me- tallic conductor, if a rapidly alternating current be employed. The tube containing the fluid, x, is joined to the terminals of a Wheatstone bridge, the current being furnished by an induc- tion coil. A telephone receiver is used in place of the galvano- meter. The connections are shown in Fig. 51. The ad- justment to equilibrium is obtained when the telephone gives the minimum sound, then A : B : : R : x. A num- ber of observations should be made. The electrodes in this case should consist of platinized platinum foil. To obtain the "Specific Resistance " of a fluid, the containing vessel should first be filled with mercury, and the resistance measured in the usual way. This gives the "mercury constant" of the vessel. This resistance divided into the resistance of the fluid gives its resistance compared to mercury, from which the resistance compared to copper can be RESISTANCE OF ELECTROLYTES. 67 calculated. If the dimensions of the containing vessel, or rather the column of fluid measured, were accurately known, then the resistance of unit volume could be calculated. CHAPTER XII. INCANDESCENT LAMPS, " DYNAMO RESISTANCE," ETC. It is often required to measure the resistances of incandes- cent lamps or arc lamps while running. The resistance of an incandescent lamp depends very largely upon the temperature of the filament, and consequently upon the strength of current flowing. It is therefore desirable that the original conditions of the circuit be interfered with as little as possible when the measurement is made. The fall of potential across the lamp may be measured with a voltmeter, and then the p. D. across a small resistance, such as an ohm, in series with the lamp (Fig. 52). The resis- tance is then calculated by a direct proportion. In place of the voltmeter, a galvanometer and high re- sistance oragalvanometerand FIG. 52. condenser can be employed. The series resistance should be of such size wire that it will not be heated appreciably by the current, and the resistance should be small compared to that of the lamp, so that the cur- rent will not be materially reduced by it. A better practical method, however, is to measure the current flowing through the lamp with an ammeter (an instrument hav- ing a negligibly small resistance), and the fall of potential across the lamp with a voltmeter. The resistance is then calculated E> from the formula R . O The resistance can also be measured directly by means of an ohmmeter. In principle, the, ohmmeter consists of two coils at right angles to each other, with a small needle at the point of intersection of the axis (Fig 53). One of the coils of low resis- tance is in series with the resistance to be measured, and the other, which is of comparatively high resistance, is in shunt. DYNAMO RESISTANCE. 69 Under these circumstances the action of the needle is due to the ratio of the difference of potential at the terminals of the unknown resistance and the current strength in the series coil, The coils are so proportioned, that when the current flows through the short thick wire, it moves the needle to the zero of the scale, while the long thin wire of the shunt coil produces a deflection directly proportional to the resistance. If the coils are large and the needle short, the instrument will follow the tangent law. In Eve'rshed's ohmmeter, the current coils are wound outside and the shunt or pressure coil is globular in form, so as to fit inside. It is placed at an angle of 45 , so as to give a long scale. Inside the shunt coil a hard steel needle is suspended by a silk fibre. A second needle is hung outside the coils, so that the instrument is astatic. The range of the instru- ment is increased by insert- ing resistance in series with the shunt coil. It is gradu- ated by experiment. An ohmmeter should al- ways be tested to see if it is accurate. A piece of thick wire is measured in the or- dinary way, and the resistance then determined with an ohmmeter. Care must be taken that the wire does not become heated. The same resistance should be measured with a large current and a small current. The apparent resistance of a dynamo, while running may be determined in the following manner : A voltmeter being con- nected across the terminals, the P. D. is measured on closed circuit. This gives the fall of potential across the external resis- tance, or the P. D. across the " line ". The current should also be measured with an ammeter. The circuit then being opened, the voltmeter indicates the total P. D. that the dynamo is capable of giving. The first reading subtracted from this shows the P. D. across the dynamo when running on the above circuit. The resistance can then be obtained from the formula R Of course, if u the resistance of the external circuit were known, the resistance of the dynamo could be calculated without using the ammeter. CHAPTER XIII. DETERMINATION OF THE OHM, CONSTRUCTION OF STANDARDS, ETC. The measurement of resistance consists of the comparison of the resistances to be determined with some other resistance taken as a standard. The derivation and determination of this standard is of inter- est, though, of course, its absolute determination is never re- quired in practice. That originally taken as a convenient unit was approximately the resistance of a mile of copper wire of a certain size. An exact value was assigned to it by Siemens, who defined it as the resistance of a column of mercury one metre in length and one square millimetre in section at the temperature of melting ice. This has been called the Siemens unit. With the application of the c. G. s. system to electrical measurement and the adoption of the magnetic definitions, the unit of resistance was defined as the ratio of the centimetre to the second. The product of this quantity by io 9 , called the ohm, was designed for practical use, the c. G. s. unit being incon- veniently small. It has nearly the same value as the Siemens unit. The exact determination of this unit has been the work of many years. The original B. A. ohm of 1864 has been replaced by more accurate determinations of the c. G. s. unit. The Paris Conference in 1884 agreed upon the so called legal ohm, and defined the resistance as that of a column of mercury, 106 centi- metres long, of one square millimetre section, at the tempera- ture of melting ice. At the British Association meeting of 1892, the results of a large number of independent measurements were compared, and what is now known as the international ohm or the true ohm was adopted. Its resistance is defined as that of 14. 45 21* grammes of mer- cury in the form of a column of uniform cross section 106.3 centimetres in length at o C. (It is equivalent to a cross- section of one square millimetre). The above value was also adopted by the Electrical Congress at Chicago in 1893. Table I. shows the relative values of the different units. STANDARDS OF RESISTANCE. An outline of the general method followed in the absolute de- termination is indicated below. A coil of wire of known area and number of turns is placed so that the axis of the coil is in the magnetic meridian, and rotated with a known velocity. By definition the c. G. s. unit of E. M. F. is that obtained when one " line of force " is cut per second, and hence the E. M. F. developed by the coil can be cal- culated. Let F = the total strength of field ; then since each line of force is cut four times in one revolution of the coil, the E.M.F. =area of coil X num- ber of turns X 4 X F x num- ber of revolutions per second. The coil is joined in series with a tangent galvanometer (Fig. 54), and the current strength obtained by the formula C= X H X tan^, 2 H 7T where B = deflection, R = ra- dius of galvanometer coils, and n = number of turns. The resistance of the circuit can then be calculated from the Tf formula R = . TABLE I. Siemens Unit. B. A. Ohm. Legal Ohm. International Ohm. Siemens Unit I OO 9535 9434 .9407 B. A Ohm Legal Ohm 1.0488 i.c6 I.OO 1.0107 .9894 I.OO .9866 .9972 International or True Ohm 1.063 1.0136 1.0028 .1.00 FIG. 55. If a resistance be added to the circuit, the above operation may be repeated and the resistance of the circuit again obtained. The difference between these two results would give the value of the resistance added. Since the resistance is measured in c. G. s. units, it must be divided by io 9 to reduce it to ohms. The secondary standards consist of coils of wire of various alloys, whose resistance are known to be very nearly constant. A form of standard resistance coil devised for the first British Association committee, and which was till recently the generally ac- cepted form, is shown in Fig. 55. ?2 ELECTRICAL MEASUREMENTS. It consists of a coil of wire on a metal bobbin with a tubular core, the ends being connected to a pair of thick copper rods, led through ebonite clamps, and bent downwards so as to be easily put into mercury cups. The whole coil is then slipped into an outside case of thin sheet metal in the form of two cylinders. The lower cylinder contains the wire coil, and the upper is filled with paraffin wax. The case up to the shoulder is intended to be placed in a bath of water, the temperature of which is taken with a thermometer placed in the central tube after the coil has been so long in the bath that it has reached the temperature of the water. The coils of a rheostat should be wound bifilar (Fig. 56) to neutralize the magnetic action of the current and prevent ef- fects due to self-induction. This winding is most easily accomplished from two bob- bins, the farther ends of the wire being soldered together. The coils should be dipped in melted paraffin to secure 6 more perfect insulation and prevent any atmospheric ac- tion on the wire that might change the resistance in the course of time. The following are the principal materials that have been employed commercially for constructing resistances. German silver, an alloy of copper, nickel, and zinc. Specific resistance about 18, but varies greatly, according to the compo- sition of the alloy. Temperature coefficient .04 per cent, per i C. Largely used in the construction of rheostat coils. Platinum silver, composed of two parts by weight of platinum to one of silver. Specific resistance about 15. Resistance in- creases .031 per cent, per degree centigrade. Used for standards. Platinoid is German silver with the addition of a small per- centage of tungsten. Specific resistance about 17. Temperature coefficient .022 per degree centigrade. Manganin, specific resistance about 20. Alloys containing manganese have been found to have very small temperature coefficients, and it is even possible to obtain them with negative coefficients. In the case of this, or any of the new alloys, a long series of observations are required to establish with any degree of certainty the permanency of the resistance. CHAPTER XIV. Electromotive Force and Potential Difference, Measurement of E. M. F. of Batteries and Direct Currents. The term " electromotive force " is not a scientifically accurate one, since in the Newtonian sense, force is only that which acts on matter. This restricted use of the term " force," however, does not seem advisable when the present state of scientific theories with regard to the ether is considered. It would be better if force were defined as that which produces or tends to produce motion, or that which produces stress. It may be well to consider briefly- the possible nature of elec- trical action, in order to show more clearly the relation between electromotive force and potential difference. Suppose some cause, an electromotive force, produces a stress in the ether. This stress, under certain conditions, produces an ether strain or displacement, and the change from stress to strain must, of course, be accompanied by motion, either vibra- tional or progressive. This motion - is known as an electric current. Its presence can only be recognized when the ethereal motion has been con- vected into jthe motion of the grosser particles of matter. Since the same effect may be produced by different causes, though any given cause must always produce the same effect, potential difference may be due to a great variety of electro- motive forces. We may then define electromotive force as the cause which produces potential difference, and potential difference as that which produces or tends to produce an electric current. From the above considerations it seems to the writer that the term " electromotive force " is a particularly good one ; it is only its mode of use that should be objected to. It is evident that, strictly speaking, electromotive force can never be measured ; it is only potential difference that may be determined. It should also be remembered that in the state- iy ment of Ohm's law, C = , that the E stands for difference of R potential, and not electromotive force. ' 73 74 ELECTRICAL MEASUREMENTS. BATTERIES AND DIRECT CURRENTS. There has been a great want of uniformity in the employment of the term " electromotive force-" By some, it is regarded as that which causes difference of potential ; others consider it as being produced by potential difference ; and still others regard it as the entire electric moving cause produced by any source ; while anything less than this is called potential difference. This last distinction between the two terms is that ordinarily used with regard to dynamos and batteries. Whenever the term " electromotive force" (E. M. F.) is used with respect to measurements, it should be understood to indi- cate " total potential difference." The abbreviation T. p. D. has been suggested in place of E. M. F. Its employment would save much confusion. f I Deflection and Resistance, j High Resistance Method *\ Equal Deflection. ( Equal Resistance. Wheatstone's Method. Lumsderi's Method. Condenser Method.* ( Five Arc (Cushman). Potentiometer* ] Quadruplex (Muirhead). ( Duplex (Varley). Current and Resistance. Electrometer. Voltmeter * For the determination of potential difference (P. D.) in direct current and battery work, a great variety of methods may be selected from. The more important of these are indicated in the above classification. Of course, the most exact measure- ment is obtained by means of the potentiometer, but other me- thods are often better suited for special cases. High Resistance Method. If a source of potential difference, for example the battery E X , is joined in series with a galvano- meter and a resistance (Fig. 57), the E. M. F. is proportional to the deflection di X RI, where RJ equals the entire resis- tance of the circuit, for from Ohm's law E= CR. 1 R I : * J ' Let another battery E 2 be used in place of E! , then the E. M. F. is proportional to 4 X R 2 , where d z equals the deflection, FIG. 57. and R 2 the entire resistance in circuit. > v . Hence, EJ : E 2 : : d l R X : 4 R . The difficulty with this method is that it requires the resis- tance of the batteries and galvanometer to be known. A modification of the above is to vary the resistance in circuit until the two deflections are equal. Then, EJ : E 2 : : R X -: R 2 . MEASUREMENT OF E. M. F. 75 If the resistance in circuit is equal in both cases, then E! : Eg : : Low Reading Voltmeter . ( f Direct Current Voltmeter We*ton\ \ s P rin g~ magnet. '] Alternating Current Volt- i meter dynamometers. Ayrton^ Perry's j$I et . Thomson's Graded Galvanometers magnet. Magnetic Vane spring. Eversheds gravity. [ Cardew expansion. CHAPTER XV. E. M. F. OF ALTER- ( Measurement of Very High E. M. F. and Very Low NATING CURRENTS. \ E. M. F. E. M. F. of Alternating Currents. The E. M. F. of alternating currents may be conveniently measured by the following in- struments : Electrostatic Voltmeter* ELECTROMETER. \ Multicellular* I Quadrant. [ Low Reading. DYNAMOMETER. \ w , eston ^ s * (Alternating Current Voltmeter.) Stetnen s. ATTRACTION OR ( Hartman and Braun's. ELECTRO-MAGNETIC < Evershed's. VOLTMETERS. ( Magnetic Vane, etc CALORIC VOLTMETER (Car dew's.} The form of electrometer known as Thomson's Electrostatic Voltmeter is very largely used in alternating current work. The construction is shown by the diagram Fig. 65. A light aluminium vane is pivoted on knife edges between two brass plates and is carefully insulated from them. The vane is provided with a pointer and to the lower end of the vane small counter weights may be added. The terminals of the source of p. D. are connected to the brass plates and the movable vane, the attraction is then proportional to the pTlx 2 . The scale is graduated in divisons proportional to po- tential differences. Three counter weights are provided and according to which is used the scale divisions are equal to 50 volts, 100 volts, or 200 volts respectively. The range of the instruments is thus very large, Si FIG. 65. 82 ELECTRICAL MEASUREMENTS. but it is liable to spark if more than 10,000 volts are used. It is provided, however, with a safety fuse. In the Multicellular Electrometer, Fig. 66, a number of movable vanes are employed turn- ing between corresponding fixed plates. The force of attraction is balanced by the torsion of the wire suspending the vanes. The scale is graduated directly to volts. The instrument is made in four different ranges, giving readings from 40 to 800 volts. It is possible with this form of electrometer to FlG 66 read as low as 15 volts. The ordinary Thomson Quadrant Electrometer may be used to measure an alternating E. M. F. if the vane and one pair of quadrants be joined to a terminal from the source of p. D. and the other terminal connected to the opposite pair of quadrants. The connections are then reversed by means of a commutator and the deflection observed. The E. M. F.'S are then proportional to 2 A/deflections. This form of instrument is somewhat difficult to use and re- quires considerable care in the adjustments. A special form of electrometer in which the moving vane is rectangular in shape and suspended by a fine wire, is known as the "Low Reading Electrometer." By means of a lamp and scale, it is possible that as low an E. M. F. as -^ volt can be meas- ured with this instrument. The employment of some form of electrometer, whenever possible, is to be most strongly recommended. Since it measures p. D. entirely by electrostatic pressure, its use produces no change in the relations of the circuit, and if the scale is graduated correctly it must indicate the true poten- tial difference. The dynamometer consists of a fixed and a movable coil of wire, the latter being normally at an angle to the plane of the former, Fig. 67, and both coils being traversed by the current whose E. M. F. is to be measured. Directive force may be given to the movable coil either by the elasticity of a spring or the torsion of a suspending wire. The deflections of the movable coil are proportional to the square of the current strength, and consequently to the square pf the E. M. F. ALTERNATING E. M. F.'S. 83 fastened to an axle provided with a counter weight and indica- ting hand, is placed with the coil to one side of the axis. When When a current passes through the coils, an attraction is exerted, and the movable coil tends to take a position parallel to the plane of the fixed coil. Change of direction of the current in the entire instrument does not alter the direction of the deflection, and hence it is suitable for alternating work. For small E. M. F.'S the dynamometer is not very sensitive, since the deflection is proportional to the square of the E. M. F. For determination of E. M. F. the coils should be given a high resistance, or a high resistance should be placed in series with them. The Weston alternating current voltmeter is a form of dyna- mometer in which the movable coil is mounted in bearings and the current lead in by watch springs fastened to the axle, the arrangement being similar to that described in the direct cur- rent voltmeter. This instrument is quite sensitive and the readings reliable. It is extremely useful for all ordinary measurements of alternating E. M. F.'S It is possible, however, that the readings may be slightly effected by the action of strong magnetic fields. In a form of the Siemen's dynamometer, the attraction be- tween the coils is measured by the angle of torsion of an elastic spring, by turning the torsion circle of which the deflected coil is brought back to zero. The E. M. F. is then proportional to the square root of the angle of torsion. The axis of the movable coil should be North and South, so that it may not be effected by terrestial magnetism. A large class of voltmeters which may be called attraction or electro -magnetic voltmeters depend on the principle that when a current flows through a coil of wire it creates a magnetic field which attracts a piece of soft iron towards the strongest portion of the field. This attraction is, of course, independent of the direction of the current. In a form of instrument manufactured by Hartman and Braun, a small soft iron coil is held by means of a spring just above the attracting coil, and the motion is multiplied by means of a lever arm moving over a graduated scale. One form of the Ayrton and Perry voltmeter is similar to the above, except that the spring is placed within the coil and the arrangement of the indicating hand is somewhat different. In Evershed's voltmeter, Fig. 68, a piece of soft iron, s s, ELECTRICAL MEASUREMENT^. FIG. 68. a current flows through the coil it tends to rotate the soft iron core to a position in the axis of the coil. In the magnetic vane voltmeter, the p. D. is measured by the repulsion exerted between a fixed and movable vane of soft iron placed in the field of a magnetizing coil, the action of the movable vane being opposed by a spring. Just what errors may be caused by hyster- esis or residual magnetism in the above class of voltmeters it is difficult to say, but it is probable that most of them are fairly correct and well adapted to the class of measurements for which they are employed. It should be understood that the instruments just described may be employed as voltmeters or ammeters, depending on whether they are given a high or a low resistance. Caloric voltmeter. When a current flows through a wire, the wire is heated and expands. The amount of heating or expan- sion is proportional to the current and also to the p. D. across the ends of the wire. In the " hot wire " voltmeter, the amount of this expansion is indicated by a pointer held in position by springs, the scale be- ing graduated in volts. Fig. 69, shows the principle of construction of the instru- ment. In the Cardew voltmeter as formerly manufactured, the expansion wire was placed in a long tube at the side of the indicating scale. In the more recent in- struments, however, a circular case is em- ployed and their appearance does not differ from the ordinary voltmeter. The expansion of the wire is, of course, independent of the direction of the current. The readings are not effected by strong magnetic fields, and hence these instru- ments are very suitable for station work. Some of these instruments, however, have a rather low re- sistance and require a considerable current to operate them, so that they are not always adapted to measurements when the re- sistance of the voltmeter is a factor in the determination. Measurement of very high E. M. F. The Thomson Electrostatic Voltmeter might be employed for the determination of E. M. F.'S considerably above 10,000 volts if the distance between the plates and the vane were made sufficiently great to prevent FIG. 69. VERY HIGH E. M. F.'S. 85 sparking and if the entire instrument were very carefully in- sulated. Heavier counter weights could be employed and each division deflection thus made to correspond to a greater p. D. In the Absolute Electrometer and Kirchhoff's Balance, the attraction between a fixed and movable plate is measured and by means of suitable formula the E. M. F. calculated. Of course, the limit of measurement is determined by the striking distance of the spark and by the insulation of the apparatus. Very great potential differences can be roughly calculated from the striking distance of the spark in air. It depends to a certain extent on the size and shape of the electrodes. The striking distance increases faster than the difference of poten tial, and the curve indicating the ratios of striking distances to differences of potential is a parabola. According to Lord Kelvin's measurements, the potential dif- ference required to produce a spark in air, between parallel plates, and of a given length, diminishes rapidly as the distance increases, approaching a limiting value of 30,000 volts per centi- metre, which may be assumed constant for distances greater than one centimetre. For sparks not under two millimetres in length the volts ne- cessary to start a spark across a length of / centimetres may be approximately calculated by the formula V = 1,500 -j- 30,000 /. Measurement of very low E. M. F. A very sensitive galvano- meter will give a deflection of one scale division for a differ- ence of potential of .00000 r volt across its terminals. The galvanometer may be calibrated by means of a standard cell in series with a high resistance. Thus: suppose the resist- ance used is 100,000 ohms, galvanometer resistance 1000 ohms, and deflection 300 divisions, then i division deflection = 1,435 volts X = .000047 volt. ioi,coo X 300 With one form of the Weston voltmeter readings as low as 3-jj-g- volt can be obtained, and if the series resistance were cut out it is probable that it would indicate about 3^^ volt. Quite small differences of potential may be observed by means of a capillary electrometer, which consists of a very finely drawn out glass tube containing mercury and 60 per cent sulphuric acid in contact with each other. A potential difference between them causes a change of capillary pressure at the point of con- tact, and hence a displacement, which for small potential differ- ence is proportional to the latter. This displacement may be accurately determined by means of a microscope. CHAPTER XVI. CALIBRATION OF VOLTMETERS AND STANDARD'S OF E. M. F. FIG. 70 Voltmeters are best calibrated by comparison with one or more standard cells by means of a potentiometer. The arrange- ment of the experi- B ment is shown in the diagram Fig. 70. Across the ends of the potentiometer RR', consisting of a slide coil bridge similar in construction to one of the forms previously described and of not less than 10,000 ohms resistance, is joined the voltmeter v. In place of a slide coil bridge two rheostats may be employed for R and R' and the adjustments so made that the joint resist- tance is always 10,000 ohms. A battery of constant cells B, pre- ferably storage cells, with a shunt resistance s' is also connected to the terminals of the potentiometer. The E. M. F. of this bat tery should be somewhat greater than the highest reading of the voltmeter. The standard cells E in series with a protecting re- sistance r, thac may be short-circuited, and the galvanometer are joined to one terminal of the potentiometer and the contact key as slider. The positive poles of testing battery and standard cells should be connected to the zero terminal of the potentio- meter. If it is desired to find the errors in a voltmeter scale already graduated the method is as follows: s' is adjusted until some convenient reading is obtained on the voltmeter, and then a balance is obtained on the potentiometer, shown by no deflec- tion of the galvanometer, the potential difference v across the ends of the potentiometer being calculated from the proportion. 86 VOLTMETER CALIBRATION. 87 R : R -|- R ' : : E : v. Example, voltmeter reading = 10.7, E = 1.435 X 2, R = 2657, R -|- R' = 10,000 ; then 2657 : 10,000 : : 2.87 : v. v = 10.8 volts ; error of voltmeter reading is therefore o. i volt and the correction -f- o.i volt. By this means the errors in various parts of the scale are de- termined and a correction table or curve constructed. When it is desired to graduate the scale or adjust the volt- meter by changing its resistance until the readings correspond with the scale, the following method is employed. Suppose a potential difference of exactly 10 volts is required across the voltmeter terminals, R is given such a value that R : R -f- R' : : E : 10, thus R : 10,000 : : 2.87 : 10, R = 2870. s' is then adjusted until the galvanometer gives no deflection. The potential dif- ference across the potentiometer and consequently across the voltmeter must then be just 10 volts. The position taken by the indicating hand of the voltmeter is therefore marked 10, and so on for the other portions of the scale. The advantage of using several standard cells is that a better average value for the E. M. F. is obtained and also that the read- ings on the potentiometer are larger, when the potential differ- ences across the terminals are high, than if a single cell were employed. For very accurate work the standard cells should be placed in a water bath or an oil bath, and the correction, if any, for the temperature coefficient applied. It should be understood that the above method is suitable for the calibration of standard laboratory voltmeters. After a volt- meter has once been accurately calibrated, other voltmeters may be checked by a direct comparison with it. A voltmeter may also be checked by taking the reading across a known resistence R through which a known current C is flow- ing. The potential difference E across R may then be calculated from the formula E C R. The difference between this and the voltmeter reading, of course, gives the correction. The arrange- ment is similar to that shown in Fig. 62 except that the volt- meter terminals are joined across R in place of the cell E, galva- nometer, etc. By varying the current different readings may be obtained. For R, a standard ohm or some accurately measured resistance that will not be heated by the current should be em- ployed. This resistance should be low compared to the volt- meter resistance. The current can be measured by means of a Thomson balance, a calibrated ammeter, or if it be constant, with a voltmeter. Standards of E. M. E. In the case of E. M. F., there is consi- derable difference in the values of the unit and of the standard. 88 ELECTRICAL MEASUREMENTS. The " absolute unit " of E. M. F. is the E. M. F. developed by a conductor when it cuts one "line of force" per second. The practical unit or volt is io 8 absolute units. The international standard of E. M. F. adopted is the Clark standard cell. Its E. M. F. is 1.434 true volts at i5 Q c. It consists of an anode of pure zinc in a concentrated solution of zinc- sulphate and a cathode of pure mercury in contact with a paste of pure mercurous sul phate. Precise directions are given for setting up these cells, and if the directions are followed they may be relied upon to give the E. M. F. stated above. The variations of the E. M. F. with temperature may be calculated with sufficient accuracy from the formula : E = i-434 ! i 0.00077 (/is);, where t is the temperature of the cell in degrees centigrade. Various other standard cells are made use of in practice. The Carhart-Clark cell employs a solution of zinc-sulphate saturated at oc. Its E. M. F. is 1.440 true volts at i5c. and the tempera- ture coefficient is approximately 0.00038 per degree c. In the Weston standard cell, a cadmium anode is used im- mersed in sulphate of cadmium. The E. M. F. is 1.025 true volts and this value is practically constant at all ordinary tempera- tures. Standard Clark-cells prepared according to the specifications are best checked by comparison with each other by the poten- tiometer method, care being taken that they are of the same temperature. If several are found to agree to the third decimal place, it may be taken as very certain that the E. M. F. is 1.434 true volts at i5c. Other standard cells may then be compared with them by the same method. The E. M. F. of standard cells may also be determined by con- necting in series with a galvanometer and protecting resistance and joining the terminals of this branch circuit across a known resistance R through which a current from a constant battery is flowing. The arrangement of the experiment is shown in Fig. 62. The current is varied by means of the resistance s' until the potential difference across R is equal to the E. M. F. of the standard cell shown by no deflection of the galvanometer. The current can be measured accurately by means of a silver volt- meter or by use of a Thomson Balance. Then E = c R. It may be well to state that the E. M F. differs according as it is expressed in true or international volts, legal volts, or B. A. volts. The ratios are the same as those existing between the the corresponding values of the ohm. CHAPTER XVII. CURRENT. The presence of an electrical current is manifested by several accompanying phenomena and it is by the observation of the intensity of these phenomena that current strength is deter- mined. A conductor carrying a current is surrounded by a magnetic field, and the strength of this field may be measured by the de- flective action on a magnetic needle, the attractive force exerted on a piece of soft iron, the attraction between two coils through which the current is flowing, etc. Besides this magnetic field there is also an electrostatic field surrounding the conductor, in other words, there is a difference of potential all along a conductor through which a current is flowing. This potential difference can be determined and the resistance across which it is measured being known, the current may be calculated. Whenever a current flows through a conductor heat is devel- oped and this calorific effect is proportional to the square of the strength of the current. If a current be made to flow through an electrolyte, chemical- action takes place and this chemical action is also a measure of the current strength. The methods and instruments for the measurement of current are quite numerous and, of course, vary according to the special cases required. One method, however, is universally applicable. This is the measurement of the potential difference across a known resist- ance. For this determination any of the methods used for the measurement of P. D. can be employed. It may, perhaps, be found more convenient at times to make use of some of the other methods, so it is well to briefly consider them. 89 ELECTRICAL MEASUREMENTS. DIRECT CURRENTS. ( Direct Method. E. M. F. and Resistance.. \ Differential Method (Cardew's). ( Bridge Method (Kempe's). P. D. and Resistance. Tangent Galvanometer. f Direct Deflection Method. | Equilibrium Method. -{ Potentiometer Method. Voltmeter Method.* Galvanometer Method.* ] ^eight. Ammeter.* ( Also the methods given for Alternating ( Currents. E. M. F. and resistance, direct method. To measure current by this method the deflection of a low resistance galvanometer is noted when placed in the circuit through which flows the current whose strength is to be determined. The galvanometer is then joined in series with a battery of known E. M. F. and a rheostat, FIG. 71. FIG. 72. the resistance being adjusted until the deflection is equal to that obtained in the first case. Then the current may be cal- culated from the formula C '- R+G + r ' Where G = resistance of galvanometer and r = resistance of battery. These latter may be neglected if small compared to R, This method is applicable to the measurement of compara- tively weak currents. Cardew's Differential Method. For this method the galvano- meter is wound with two coils g g^ Fig. 71. Through the coil^, which is of low resistance, is passed the current to be measured. To the other coil g is joined a cell of known E. M. F. and a re- sistance JR. This resistance is adjusted until there is no deflec- tion, then MEASUREMENT OF CURRENT. where I produced ; then l ' ^ Kempe's Bridge Method. This method is a modification of the preceding one, and has the advantage that it does not require a special form of galvanometer. In making the measurement the resistance R, Fig. 73, is ad- justed until no deflection is observed, then Er where C l is the current to be measured and E the E. M. F. of the auxiliary cell whose resistance should be negligible compared to R. It is well to give the resistances r and r lt a ratio of say 100 : i. IOO Example : C, = [ ' 8 X , i (4000 -f- 100) = .026. V FIG. 74. FIG. 73- P. D. and Resistance. The p. D. across a known resistance through which a current is flowing may be determined in a great variety of ways and from this the value of the current is readily calculated. If a galvanometer in series with a high resistance R, Fig. 74, be joined across a low resistance r through which a current is flowing and the deflection d^ observed, and then if the galvano- meter and high resistance be joined up with a cell E of known E. M. F. and the deflection d read, the P. D. across r> V V ly is obtained from the proportion V V^\ E \ \ d^\ d. A galvanometer and cell E of a known E. M. F. can be con- nected across r and this resistance varied until equilibrium is obtained, then E V V^ It is evident that such a method would only be applicable in special cases. A potentiometer might be employed to measure the p. D. where considerable accuracy was required. The p. D. could also be determined by charging a condenser across /-. 9 2 ELECTRICAL MEASUREMENTS. One of the most convenient and accurate methods of measur- ing current is to employ a Weston voltmeter with a low reading scale across a shunt R through which the A V Z current is flowing, Fig. 75. Then if E be the voltmeter reading, C = -. R It is well to have a set of shunts of "*" say the following values, .001, .01, o. i, i. FJG ohm respectively. The low resistances to be used for heavy currents and the higher resistances for light currents. Where very small currents are to be measured, a high resist- ance galvanometer should be joined across a i-ohm shunt, through which the current flows, and the deflection observed. The value of the galvanometer deflection per scale division in microvolts can afterwards be obtained by means of a standard cell and high resistance. Since the best galvanometers have a sensitiveness of i microvolt, it is possible to measure current to the one-millionth of an ampere with a one-ohm shunt. The strength of current that can be determined by this method, when voltmeters and shunts of very low resistance are employed, is, of course, practically unlimited. Tangent Galvanometer. If the diameter of the coils of a gal- vanometer is great, compared to the length of the needle, the tangent of the angle of deflection is proportional to the current flowing through the instrument. The same effect may be obtained by placing the coils sym- metrically each side of the needle. For strong currents, a sin- gle turn of very thick copper wire should be employed. The " constant " of the galvanometer, or the amount of current necessary to produce i deflection, depends on the ra- dius of the coils, number of turns, and strength of field. The value of this constant can be obtained by observing the de- flection with a battery of known E. M. F. and a known resist- ance in circuit, or by comparison with a voltmeter, calibrated ammeter, standard voltmeter across shunt, etc. The tangent galvanometer gives a ready means for the com- parison of current strengths, but the use of the ammeter or shunted voltmeter, for most work, is much to be, preferred. Voltameters. According to the resolutions adopted by the Electrical Congress of 1893, the international ampere is con- sidered as represented sufficiently well for practical use by the unvarying current which, when passed through a solution of nitrate of silver in water, and in accordance with the specifica- MEASUREMENT OF CURRENT. 93 tions given, deposits silver at the rate of 0.001118 of a gramme per second. A neutral solution of pure silver nitrate, containing about 15 per cent, by weight of the nitrate and 85 per cent, of water should be employed. A current strength of about one ampere should be used and the specifications strictly followed if the most accurate results are desired. The value of the current can be obtained from the formula, C = Weight of silver deposited -=- (0.001118 X Time in seconds). For approximate work a voltameter consisting of copper in a solution of copper sulphate may be employed. An ampere will then deposit 0.0003281 of a gramme of copper per second. The objection to the use of voltameters is that the conditions of experiment, such as the strength of the current, size of the electrodes, strength of the solution, etc., may effect the accuracy of the results. If a current flows through water to which sulphuric acid has been added, the water is decomposed and hydrogen and oxygen liberated. These gases can be collected in graduated tubes and their volume measured from which the Current strength can be calculated. It is better in practice to measure only the hy- drogen, for a portion of the oxygen is condensed to ozone, and it is also slightly soluble in the solution. An ampere liberates .1155 cubic centimeters of hydrogen per second, if the volume be taken at the barometric pressure of 760 mm. and the temperature of o C. The volume observed must therefore be reduced to these standard conditions by the use of suitable formulae. Then the current in amperes = Volume in C. C. ~- (1155 X Time in seconds). Ammeters. The following classification indicates a few of the more important forms of instruments whose scale readings give current strength directly. f We s ton. AMMETERS. iAyrton and Perry. Hartman and Braun. Evershed's. Schuckerfs Magnetic Vane. The Weston ammeter is almost precisely similar in construc- tion to the Weston voltmeter, shown by Fig. 64. The movable coil, however, instead of being connected in series with a high resistance, is joined in parallel with a low resistance. This shunt in some of the instruments consists of a number of copper wires wound in parallel about the magnet and has about .002 ohm resistance. 94 ELECTRICAL MEASUREMENTS. FIG. 76. It is hardly necessary to say that the portable standard form of these ammeters are extremely reliable and accurate instru- ments. One form of the Ayrton and Perry ammeter is shown in Fig. 76. A short magnetic needle is placed between the pole pieces of a powerful perm- anent magnet which controls its direction and renders it independent of the earth's magnetism. When a current flows through the solenoid, it tends to rotate the needle toward the axis of the coil. This coil is of very low resistance and consists of but few turns of copper wire. By the proper shap- ing of the pole pieces, needle, and coil, the angular deflections are made proportional to the strength of the current. An ammeter largely manufactured by Hartman and Braun, of Frankfort, and used to a considerable extent abroad, is shown in Fig. 77. A very small tube, made of soft, thin sheet iron, is attached to a spring and lever arm, and placed near the end of an attracting solenoid consisting of a few turns of stout copper wire. By correctly .shaping the tube, the deflections can be made proportional to the strength of current. It is claimed in the most recent instruments, that the effects of residual magnetism and hysteresis are practically eliminated. This instrument in somewhat simpler form is known as the Kohlrausch ammeter. The Evershed instrument, known as the "Gravity" ammeter, consists of a magnetizing coil, placed with its axis horizontal. In the older form of these instruments, a small cylindrical piece of soft iron fixed to a spindle pivoted at its extremities, is placed within a coil and counter-weighted to maintain in certain posi- tion. When a current flows through the coil, the iron is rotated toward a position between the ends of two plates of iron also within the coil, but not shown in the diagram. For very heavy currents, the magnetizing coil consists of a massive tubular casting of copper divided by saw- cuts to form a "coil." V, In the more recent form of this instrument, two curved pieces of iron are placed within the coil. The outer is fixed and con- centric with the inner one, which is mounted on the counter- weighted spindle. When a current flows through the coil, the FIG. 77. AMMETERS. 95 movable piece of iron is urged round towards the position where the two pieces would form approximately a complete tube of iron. This same construction is also used for the Evershed volt- meters. A possible source of error in the above described am- meters is the retentivity of the iron. It is, therefore, well to test the readings with an increasing and decreasing current. In the Schuckert ammeter, an index is pivoted in the axis of the magnetizing coil, and carries a light strip of soft iron. An- other strip is fixed with the coil. When a current flows through the coil, these strips become magnetized and repel one another. The controlling force is gravity. The principle of the " Magnetic Vane " ammeter is similar to the above, the motion of the movable vane being opposed by a spring. With regard to the various forms of ammeters just described, depending on the magnetic effect of a coil on iron, it is not easy to say just how reliable or unreliable any particular instru- ment under varying conditions may be. Their chief advantage is, that they can be made more sensitive for a certain portion of the scale, that is, for a given strength of current, and that they may be employed for alternating as well as .direct currents. Whenever possible, however, the use of a Weston ammeter is to be recommended, or, better still, a standard Weston volt- meter, across a shunt, for in this case, by varying the resistance of the shunt, the range of measurement is unlimited. f Dynamometer. I Current Balance. ( , c i "Attraction " or Electro-Magnetic A mmeters. rs ' | P. D. and Shunt. [ Calorimetric Method. It should be understood that the methods and instruments described for alternating currents are also suitable for the measurements of direct currents. The dynamometer and current balance might have been classified with ammeters, since they are current measuring instruments, but on account of their importance it is perhaps better to treat them separately. Dynamo me tcr.-*- r \& principle of the electrodynamometer has been previously explained, and is shown in Fig. 67. For the measurement of current, the coils should be of very low resis- tance. In the Siemens dynamometer, much used for the measure- ment of strong currents, whether direct or alternating, one coil 96 ELECTRICAL MEASUREMENTS. is fixed permanently, whilst the other coil, of one or two turns, dipping with its ends in mercury cups, is hung at right angles, and controlled by a special spring below a torsion head. When a current passes, the movable coil tends to turn parallel to the fixed coil, but is prevented ; the torsion index being turned un- til the twist on the spring balances the torque. The angle through which the index has had to be turned is proportional to the square of the current strength. The axis of the movable coil should be in the line of the magnetic meridian, and the coils should be accurately perpen- dicular to each other. Where current strength is determined by the deflections of a dynamometer, the mean current strength of an alternating cur- rent is T V of the strength of the continuous current, which would give the same deflection. Current Balance. The principle of the Thomson current balance is indicated by Fig. 78. There are four fixed coils, A, B, c, D, between which is suspended, J~^ s-^^2 by a flexible metal ligament of fine ^h^ i ( r 2 ^ wires, at the ends of a light beam, a pair of movable coils, E and F. The current flows in such directions through the whole six, that the beam tends to rise at F, and sink at E. The beam carries a small pan at the end F, and a FIG. 78. light arm along which a sliding weight can be moved to balance the torque due to the current. The current is proportional to the square- root of this torque, the force being proportional to the product of the current in the fixed and movable coils, as in all electro- dynamometers. The current balance is in fact a current weigh- ing dynamometer. A complete range of these instruments has been designed, reading from .01 ampere to 2,500 amperes. The Thomson balance forms a most reliable standard for the measurement of current and the calibration of other instru- ments. When these instruments are made so as to measure alternat- ing as well as continuous currents, the current is carried by a twisted rope of copper wires, each of which is insulated. The object of this arrangement is to prevent inductive action. *' Attraction " or Electro-Magnetic Ammeters. Alternating cur- rents may be measured with more or less accuracy by the vari- ous forms of these ammeters, such as the Evershed, Schuckert, etc., previously described. AMMETERS. 97 When such an electromagnetic ammeter is employed for the measurement of alternating currents, the general tendency is for its readings to be lower than the correct value, if it is calib- rated to be correct for direct currents, chiefly on account of the ddy currents which are set up in the framework and metal parts of the instrument. It is found that the Evershed am- meters indicate about two per cent, lower than the true value of such an alternating current. This error, however, is corrected by permanently shunting the main ammeter coil by a smaller coil of copper wire which is overwound with thin iron wire, in order to raise its self-induction to the desired value. If there be any hysteresis or retentivity in the iron used in this class of ammeters, the error caused by it may be considerable. P. D, and Shunt. An alternating current may be conveniently and accurately determined, if the potential difference across a shunt of known resistance be measured by means of a Weston alternating current voltmeter or some form of electrometer. Since these instruments are not very sensitive for small poten- tial differences, and the resistance of the shunt must necessarily be low, the above applies especially to strong currents. Calorimetric Method. The heat units, or calories developed by a current in a given time, is equal to .24 C 2 R T, where C is the current in amperes, R the resistance, and T the time in seconds. Therefore, if this amount of heat be determined by means of a calorimeter, the current strength can be calculated. The method, however, is not a very practical one. If the expansion of a wire were used to indicate the current, as in the case of the Cardew voltmeter, the resistance would be too high to introduce into the circuit. Very High Currents and Very Low Currents. It has been stated that the measurement of potential differ- ence across a shunt of known resistance is a universal method for the measurement of current, and it is especially desirable for the determination of very strong or very weak currents. Suppose the standard form of Weston voltmeter be employed, with which readings can be made from ^^ volt to 150 volts, and that a shunt of .0001 ohm be used. Then the range of measure- ment would be from 33 amperes to 1,500,000 amperes. Now, the resistance of such a current could be very accurately measured by means of the double bridge, the best plan being to determine the resistance between two marks on a heavy bar of copper. The leads from the voltmeter should then be connected 9 8 ELECTRICAL MEASUREMENTS. to knife edges resting upon these marks. Since the resistance of the Weston voltmeter, even when the low reading scale is used, is about 500 ohms, the resistance of the leads and contacts would be entirely negligible compared to it. A mistake probably often made when very heavy currents are to be measured, is that of shunting a low reading ammeter. Here the case is entirely different, for then the contact resis- tances are added on to the low resistance of the ammeter and may produce a considerable error, even though the shunt has- been most accurately adjusted. Since a sensitive high resistance galvanometer will indicate a. micro-volt, if the galvanometer be shunted across one ohm, it is- then possible to measure current to one millionth of an ampere. Calibration of Ammeters. The best method of calibrating an ammeter is to compare the readings with those of a standard Weston voltmeter shunted across a known resistance. The ar- rangement is shown in Fig. 79, R being the resistance, and r an adjustable resistance to vary the current. The correct strength of current is, of course, given by the voltmeter reading divided by the resistance of the shunt In place Illlllll \AV\A/ of the voltmeter, the potentiometer can be used, according to the method given for calibrating a voltmeter. vSince the voltmeter may be com- pared to the Clark cell by means of the potentiometer, and the shunt resis- tance to the standard ohm, the stand- dards of E. M. F. and resistance become . FIG. 79. also the standards for current. By means of the Thomson balance, an ammeter can be very accurately calibrated. The ammeter can also be checked by comparison with the voltmeter. When it is desired to compare a low reading ammeter that has been calibrated with a high read- B ^y m g ammeter, the arrangement shown, vVW v in Fig. 80 can be employed. If the resistance of the shunt r is equal to ^ of the resistance of Ammeter i 4- R r then ammeter i will only receive .01 of the entire current that flows through, FIG. 80. ammeter 2. By this means an am- meter only reading to 15 amperes could be compared with one reading to 1,500 amperes. AMMETERS. 99 Absolute Determination of Current. Current strength can be measured in absolute units from the deflections of a tangent galvanometer, if its radius, number of turns, and strength of surrounding field be known. The equation is : C= X & X tan a , 2 W 7T where r is the radius of the galvanometer coils in centimetres, n the number of turns, H the strength of field, and a. the de- flection. Considerable care should be used in this determination, if accurate results are desired. This method is interesting on account of its employment in the determination of the value of the standard ohm, and also- forms an additional check on the other methods of current measurement. CHAPTER XVIII. r j Weston's. ENERGY.] Wattmeter. \ Siemens'. [_ Voltmeter and Ammeter. The amount of electrical power consumed by lamps, motors, etc., can be directly measured by means of instruments known as voltmeters. The unit of electrical energy is the watt, or kilowatt (= 1,000 watts), and a horse-power is equivalent to about 746 watts. Most of these wattmeters are modifications of Weber's dynamo- meter, in which a fixed coil produces a field, and tends to turn a movable coil. One of the best known wattmeters is Siemens' dynamometer, in which one coil is wound with fine wire and is put in shunt to the part of the circuit in which the power is to be measured, and a thick wire coil which is joined in series. The force is then proportional to the product of the currents in the two coils, that is, to the product of the potential difference and current, or to the power. In the Weston wattmeter, the motion of the movable coil is opposed by a spring in a manner similar to that used in the voltmeter and ammeter. The resistance of the pressure or shunt coil should be as high as possible, since the current that it takes also passes through the series coil, and may thus cause a considerable error. As the pressure coil generally takes more power than the current coil, it is best to put it in shunt to the current coil in addition to the lamp or other device across which the power is to be deter- mined. Some wattmeters are compensated for this error. Electrical energy can be very readily determined by means of the voltmeter and ammeter. The voltmeter is _______ used in shunt and the ammeter FIG. 81. in series (Fig. 81), and the power is then obtained by multiplying the potential difference 100 ENERGY. lor indicated by the voltmeter by the reading of the ammeter. If a Weston standard voltmeter be employed, the error caused by the current taken by the voltmeter is very small. This error may be still further reduced by placing the voltmeter also in shunt to the ammeter. ( Voltameter. (Edison Meter.) QUANTITY. \ "Meters." ( Ballistic Galvanometer. The amount of electrolytic action in any voltameter is pro- portional to the strength of current and the time ; that is to say, it is proportional to the quantity of electricity. The unit of measurement is the ampere second or coulomb. The practical unit is the ampere hour. The voltameter generally used in practice is the Edison " chemical " meter. It consists of two jars of zinc sulphate with zinc electrodes so connected across a shunt that they receive, say, J^VTT f tne entire current. The resistance of an electrolyte decreases with a rise in temperature. To compensate for this error, copper wires are joined in series with the cells. Two cells are used for greater accuracy, the amount the electrodes lose in weight in each being determined. These two results should, of course, check each other. The coulomb deposits 0.33696 milligramme of zinc, and the ampere- hour 1,213 milligrammes. The arrangement of the Edison meter is shown in Fig. 82. It is extremely difficult to measure satis- factorily electrical quantity on a commercial scale. A number of instruments have been devised for this purpose, and they are known under the general name of " meters." Prob- ably one of the best of these meters is the Thomson-Houston recording wattmeter. It consists essentially of two thick wire coils placed in series in the circuit, and a thin wire coil placed in shunt around the circuit whose power is to be measured. The shunt coil is mounted on an axle carrying a copper disk moving between the poles of permanent magnets. Under these condi- tions, the rate of rotation produced in the movable coil is pro- portional to the energy consumed in the main circuit. The number of revolutions is recorded by clockwork and the instru- ment is graduated to indicate watt-hours, etc. In the Forbes' meter, the current passes through a number of fine wires placed in parallel. These wires becoming heated, produce a rising current of warm air, and this rotates a spindle carrying mica vanes. 102 ELECTRICAL MEASUREMENTS. The Ferranti meter consists of a vessel containing mercury, above which is placed a solenoid. The current is led to the mercury at the centre of the vessel and leaves it at the cir- cumference, then passing through the magnetizing solenoid, the mercury is urged to move in a direction at right angles to that in which the current is flowing through it, and also at right angles to the lines of force of the field. This, of course, pro- duces rotation. The amount of rotation is measured by means of a float geared to the proper indicating device,. The Aron meter consists of two clocks geared differently. The pendulum of one clock carries a permanent magnet. Be- neath this is placed a solenoid, through which flows the main current. When both pendulums oscillate at the same rate, no movement of the indicating pointers takes place, but they begin to indicate if one of the pendulums is accelerated. This accel- eration is proportional to the strength of the current flowing through the solenoid. They can be adjusted to indicate ampere- hours. In order to make this or any similar meter show the energy consumed, or watt-hours, it is necessary to multiply the ampere- hours by the pressure at which the current is supplied. There- fore the accuracy of the result depends upon the constancy of the pressure as well as the accuracy of the instrument. The deflections of a ballistic galvanometer are proportional to the quantity of electricity passing through the galvanometer, if the discharge occupy a very short time compared to the time of vibration of the galvanometer needle. The application of this fact, however, is in the absolute determination of capacity and inductance. CHAPTER XIX. CAPACITY. DEFLECTION Direct Deflection* Direct C rr .T ( Bridge Method. ZERO METHODS., -j Pote * tiometer Method (Mixtures.)* ABSOLUTE DETERMINATION (Ballistic Galvanometer.) Electrostatic capacity may be defined as the ratio of the quan- tity of any electrical charge to the E. M. F. producing that charge, or F = Sr, Scientifically speaking, it is the ratio of dielectric strain to dielectric stress, the term " quantity " of electricity be- ing used only as a matter of convenience. The unit of capacity, or the farad (^), is such a capacity that the unit quantity, one coulomb, is obtained under the pressure of one volt. This ca- pacity is far too large tor ordinary measurements, so the prac- tical unit employed is a millionth of this, or the micro-farad. The accurate determination of capacity in many cases is im- possible, since most condensers, to a certain extent at least, and practically all cables exhibit the phenomena of absorption and residual charge. Therefore, when the capacity is stated, all the conditions of measurements should be given. Direct Deflection. In this method, a standard condenser, F, is charged by a battery, B, Fig. 83, and then dicharged through a high resistance galvanometer, and the de- flection d observed. The unknown condenser, F 2 , is then substituted, and the deflection d z noted. Then F! : F 2 : : ^ : 4- Some uniform time of charge, such as five seconds, should be adopted. Several observa- tions should be taken in each case, and the F *G. 83. mean used in the calculation. The method is suitable and con- venient where only approximate results are desired, 104 ELECTRICAL MEASUREMENTS. The absorption of various condensers may be studied by this method by observing the deflection after charging for dif- ferent lengths of time, such as i second, 30 seconds, i minute, etc. The residual charge can be determined by discharging, in- sulating for one minute, and discharging again, insulating for another minute, etc. It is important in the above method that there be no self-induc- tion in any portion of the circuit, or in the galvanometer shunt r if it be employed, for, of course, this would change the value of the deflections and thus cause an additional error in the measurement. Divided Charge. The connections for this method are shown in Fig. 84. The standard condenser, F, is charged by closing the battery key, k. It is then discharged, and the deflection, d, noted. It is again charged, the key k is opened and the key K depressed for a few seconds, by this means allowing the charge to divide between the two con- densers, F 2 , being the unknown condenser or eable. The standard condenser is then once more discharged. Call this deflection 4, then ^i 4, f r the quantity of charge in each con- denser is proportional to the capacity. This method is said to be very accurate for the measurement ot the capacity of long cables. Loss of Charge Discharge. The capacity of a condenser can be calculated from the formula T 2.303 R (log 4 log 4) when d is the discharge deflection obtained immediately after charging, 4 the deflection after charging, and then insulating for T seconds, R the resistance between the poles of the con- denser (if this be expressed in megohms, the capacity will be obtained in micro -farads), and 2.303 the modulus to convert the ordinary or Brigg's logarithms to natural logarithms. The con- nections are the same as Fig. 83. If a mica condenser be used, a resistance of several megohms may be placed between the poles. To measure the capacity of cables by^this method, the insulation must be determined and this value substituted for R. Since the insulation is such a variable quantity, the above method is only very approximate. Deflection. K modification of the method just described is shown in Fig. 85. CAPACITY. 105 The steady deflection is first observed with the key closed, d\ it is then noted after T seconds 4, and the capacity calulated from the formula given above. The resistance, R, should be great enough, several megohms, so that the charge will not be lost too rapidly. If the resistance of the condenser be low or if a cable is used, and if this resistance be callled r, then the value of the resistance to be used in the above equation Rr Bridge Method. Zero methods have the advantage that the errors due to reading the galvanometer deflections are avoided, and that the effects due to induction may be partially, if not entirely, eliminated. The Bridge method is applicable to ordinary condenser work and to short lengths of cable, but is not suitable for great lengths of cable, on account of the influence of inductive retardation. The connections for the measurement are shown in Fig. 86. The method is very similar to the Wheatstone bridge. When the resistances R l R z , which should be high, are so adjusted that there is- no deflection of the galvanometer on making contact at a or b, then R l : R : : F* : F^. That is, the capacities are inversely proportional to the resistances, During the adjustment of R^ R.,, contact should be made at the point b, in order that the condensers are kept discharged. If the insulation of the condensers be not good, of course, an error may be caused by the current flowing through the con- densers. Method of Mixtures (Thomson's Method). This method may be considered the standard for cable work, and is also very- suitable when the most accurate comparison of condensers is desired. The method de- pends on the principle that the "quantity" of electricity in a condenser is equal to its ca- pacity, multiplied by the p. D. of the charge, or Q = F E. If, then, two condensers F l F z have the same charge, Q = F l E^ = F 2 E%, or F v : F. 2 : ; E z : E. In this method the ratios of E^ E z are the same as the resistances R R*, ; hence, F 1 : F z : R z : R r The arrangement for this measure- ment is shown by the diagram, Fig. 87. FIG. 87. io6 ELECTRICAL MEASUREMENTS. The rheostat ^ R z should be of high resistance. It is con- venient to use in place of them one of the " potentiometers " or slide coil bridges previously described. It is best to employ a special key, known as the Lambert capacity key, indicated in the diagram by L. The manipulation is as follows : Contact is made at the points ab, and the condensers are thus charged across R v and j? 2 . Contact is then made at the points c d, and by this means the charges of the condensers are allowed to mix. Finally, contact is made at e, and the galvanometer, being thus placed in circuit with the condensers, is deflected, if the charges are unequal. The adjustment of R l R z is repeated until the gal- vanometer shows no deflection. Some standard time of charg- ing should be employed, say, ten seconds, and the charges should be allowed to mix ten seconds. For long cables, a five minute charge is recommended and a time of mixture of ten .seconds. The values of F^ F 2 should not be very unequal that is, F should not be much less than \ of F& for if the capacities are very different, the potential of one charge may be so much higher than that of the other that an error may be caused by .absorption. Absolute Determination. The " quantity " of electricity which -discharged through a ballistic galvanometer will produce a given deflection is expressed by the equation In the above equation -- * is the " constant " of the galvanometer, EI that is, if a potential difference E be used through a resistance R, a steady deflection d is obtained. 4 is the throw of the galvanometer produced by the quantity Q, T the time in seconds of a complete or double vibration of the galvanometer on open circuit, and / is the logarithmic decrement. If a condenser of capacity F be charged by a potential differ- ence -#2 , then since consequently 4 T((I + E, V 2 TT In a ballistic galvanometer, the time of vibration of the mov- ing system should be slow, the moment of inertia large, and the CAPACITY. 107 decrement or damping but slight. These conditions are fulfilled by several forms of galvanometer. One in which bell magnets are employed, shown in Fig. 7, and also the special forms of the D'Arsonval and the Ayrton and Mather galvanometer previ- ously described. Either of the two latter galvanometers is. much to be preferred for practical work over the first form, in which the magnetic system is movable. To observe the time of vibration T, the galvanometer is given a vibration of 200 to 300 scale divisions and time of, say, 10 or 20 vibrations determined, the mean of several sets of observa- tion should be taken. If a galvanometer with movable magnetic system is employed, the deflections are con- trolled by means of a " check coil," that is a solenoid in series with cell placed near the galvanometer, Fig. 88. If the D'Arsonval form of galvanometer is used, a cell and key may be placed in series with the galvanometer, or the galvano- meter may be brought to rest by short circuiting. The decrement is the ratio of the amplitude of any vibration to that of the next succeeding vibration. To obtain this, the tenth vibration after the first should be observed. Suppose this ratio is 1 140 ; then the decrement equals 1.04. If the decrement is small, such as the above example, then it is sufficiently ac- curate to call the factor f i 4--1 equal to 1.02. Actually A is FIG. 88. f i -f" -) equal equal to the log. of the decrement X 2.303. To determine the " constant " of the galvanometer, the deflec- tion ^ is observed when a constant cell, such as a Daniell cell, or preferably a storage cell, is used. The galvanometer may be shunted, a high resistance placed in series with, or better still, the cell can be shunted. This last arrangement is shown in Fig. 89. In this case R is the resistance of the galvanometer and E l is equal to E x .004. Then condenser F is charged by the same cell, shunted if need be, and the deflection d z observed. The arrangement is shown by Fig. 90. Here 2 is equal to E x .700. Thus the E. M. F. of the cell need not be known, since it cancels the equation given above. This method of measuring capacity is of considerable importance, for by it a standard condenser may be accurately calibrated. Of course, after the capacity of a standard is once accurately known, other standard con- densers can be compared to it. FIG. 89. CHAPTER XX. INDUCTANCE. BRIDGE METHOD (Maxwell's.) COMPARISON WITH STANDARD. SECOHMMETER j With Standard. METHOD. \ Without CONDENSER \ Deflection. METHOD. { Zero. CALCULATION. [IMPEDANCE.] By the term " inductance " is meant the coefficient of self-in- duction. When a current flows through a circuit, a magnetic field is established about the conductor carrying the current. If the strength of the current rises, the strength of the field also varies. This has the effect of producing or withdrawing "lines of force," and if these cut adjacent wires in the circuit r an E. M. F. is developed in a direction opposite to that in which the current is flowing. The unit of the inductance (L) is the henry or such an induct- ance that if the current varies one ampere per second, a counter E. M. F. of one volt is developed. From a consideration of the absolute system of units and dimensional formulae, this has also been known as the " secohm " or "quadrant." This coefficient may be determined by several methods. Bridge Method. This method requires a ballistic galvano- meter. The coil s, whose inductance is required, is placed in the arm, c d, of a P. O. bridge, Fig. 91. The bridge coils, A, B, are made equal to each other, and as nearly equal to s as possible. An extra rheostat, R 2 , is multiplied with R X ; by this means, an exceedingly fine adjustment can be obtained. All the resistances, except s, should FIG. 91. foe non-inductive. The resistance in the arm e c is adjusted until on closing, first the battery key and then the galvanometer key, no deflection is 108 INDUCTANCE. 109 observed. The galvanometer key is then first closed, and after- wards the battery key and the throw of the galvanometer, d z caused by the inductance of s obtained. The resistance in the arm e c is changed a small amount by altering the resistance in R 8 . Call this change of resistance in the arm e e equal to r. The bat- tery key is then closed, and the steady deflection, d l obtained on closing the galvanometer key observed. The inductance is then obtained by the equation L = T -Ji X Tic X (' + - where T is the time in seconds of a complete or double vibra- tion of the galvanometer, and A the " logarithmic decrement." These latter constants should be determined in a similar man- ner to that given for the absolute measurement of capacity. The complete equation requires in place of the expression 2 sin. /2 2^ k u t s i nce the angle corresponding to d z is usually tan. , obtained either by means of a telescope and scale, or a slider and sight moving directly on the scale. For approximate work, the deflections of an ordinary compass needle can be taken in place of using a mag- netometer. The magnet is then placed at a less distance, r', from M, and the angle of deflection ^ observed. From these observa- tions the value of is obtained from the equation : OC nil __ i r* tan