LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class Electric and Magnetic Measurements and Measuring Instruments BY FRANK W. ROLLER, M.E. v MEMBER, A.I.E.E., A.S.N.E., A.E.S., ETC., NEW YORK McGRAW PUBLISHING COMPANY 1907 COPYRIGHT, 1906, MCGRAW PUBLISHING COMPANY PEEFACE. THE following volume has been written for the use of those who have to do with electrical and magnetic measurements in one form or another, and as these must be made in practically all branches of the profession, from the simple testing out of lines and resistances to the most elaborate determination of designs, it is hoped that its sphere of usefulness will be quite large. The subjects have, throughout, been approached with a view toward their use by users, not manufacturers, of measuring apparatus, that is to say the book is in no sense intended as a treatise on the design and construction of instruments, the circle interested being decidedly limited. Descriptions are, however, given of apparatus as well as of methods of test, because knowl- edge of the manner in which a principle is utilized in concrete instruments often suggests, to one having a determination to make but is at the same time without the particular form of appliance ordinarily employed for that purpose, means of adap- ing thereto some other device which is at hand. Further, in illustrating examples of instruments for different kinds of work, there has been in mind the idea that these will enable engineers to decide, with the aid of their general engineering knowledge, which are the best suited to their particular requirements. In line with the general idea of making the volume of value to the profession at large, there has been adopted the use of an appendix which is thought to be novel in character and to which attention is invited. It will be seen by reference thereto that, without cumbering the text with numerous reiterations ol manu- facturers names or the description of multitudinous instruments of a given class differing one from the other only in minor iii 235472 iv PREFACE. detail, those who are confronted with the necessity of procuring apparatus for making given tests have provided a convenient means of ascertaining not merely the names but also the addresses of the majority of manufacturers of that particular kind of goods. Another point which is thought to be novel and useful is the employment in diagrams of connection of the actual word or reference letter that occurs at each point, instead of the more or less conventional symbol therefore plus a reference letter for the text. The author has used this system in his own work for some time past and finds it of decided utility as a time saver in making sketches and in the interest of clearness. Owing to certain vexatious delays in connection with some of the illustrations, the issue of this book has been deferred^for a considerable period after the completion of the manuscript. It is not, however, thought that the developments in the field in the interim have been of sufficient general interest or applicability to warrant revision. The author in conclusion desires to make acknowledgment of the courteous services of Mr. Townsend Wolcott, who was good enough to read and correct a large portion of the proofs. - F. W. R. NEW YOKK, November, 1906. CONTENTS. PART I. CHAPTER. PAGE. I. DEFINITIONS OF UNITS 1 II. LABORATORY AND COMMERCIAL STANDARDS OF RESISTANCE, CUR- RENT, E.M.F., CAPACITY, AND INDUCTANCE III. GALVANOMETERS 38 IV. POTENTIOMETERS , 73 V. THE MEASUREMENT OF RESISTANCE 93 VI. MEASUREMENT OF CURRENT 152 VII. MEASUREMENT OF POTENTIALS 193 VIII. MEASUREMENT OF POWER 215 IX. MEASUREMENT OF CAPACITY 234 X. MEASUREMENT OF INDUCTANCE 247 XI. MISCELLANEOUS DETERMINATIONS , 257 XII. THE LOCATION OF FAULTS 288 PART II. I. RECORDING INSTRUMENTS 304 II. INTEGRATING METERS 324 III. MAXIMUM DEMAND METERS 339 PART III. I. MAGNETIC UNITS , 343 II. MEASUREMENT OF FIELD STRENGTH 347 III. MEASUREMENT OF PERMEABILITY , 354 IV. HYSTERESIS 380 APPENDIX . 389 ELECTRIC AND MAGNETIC MEASUREMENTS AND MEASURING APPARATUS. PART I. CHAPTER I. DEFINITIONS OF UNITS. IN order to measure a quantity, condition, or state of matter, we must first have a standard of reference. For although such quantity, condition, or state of one body can be compared directly with the similar property of another body, this direct comparison cannot be extended to three or more of them, unless the property of all the other bodies be referred to the said prop- erty of some selected one, in which case the said one becomes, provisionally, a standard of reference. Authorized and com- monly accepted standards are called units ; and as we have here to deal with electrical measurements, definitions of electrical units will be first in order. UNIT OF RESISTANCE. When an electric current flows through a conductor of electricity, a resistance to this flow is always offered by the conductor. The amount of the resistance is dependent upon the material of the conductor, its physical condition, geometrical dimensions, temperature, and, under certain circumstances to be treated later, other conditions. The unit of resistance, with which all other resistances are compared, is that which is offered to a current of uniform strength and constant direction by a column of pure mercury at the temperature of melting ice, having a mass of 4.4521 grains, a constant cross-sectional area, and a length of 106.3 centimeters. This unit is called the ohm, and its value as just given is that determined upon by the "International Congress of Electricians," in 1893, and made legal in the United States 1 MAGNETIC MEASUREMENTS. by Act of Congress in 1894. It is officially designated and commonly known as the " International Ohm " and is the recognized standard to-day. Before the adoption of the " Inter- national Ohm " three other standards were in use at various times. The first was the "Sie men's Ohm," this being repre- sented by the resistance offered by a column of mercury having a cross-sectional area of one square millimeter, and a length of one meter. The second unit is that commonly known as the " B. A. Ohm," "B. A." being an abbreviation for "British Association for the Advancement of Science," who proposed its adoption. In it the length of the cylinder of mercury is 104.8 centimeters. The third standard adopted was the so-called " Legal Ohm" (about which, however, there was nothing legal), which was adopted as a temporary standard by an International Committee, in 1882. It is represented by the resistance of a column of mercury having a cross-sectional area of one sqtiare millimeter and a length of 106 centimeters, at the temperature of melting ice. As there are many pieces of apparatus, more particularly resistance boxes and Wheatstone bridges, calibrated in the last-named units still in use, the following comparison table is given: TABLE I. Siemen's Ohm = .9408 International Ohms. B. A. Ohm = .9866 International Ohms. Legal Ohm = .9972 International Ohms. UNIT OF CURRENT STRENGTH. The unit of strength of electrical current is called the ampere. A current of one ampere strength when passed through a solution of nitrate of silver, under the conditions named in the footnote below, will cause the deposition of .001118 grams of silver per second. This value of the ampere is as defined by the International Congress of Electricians, in 1893, already referred to, and is commonly accepted as the standard to-day.* * The specification for the construction and use of the " Silver Voltameter" used in laboratories as a primary standard for determining current strength is substantially as follows : The voltameter consists in general of a platinum bowl having a diameter of not less than 10 cm. and a depth of 4 to 6 cm., in which is suspended horizontally, by tine platinum wires, a plate of pure silver having an area of about 30 sq. cm., and a thickness of 2 to 3 mm. The silver plate is wrapped around with clean filter paper secured at the back with DEFINITIONS OF UNITS. 3 It is, however, simply the commercial standard of current, the fundamental standard from which it is derived being ten times as great, and represented by a current of such strength that when passed through a conductor having a length of one centimeter bent into an arc of a circle having a radius of one centimeter, it will attract or repel a unit magnetic pole placed in the center of the circle with a force of one dyne. Later determinations seem to show that 1 ampere flowing through a silver voltameter for 1 second will deposit .001119 grams of silver, instead of .001118 grams, and that the International Congress definition is that much in error. It nevertheless remains in almost uni- versal use. UNIT OF ELECTROMOTIVE FORCE. Electromotive force, commonly abbreviated to E.M.F., is the force or stress which sets up or tends to set up a flow of electric current, just as in hydraulics pressure tends to set up a flow of liquid. As the unit there is taken that E.M.F. which, contin- uously applied in a constant direction to a circuit having a resistance of one ohm, causes current to flow at the rate of one ampere. This unit is called a volt, and as defined by the Inter- national Congress already mentioned, is represented with suffi- cient exactness for practical purposes by ^f f ^ -of the E.M.F. at 15 degrees C. of the cell known as the Clark cell, a descrip- tion of which will be given later (see page 24). It should here be noted that, as the ampere is definitely determined and of a sealing wax, in order that no detached particles may fall into the platinum bowl. A solution of nitrate of silver, containing about 15 parts by weight of the nitrate to 85 parts of water, is poured into the platinum bowl to a depth sufficient to completely submerge the silver plate. The current to be measured is passed through the voltameter thus formed, entering through the silver plate and departing through the platinum bowl. The bowl is thoroughly cleaned, dried, and weighed before pouring in the solution. After the current of constant strength has been passed through the voltameter for a given period, carefully measured by a good watch, the bowl is emptied, thoroughly washed, and dried with alcohol. It will be found on again weighing the bowl that it has gained in weight, the added weight being that of the pure silver deposited by the action of the current. To find the current in amperes that was flowing, divide the increase in weight measured in grams by the number of seconds that the current was flowing and by .001118. To obtain concordant results some manipulative skill is required, and the nature of the voltameter renders experiments expensive. For this reason this form is used but seldom outside of the laboratory, and it is not thought that a sufficient number of readers will be interested in the minutiae to warrant the devotion of further space to this subject. 4 ELECTRIC AND MAGNETIC MEASUREMENTS. fixed value, the volt which is dependent on the ampere and the ohm has not, because as before stated the ohm has had differ- ent values from time to time. The system under which the volt is measured should hence always be stated. If it is under the old B. A. or the legal system, the value may be converted into the now commonly accepted International volt with the aid of Table I. UNIT OF CAPACITY. Any two electric conductors separated by a dielectric, such as air or any other nonconductor, will store up a charge of electricity if a difference of potential be applied to them. The apparatus formed by the conductors and the intervening dielec- tric is called a condenser, and its property is known as capacity. A condenser is of unit capacity when one volt difference of potential applied to its terminals causes the flow and storhfg up of the unit quantity of electricity (one ampere for one second, namely, one coulomb). The unit of capacity as just defined is called the farad. Being far too large to be conveniently used in commercial work, the microfarad, which is one one-millionth part of a farad, has become the commercial standard for the comparison of capacities of condensers, cables, etc. UNIT OF INDUCTANCE. In addition to the ohmic resistance offered to the flow of the electric current, every electric circuit has another property known as inductance which is analogous to inertia in mechanics, and which opposes any change in current strength. This op- position is offered for the following reasons. A conductor carrying an electric current is surrounded by a magnetic field, the paths of whose lines of force are circles concentric with and whose planes are at right angles to the conductor. The strength of the field is proportionate to the strength of the current and varies therewith. If, therefore, the current's strength increases, an additional number of lines of force is sent out by it, and expanding like the wavelets in a pond when a stone is thrown into the water, cut other proportions of the circuit. In accord- ance with the laws of electro-dynamics, these waves, as they cut the conductor, set up an E.M.F. which is opposite in direc- tion to the E.M.F. causing the current flow, and therefore DEFINITIONS OF UNITS. 5 makes it impossible for the current to reach instantaneously the value due to the E.M.F. impressed upon the circuit. The unit of inductance is called the henry, and is the induc- tance of a circuit of such character that when the current therein changes in strength at the rate of one ampere per second, there is set up a counter electromotive force of one volto OHM'S LAW. From the definition of a volt above given it is evident that there exists a certain relationship between volts, amperes, and ohms in a given circuit. To state the law more concisely than in the definition : The current flowing through a circuit is di- rectly proportional to the E.M.Fo impressed thereon, and in- versely proportional to the resistance of the circuit. If we use the letter I to designate current, the letter E to designate E.M.F., and the letter R to designate resistance, the formula W expressing this law of relationship is, I = . This law is \> known as Ohm's law and holds good when I is maintained constant in value and direction. Where the value of I or its direction varies, other elements enter which modify this simple relationship, a matter which will be enlarged upon later. CHAPTER II. LABORATORY AND COMMERCIAL STANDARDS OF RESISTANCE, CURRENT, E.M.F., CAPACITY, AND INDUCTANCE. RESISTANCE STANDARDS. The Mercury Ohm. As mercury at the temperature of melting ice is a liquid, and, moreover, readily oxidized when exposed to air, it is evi- dent that the only way to make a standard International ohm in accordance with the specifications laid down in the defini- tion is to enclose the proper quantity of mercury in a tube of glass or similar material. The difficulty of preparing such a tube so that the proper length holds the right weight of mer- cury, of making contact with the mercury at proper points, of obtaining mercury of perfect purity, and of maintaining the whole apparatus at an accurate uniform temperature, together with other minutiae which must be taken into account if accu- rate, results are to be had, evidently call for considerable care and manipulative skill of the highest order, and prohibit the use of standards so made, except under very exceptional circum- stances. In Fig. 1 there is shown the standard mercury ohm that is used in the Physikalische-Technische Reichsanstalt, in Berlin. The illustration is given to emphasize the bulk and real com- plexity of this apparently simple apparatus. As can be gathered from the proportions, it is in the neighborhood of six feet long. Even when a mercury standard ohm is prepared which com- plies with all of the conditions laid down in the official desig- nation of the unit, we have a piece of apparatus that is only a secondary standard, and not one directly derived from fun- damental units of length, mass, and time. Lorenz Apparatus. The standard of resistance can be fundamentally derived by means of the so-called Lorenz apparatus, whose method of opera- tion is based on the following principle : 6 STANDARDS OF RESISTANCE. 8 ELECTRIC AND MAGNETIC MEASUREMENTS. Referring to Fig. 2, >&S', is a coil of several turns of insulated wire, whose diameter is very accurately measured. Mounted co-axially with this coil and within it is a metal disc, D, rotating about a shaft, 0. If current is passed through the coil, S, lines of magnetic force flow through the interior of the coil, parallel to its axis and cut the disk, D, in consequence of which a difference of potential exists between the center, 0, of the disk and its periphery. If suitable means of making contact with the center and periphery are provided, that poten- tial can be measured in an external circuit. PQ is a bar of resistance metal and B a set of batteries of appropriate strength, the whole being interconnected as shown in the diagram. If now current be allowed to flow from the batteries through the coil, $ and bar, PQ, connected in series therewith, we have a drop of potential along the bar. If G- be a galvanometer in- serted in the circuit through which flows the current cfue to the difference in potential between the center and the periphery of the rotating disk, and if the terminals of that circuit be attached to the bar, PQ, at the points X, Y, with the positive terminal nearest the positive end of the bar, the distance between X and Y may be varied until the galvanometer shows that no current is flowing through the disc circuit, in which circum- stances the E.M.F. supplied is of course equal to that due to the difference in potential between the points X and You the bar. Write : R = resistance between X and Y, I = current flowing through the coil and the bar, M = coefficient of mutual inductance between the coil and the disc, n = the speed of revolution of the disc, E = the E.M.F. set up in the disc, then E = MIn By Ohm's law, the difference of potential between the points X and Y on the bar equals RI, and by hypothesis this also equals the E.M.F. in the disc, hence, E = MIn = RI, or R = Mn. The resistance between the points X and Y can therefore be determined directly by calculation from the geometrical STANDARDS OF RESISTANCE. 9 dimensions of the apparatus and from measurement of the speed of rotation of the disc. It might seem that it would be a very simple matter to measure resistance in this way, but as a matter of fact it is extremely difficult to determine the dimensions of the apparatus with a sufficient degree of accuracy, and almost impossible to measure the speed of rotation as closely as is necessary for accurate work. These physical difficulties are so great that, we understand, what is probably the only Lorenz apparatus on this continent has remained idle for years because no one who has access to it has sufficient leisure or sufficient mechanical FIG. 2. skill to get from it results that can be considered as accurate as those derived from a mercury standard. Metallic Alloy Standards. Practically all commercial and the majority of laboratory standards of resistance are formed of wires or plates of high resistance, low temperature coefficient, resistance alloy cali- brated by direct or indirect comparison with one of the stand- ards already described. Fortunately, as will be demonstrated later on, electrical resistance can be measured with the highest degree of accuracy more easily perhaps than any other electrical quantity or property, and there are numerous reputable manu- facturers who are prepared to supply secondary standards guaranteed to be correct within one fiftieth or even one one- hundredth of one per cent, accompanied, if necessary, by a 10 ELECTRIC AND MAGNETIC MEASUREMENTS. certificate of this degree of accuracy from national standardizing bureaus. As this degree of accuracy is more than sufficiently good for all commercial purposes, and the value of a properly constructed resistance is very stable, such secondary standards are in universal use in commercial work. The number of resistance alloys is exceedingly large and the number of trade names for them as varied. Platinum silver, an alloy of one part platinum with two parts of silver, is in extensive use for fine standards, as is also manganin, an alloy of copper, manganese, and nickel. The latter alloy is preferable to the former in that it has a higher specific resistance and a lower temperature coefficient, but it is somewhat oxidizable and must be protected from atmospheric influences by gilding or varnish- ing, when in the form of small wires or thin sheets. German silver, an alloy of copper, nickel, and zinc, although frequently used in rough commercial resistances, is not suitable for stand- ards because of its comparatively high and somewhat uncertain temperature coefficient. German silver is the name given to a great variety of alloysjiaving the qualitative compositions just stated but differing widely in the quantities of ingredients. Appended Table II gives the properties of several common resistance alloys. TABLE II. Alloy. Resistance per cm. 3 in C.G.S. unit at C. Temperature coefficient at 15 C. Composition in per cents. Platinum Silver 31 582 000243 Pt 33/ AP- 66/ Platinum Iridium 30 890 000822 J. U 00 / , ^Yg UU / Pt 80 / Tr 20/ Platinum Rhodium 21,142 0.00143 Pt 90%, Rh 10% Gold Silver Manganese Steel 6,280 67,148 0.00124 0.00127 Au 90%, Ag 10% Mn 12%, Fe 80% Nickel Steel 29,452 0.00201 Ni 4.35% German Silver Platinoid 29,982 41,731 0.000273 0.00031 Cu 50%, Zn 30%, Ni 20% Manganin 46,678 4,641 2,904 0.0000 0.00238 0.00381 Cu 84%, Mn 12%, Ni 4% Al 94%, Ag 6% Al 94%, Cu 6% Aluminum Silver Aluminium Copper Copper Aluminium Copper Nickel Aluminium Titanium Aluminium .... 8,847 14,912 3,887 0.000897 0.000645 0.00290 Cu 97%, Al 3% Cu87%, Ni6.7%A16.5% Standards of resistance made of solid alloys take on different forms according to their resistance and the amount of current STANDARDS OF RESISTANCE. 11 that they are to carry. For accurate work they must be arranged to be immersed in oil baths, which will keep all of the parts at a uniform temperature, which can be measured t>y a thermometer that is also immersed in the oil. We will not describe here the old British Association form of standard re- sistance, as this proved unsatisfactory because of the difficulty of determining exactly the coil temperature. The form adopted by the Reichsanstalt is shown in Fig. 3. The resistance wire, J., is heavily insulated with silk and soldered at its ends to the copper terminals, BB. The long loop made by the wire then FIG. s. has its two sides brought close together and is wound spirally about the thin brass cylinder, (7, as shown. This form of wind- ing makes the self inductance very small. The wire loop is purposely made of a somewhat higher resistance than th.it to which the standard is to be adjusted and is then shunted by a fine resistance wire, whose terminals are likewise soldered to the ends of the rods, BB. If the fine wire has, say, one hun- dred times the resistance of A per unit of length, a change of one inch in its length will correspond to a change of one one- 12 ELECTRIC AND MAGNETIC MEASUREMENTS. hundredth of an inch in the length of the main wire, and very fine adjustments are thus made possible. The resistance unit as a whole is placed within a vessel, D, filled with oil, and the temperature is read off by means of a thermometer placed therein. It is common to supply also a stirring apparatus to keep the oil in circulation, and to insure that all of the parts are of the same temperature. Resistance standards of a very low value in ohms are usually made of a size sufficient to carry a great deal of current with- out overheating, as they are ordinarily wanted to measure current in amperes by observing the potential drop in volts at their terminals when the current is flowing. Such resistances often take the form shown in Fig. 4, in which the resistance metal is in the shape of strips or ribbons instead of wires, electrically connected in parallel and sweated into heavj* termi- nal .blocks. The use of ribbons exposes a large surface to the air for ventilation, and the end terminals, by their heat- conducting properties, assist in dissipating the heat generated and so keeping the temperature down. A not generally appre- ciated but very common source of possible error existing in resistances made in this manner is a difference of potential set up between the ter- minal blocks and the thin blades, by thermo- electric action. These potentials are opposite, and will neutralize each other if the tempera- tures at both ends of the resistance be the same, but if they be different, due, say, to de- fective soldering of the blades at one end, there is a resultant E.M.F. at the terminals secured to the end blocks where the drop is measured which is superposed on the drop of potential due to the current flow, so that a measurement of the drop is no longer a correct indication of the current strength. This point is of practical, not merely academic importance, the writer having known errors in excess of ten per cent due to this cause. When a low resistance is to carry an extremely heavy current and it is undesirable to make the large investment that would be necessary for the air-cooled form just described, a water- cooled type is sometimes employed. This often consists of a tube of the resistance metal equipped with appropriate terminals STANDARDS OF RESISTANCE. 13 for connection to the current circuit, and with nipples to which rubber tubing may be attached, and a stream of water at a fixed temperature kept constantly flowing. With this expedient the amount of current that can be handled by the resistance may rise as high as 15,000 amperes per square inch cross-sectional area of conductor without danger of overheating. Where the resistance standards are to be of high value, say 10,000 ohms or more, the currents that they are to carry are usually very small and give little trouble from heating. The re- sistances are then formed of very fine long alloy wires wound on spools, as in the case of the Reich- sanstalt form above described, but several layers deep. For exact work they too must be immersed in oil, both to keep the tempera- FlG - 5 - ture uniform throughout and in order that the temperature may be measured ; but for commercial work of moderate accuracy this is superfluous. A convenient form of high-resistance box, shown in Fig. 5, contains four coils of 10,000, 20,000, 30,000, and 40,000 ohms respectively. The coils can be used sepa- rately or in any desired combination to give a resistance of from 10,000 ohms to 100,000 ohms by steps of 10,000 ohms value. With still higher resistances it becomes necessary to take special precautions in insula- ting the coil terminals from each other, as otherwise the resistance of the path between FIG. 6. them offered by a semi-con- ducting film of moisture becomes comparable to that of the coils and seriously affects the accuracy. A resistance box, containing resistances that may be coupled together to give a total resistance of 1 megohm and provided with special insulating terminals, is shown in Fig. 6. In this, as will be noted, the contacts are supported on tall hard rubber blocks that greatly increase the length of the surface between adjacent contacts over which leakage may take place. This 14 ELECTRIC AND MAGNETIC MEASUREMENTS. particular box is arranged in ten groups of coils of 100,000 ohms resistance each, which may be interconnected either in series or parallel or any combination of series and parallel. The rubber blocks are so drilled that they do not touch the rods connected with the resistance coils except at the top, thus giving a very long leakage surface. Such wire resistances of high value are naturally very ex- pensive, and the extreme fineness of the wires frequently causes trouble, because they may become corroded, due to the presence of a small trace of acid or something of that kind. For this reason a resistance made of carbon, often in the form of a streak left by a soft pencil when drawn over ground glass, is frequently employed when a resistance having a value in the order of a megohm is to be constructed. Such a resistance is shown in Fig. 7. The " carbon megohms " are not celebrated for their constancy, however, and it is always advisable be- fore using one to compare FIG. 7. it with a wire standard having a resistance of 10,000 ohms, or preferably of 100,000 ohms value by one of the methods to be described presently, in order to determine that it has not deteriorated. CURRENT STANDARDS. The Voltameter. In the definition of the ampere given on page 2 there is stated the method of determining the ampere by means of the silver voltameter. This device, however, is but seldom used outside of a laboratory, both for the reasons named and because the cost of the materials entering into its construction, when of a size suitable for measuring currents of some magnitude, is almost prohibitive. The copper voltameter, in which the two electrodes are of copper, and the solution of copper sulphate, gives, when handled with reasonable skill, results that are more than sufficiently close for all commercial purposes. The copper voltameter is easier to manipulate, and the deposit on the plate through which the current leaves the device is strongly ad- STANDARDS OF RESISTANCE. 15 herent; whereas in the silver type the deposit is very apt to be loose enough to be washed off when the platinum bowl is being cleaned preparatory to final weighing, unless a very large sur- face has been allowed per unit of current. The copper volta- meter can, further, be satisfactorily used with current density, namely, current per unit of area of plate surface, about five times as great as that permissible in a silver voltameter, so the former type is much more compact. A serviceable copper voltameter may be made as follows: A containing vessel, usually of glass, is selected of sufficient size to hold all the plates. Into this is poured a solution of sulphate of copper made by dissolving crystals of pure sulphate of copper in distilled water, with the addition of a small amount (about 1 per cent), of sulphuric acid. It is essential that the solution should be sufficiently acid to turn blue litmus paper red. The solution should have a specific gravity of about 1.15, but this may be as low as 1.1 or as high as 1.2 without vitiating results. The voltameter plates of pure electrolytic copper are immersed vertically in this solution. The plate through which the current leaves the voltameter must be carefully cleaned, dried, and weighed before being placed in the cell, in order that the gain in weight may subse- quently be determined, and the strength of the current flowing calculated therefrom. Where large currents are to be handled O several positive and negative plates may be used to advantage, they then being interleaved like the plates in a storage battery cell. No more than one ampere per 10 sq. cm. of surface should be passed out of the negative plates, namely, the ones through which the current leaves the voltameter, and the posi- tive plates, through which the current enters, should afford twice this area for the same current. The copper plates should preferably be arranged with one or two short strips or lugs left attached above, so that the current may be led to and from them, instead of leaving the whole plate width to emerge through the surface of the solution, and these lugs should be of as small an area as is consistent with their properly performing their functions. All corners and edges of the copper plates should be rubbed off with sandpaper before the initial measurement is attempted. Where very large currents are to be handled the plates may be corrugated, so as to present a larger area for a given sized plate ; 16 ELECTRIC AND MAGNETIC MEASUREMENTS. but in this event it is more difficult to determine with certainty that the plates are clean and in condition for use before being placed in the voltameter. The copper voltameter gives results that are dependent both on the temperature of the solution and on the current density employed. The following Table III, taken from the Elec- trician, London, gives the electrochemical equivalent of copper for various conditions of temperature and current density, and the values there given must be used if accurate results are to be had. TABLE III. Values Meikle. Square Centi- Temperature. per Ampere. 12 C. 23 C. 28 C. 50 .0003288 .0003286 - V .0003286 100 . 0003288 .0003283 .0003281 150 .0003287 .0003280 .0003278 200 .0003285 .0003277 .0003274 250 .0003283 .0003275 .0003268 300 .0003282 .0003272 .0003262 All voltameters are more or less objectionable for use in determining the ampere, for two reasons. First, they are merely more or less reproducible copies of a device which the International Congress thought suitable for the accurate meas- urement of current strength, but which does not involve determi- nation from fundamental physical units. Second, they involve, in addition to the element of current strength, that of time, and a current must be kept of strictly uniform value for a consider- able period in minutes in order to obtain results. In other words, the voltameter gives the average value of the current that has been flowing through any circuit for a given length of time, but does not show the instantaneous values. The Tangent Galvanometer. The definition of the absolute unit of current strength states that this is represented by a current of such value that when passed through a conductor having a length of 1 cm. bent into the shape of an arc of a circle having a radius of 1 cm., it will attract or repel a unit magnetic pole placed at the center about STANDARDS OF RESISTANCE. 17 which the radius is drawn with a force of 1 dyne. It is hardly feasible to make an instrument for the absolute measurement of current based on this principle, but the unit may be derived from fundamental measurements of length, mass, and time in other ways. One of the oldest devices for the accurate determination of current strength is the tangent galvanometer, which is an instru- ment in which a magnetized needle assumes a position deter- mined by the resultant of the action thereon of the earth's magnetic field at a given point, and the magnetic force due to a coiled conductor through which flows an electric current. The strength of the earth's magnetic field at any point may be deter- mined to practically any desired degree of accuracy by means of a cumulative method, which need not be enlarged upon here. By suitably proportioning the diameter of the coil of wire to the length of a magnetized steel needle suspended at its center so as to be freely rotable, the force with which the current tends to deflect the needle by reason of the magnetic field surrounding the conductor will vary in direct proportion to the strength of the current. Without going too deeply into theory the action may be understood from the following : In Fig. 8, let the length of the line,, OA, represent the magnitude of the force ^ ^ due to the earth's magnetism tending to re- strain the needle, and the direction of the line represent the direction in which it tends to hold it, and let the line OB, in a similar man- ner represent the magnitude of the force ex- erted on the needle by the current flowing through the coil and the direction in which it tends to hold it. This direction is made to be at right angles to OA, by placing the tangent galvanometer in such a position that the earth's field holds the needle at right angles to the plane of the coil when no current is flowing. From the law of the parallelogram A of forces the resultant of the two forces, OA and OB, acting on the needle will cause it to assume the direc- tion AB. OB, representing the strength of the current, is the tangent / / / / / / / / / / / / / / / / / / t / 18 ELECTRIC AND MAGNETIC MEASUREMENTS. of the angle OAB through which the needle has moved, and therefore the tangent of the angle of deflection of the needle is a measure of the current strength. The strength of the mag- netic needle is of no consequence, as, if it were increased, the action on it of the magnetic field due to the current and that of the earth's field would be increased alike, and if decreased, decreased alike, the angular deflection remaining the same for a given current as long as the strength of the earth's field remains constant. Tangent galvanometers are of value in that they enable us to derive fundamentally the unit of current strength ; but they are in very limited use, as we have forms of secondary standards of satisfactory accuracy and more convenient of manipulation. Moreover, it is necessary to place tangent galvanometers in very inaccessible locations in order that the directive action 014 their needles due to the earth's field may not be seriously and con- stantly disturbed, in ever changing degree, by the other magnetic fields due to electric currents such as are in use in every civilized community. The Ampere Balance. A different class of apparatus in wide use as a standard for the measurement of electric, current is the ampere balance, the most generally known example of which is that invented by Lord Kelvin. While this must primarily be calibrated with the aid of a silver or copper voltameter, or a tangent galvanometer, it contains no parts liable to change under proper usage, and has the great advantage that it indicates the current's strength at every instant, not the product of the average current by the time that it has been flowing as in the case of the voltameter. It is, further, simple of manipulation considering that it is a stan- dard. The apparatus is based on the well-known law that cur- rents flowing in the same direction in parallel adjacent conduc- tors attract each other, and those flowing in opposite directions in parallel adjacent conductors repel each other, and that the forces of attraction and repulsion at a given fixed distance are in direct proportion to the squares of the strength of the currents. It is evident that in an apparatus embodying this principle one of the conductors must be freely movable in order that any tendency to change in relative positions may at once be STANDARDS OF RESISTANCE. 19 observed by suitable means and equilibrium restored by the application of appropriate restraining forces. There is some difficulty in providing a means for making electrical connection with a movable conductor which will carry considerable current and at the same time be perfectly flexible. In the Kelvin apparatus this problem was solved as follows : Referring to the diagrammatic perspective in Fig. 9, T and T' are pairs of semi-cylinders of brass, the upper ones of which are rigidly secured to the base frame of the instrument. To the upper surfaces of the upper pairs far back from the edge are sold- ered a large number of exceedingly fine copper wires, which are combed out to be parallel with each other and then led over the rounded surfaces of the upper semi-cylinders, across the /" FIG. 9. short gap separating them from the lower semi-cylinders and nearly around the latter where they are finally soldered in place in a similar way. These fine wires, or ligaments as they are called, serve both to sustain the movable conductor and as a means of conveying the current. Their flexibility alone would enable the coils of wire, MM' , to swing about the point of sus- pension with perfect freedom ; but making the surfaces cylin- drical gives an additional factor of assurance that there shall be no restraining due to the bending of the ligaments, in that the cylinders allow a kind of rolling motion which greatly decreases any opposition to motion that the almost inappreciable rigidity of the ligaments might tend to offer. Having now a pair of coils, MM', at the opposite ends of a freely suspended lever and through which current may be 20 ELECTRIC AND MAGNETIC MEASUREMENTS. passed, all that is necessary in order to have the elements of a complete measuring instrument is a set of stationary coils simi- lar to the freely suspended ones and placed parallel thereto, to- gether with a suitable measurable restraining force to keep the movable coils in a position of equilibrium when current is passed. In the actual instrument, two stationary coils are used in con- nection with each movable one ; all being interconnected so that at the right-hand end of the apparatus the reaction between the upper stationary coil and the movable one tends to move the latter in one direction and the lower stationary coil assists in that action, the stationary coils on the other end of the apparatus being coupled in a reverse manner, the sum total of all of the efforts thus being to cause the lever to go downward at one end or the other. In the figure, the connections are such that the left- hand end of the balance tends to rise when current is applied. As the direction of current flow is opposite in the two halves of the instrument, it can be seen that if the whole apparatus is placed in a uniform magnetic field, such as the earth's field, the results will not be vitiated; as any tendency to a decreased or increased effort on one arm of the balance, because of the pres- ence of that field, is offset by the decreased or increased force exerted by the other half. An apparatus that is made indepen- dent of the influences of outside magnetic fields, by composing it of halves equally and oppositely affected by such fields, is said to be astatic. The measurable restraining force applied to hold the movable element of the balance in a position of equilibrium is supplied by a movable weight, whose distance from the fulcrum of the balance arm is adjustable. An index finger is attached to the movable element, so that its position relative to a fixed mark maybe observed and the fact that equilibrium exists established. These details are shown in Fig. 10 where Jis the index finger, D the fixed scale, and R the movable weight sliding along the movable arm, P. Only one of the trunions, T, supporting the movable arm is shown. It will be noted from the illustration that the apparatus is provided with two scales, one of them having equally spaced divisions and the other in which the spaces between the scale markings progressively increase in size from zero on. The equal scale shows the distance that the movable weight, 72, has been moved and the non-equal one, the STANDARDS OF RESISTANCE. 21 current's strength, which can thus be read off directly from the position of the weight. It will be noted that the zero of the scales is not in the center, as would be the case if the ordi- nary mechanical balance arrangement were employed, but at the extreme left-hand end. This feature is made possible by the following plan : At the right-hand end of movable element there is secured the trough, A, in which is placed a certain definite weight that is just sufficient to counterbalance the weight of the movable piece, R, when that piece stands at zero on the scales. During that part of the path of R included between the zero and the point opposite to the fulcrum, II is opposed to the weight placed in A, and their difference is the FIG. 10. force balancing the pull of the current. At the center of the scale, the opposing force is that due to the weight in A only, and from that point on to the extreme right-hand end of the scales that due to the sum of the moments (weight times dis- tance from the fulcrum) of R and A. The scale that is not equally divided is attached to the stationary portion of the instrument, and from it ampere values may be read off directly. The equally divided scale is part of the movable balance arm, and is supplied because it is easier to estimate correctly the value of a fraction of scale division when all divisions are of uniform value than of a division in a series which is progressively increasing or decreasing. The latter scale is used only when 22 ELECTRIC AND MAGNETIC MEASUREMENTS. exact measurements are to be made, and the value of the cur- rent then computed with the assistance of tables that come with the instrument and which give the doubled square roots directly. The balances are provided with glass covers to shield them from draughts, and the movable weight, R, is slid along the balance arm through the aid of- a carriage, B, which may be oper- ated from outside by means of silk cords, (7(7, the whole being so arranged that no part of the weight-moving device is in contact with the weight when the cords are released, thus obviating any chance of error due to friction between the pusher and the weight. These balances are made in a variety of sizes suitable FIG. ll. for measuring currents as low as .025 amperes to as high as 2500 amperes. They are particularly valuable in that they may be used to measure alternating currents as well as direct currents, the wire windings in the large sizes being composed of cables of many fine insulated wires in parallel, so as to insure proper and uniform distribution of current irrespective of inductive influences. It has become of late the fashion in some quarters to ridicule the Kelvin balances because they are somewhat tedious to manipulate as compared with direct reading meters of commer- cial patterns to be described in a latter chapter, because they STANDARDS OF RESISTANCE. 23 are not portable, and because it takes some time for a balance to be obtained, as the period of oscillation of the movable element is very long, approximately three or four seconds. It is true that all of these objections exist ; but, on the other hand, the apparatus contains 110 parts liable to change, except the windings themselves, which might deteriorate if heavily overloaded, they have exceptionally long scales, they are astatic, and good on both direct and alternating current. The latter quality renders them specially valuable in the accurate measurement of alternating current by transfer methods and in the calibration of alternating instruments. Other forms of balances have been devised from time to time, notably, the Pellat balance, shown in Fig. 11. In this there is but one stationary and but one movable coil which are arranged at right angles to each other. The current is led into and out of the latter through fine spirals of silver, which afford but little opposition to its movement, and a scale pan with weights is used to supply the restraining force. The Potentiometer. Another method of accurately measuring a current is to pass it through a known standard resistance and measure the re- sultant drop in potential. If the current is continuous the most suitable instrument for this method of measurement is the potentiometer. As a special chapter (see page 73) has been devoted to this instrument and its uses, the reader is referred to it for a description of this very satisfactory method of current measurement. ELECTROMOTIVE FORCE STANDARDS. Determination ly Drop of Potential. The definition of the volt suggests a practicable method of establishing this unit. We have only to pass a current of known strength through a known standard resistance when the difference of potential at the terminals of the resistances ca^ be calculated from Ohm's law, E = EL In measuring E.M.F. in this way, it must be borne in mind that unless the device that indicates the voltage is of practically infinite resistance, R in the formula is not the resistance of the standard resistance coil but 24 ELECTRIC AND MAGNETIC MEASUREMENTS. that of the circuit formed by the coil shunted by the measuring apparatus attached to its terminals. In. Fig. 12 herewith, let B re present a source of current, and .A represent a balance or other device for accurately measuring the current strength, R the standard resistance, whose value may be assumed to be one ohm, and V the device that indicates the voltage. When V is not attached to 11, the difference of potential between the terminals rand / of the latter, when one ampere is flowing, is from Ohm's law, one volt. Assume that the resistance of J^is 49 ohms. If this is now connected to the terminals of J?, the resistance be- tween the points r and / is no longer 1 ohm, but from the law of divided circuits (see page 93) .98 ohm, and the difference of potential with one ampere flowing .98 volt instead of one volt, B ff( I- Ohm.} V (49 Ohms) FIG. 12. or an error of 2%. Therefore, if V is of a resistance compara- ble with that of the standard resistance coil, the value of its resistance must be known and allowed for, in accordance with the above illustration. With the aid of the potentiometer, measure- ments may be made without necessitating this correction, as will develop later in the chapter devoted to this instrument. Standard Cells. The Clark Cell. According to definition the International volt is an E.M.F. whose value is represented with sufficient ac- curacy for practical purposes by -i| -| | of the E.M.F. between the terminals of the battery known as the " Clark Cell." The Clark cell is one in which the negative electrode is a pure zinc rod or amalgam of zinc and mercury, the positive electrode pure mercury, and the electrolyte a saturated solution of pure mer- STANDARDS OF RESISTANCE. 25 curous sulphate and zinc sulphate. Many precautions must be taken in the preparation of the materials forming this cell so that they may be of sufficient purity, and considerable skill is re- quired in putting such a cell together. As they may be pur- chased from numerous manufacturers who have the requisite facilities, the detailed instructions for constructing them will not be given here. Those who are interested may refer to the report of the International Congress which selected the cell as a standard, or the fairly complete abstracts which will be found in Fleming's " Handbook for the Electrical Laboratory and Testing Room," Carhart's " Electrical Measurements," etc. The cell is usually set up in small glass tubes having a diame- ter of about f of an inch and a depth of H to 2 inches, the Maiine Glue Glass Tube Platinum Wire Glass Cell Zinc sulphate Paste Mercury FIG. 13. elements being often arranged as shown in Fig. 13. This is the original form of the Clark cell, and is objectionable for the following reasons : It is not portable, as its inversion would cause the mercury to contaminate the zinc, the electrolyte must be kept concentrated, and when the temperature rises it takes a considerable length of time for the solution again to become saturated. The latter fault is particularly serious, as it means that there is a lag of several hours, or perhaps days, before the E,M.F. will correspond with that of a normal cell at the new temperature. 26 ELECTRIC AND MAGNETIC MEASUREMENTS. To insure that all portions of the cell may quickly attain any new temperature, Mr. Hamilton has adopted the expedient of precipitating chemically a thin film of silver on the outside of the glass containing tube and then heavily plating this coating with copper. Copper, of course, is an excellent heat conductor, and since it is in such intimate contact with the glass, the attainment of a new temperature throughout the cell is greatly accelerated. The difficulty due to the presence of a large mass of free mercury may be overcome by the use of an electrode which con- sists of a flattened spiral of platinum wire amalgamated, either by electrolytic methods, or by heating to redness and plunging into mercury. By virtue of capillary attraction this spiral will take up and hold enough mercury between its convolutions to make it an excellent electrode. It performs its functions well that the tube may be inverted or even sent through the mails without shaking any of the mercury loose. The use of such amalgamated spirals is due to Dr. Muirhead. A cell of this form, according to the International Congress, has an E.M.F. of 1.434 true volts. If, however, we use the later and more generally accepted chemical equivalent of silver, .001119, in- stead of .001118, as used by the said Congress in defining the value of the ampere, the E.M.F. of the Clark cell is 1.4327 volts, a value which is now used abroad and is probably more nearly correct. Another form of cell better than the original Clark cell is a modification devised by Professor Callender, which is often called the Inverted Clark Cell. In this the order of the ele- ments entering into the construction is reversed and the lag between the temperature of the cell and the E.M.F. is nearly absent. The Carhart- Clark Cell The Carhart-Clark cell, a form that is widely used in this country, is shown in section in Fig. 14. The figure shows a globule of metallic mercury used for one pole, but it is not uncommon to use the amalgamated platinum spiral described above. The paste of mercurous sulphate is separated fr mi the zinc by a wad of asbestos on which the zinc rests. The most important change from the original Clark form is in the use of a zinc sulphate solution that is not kept saturated at all temperatures, but on the contrary is saturated only when V STANDARDS OF RESISTANCE. 27 the temperature falls to C., at which temperature no cell is ever used in practice. No time is therefore expended in wait- ing for the solution to become satu- rated if the temperature should rise, and there is no consequent increase of solution density that lowers the E.M.F. This cell not only responds far more quickly to temperature changes, but has a lower temperature coefficient which figures out just about one half of that of the original Clark form. Professor Carhart gives the formula connecting the tempera- Asbesto> ture and E.M.F. as Seal = 1.4401 -.0004 - Soluti ZnS0 4 Zrt Hg,S0 4 Paste FIG. 14. this being correct at temperatures around 15 C. A drawback to these and all other standard cells containing non-saturated solutions is that, if improperly sealed, the evapora- tion of the liquid causes a change in concentration, with a resultant change in E.M.F. Cadmium Cells. The comparatively high temperature coef- ficient of the Clark cell led many experimenters to investigate other combinations that would be equally reliable, but in which this drawback would be less prominent. The best is probably that patented by Weston (U. S. Patent No. 22,482 of 1891). It is similar in all respects to the Clark cell, except for the fact that cadmium is used instead of zinc and cadmium sulphate instead of zinc sulphate. According to the specifica- tions, this cell has a temperature coefficient of but .018 percent per degree C., this being only one fourth of the temperature coeffi- cient of the Carhart-Clark cell, and one eight of that of the original Clark cell. Its E.M.F. is given as 1.019 volts. The Reichsanstalt in Berlin have carefully tested this type of cell and recommend the form shown in Fig. 15. Its H -shape is that suggested in 18 Q 5 by Lord Rayliegh for the Clark cell, and frequently used for that purpose. The preparation of the materials and the assemblage of the cell calls for the same minute observation of details, as is the case with the Clark cell in any of its forms. 28 ELECTRIC AND MAGNETIC MEASUREMENTS. Care and Use of Standard Cells. Standard cells form a most valuable basis for the accurate measurement of potential and current for both laboratory and commercial conditions, and they should be more generally used than they are. It is not recom- mended that the user attempt to make his own, in fact the results in that event would probably be very unsatisfactory, but the cells themselves, as before stated, can be easily and inexpensively purchased in many quarters. They are by no means the delicate fussy devices that they have somehow the reputation of being ; on the contrary, they are really very rugged and will stand an incredible amount of misuse without injury. The writer has even known of one being dead-short Cadmium Sulphate Crystals FIG. 15. circuited for an appreciable interval, certainly as long as two minutes, after which the potential, although at first far below normal, rapidly rose, and after the expiration of several hours again became normal. The power of the form in which the amalgamated platinum spiral is used to withstand tumbling about has already been mentioned. It must always be borne in mind that these standard cells give their stated E.M.F. only on open circuit, namely, when not delivering any current. When, therefore, they are attached to the terminals of a commercial form of voltmeter (all of which, as explained further on, require current for their operation), the resulting indication will be meaningless. Students seem to be particularly prone to attacli a standard cell to the low-reading coil of a commercial voltmeter having a resistance that is almost STANDARDS OF RESISTANCE. 29 as low as that of the cell itself, with the result that the voltage indicated by the instrument will steadily and rapidly continue to fall until nearly zero because of the polarization due to the current output that is demanded. To guard against this abuse it is usual to build into the base of the case containing a standard cell, such as is shown in Fig. 16, a high resistance of a value of at least 10,000 ohms, connected permanently between one battery terminal and its binding post, so that it is im- possible under any circumstances to dead-short circuit' the apparatus. The device that is almost al ways used for determining E.M.F. in terms of the E.M.F. delivered by a standard cell is the poten- tiometer. With this the E.M.F. is measured when the cell is not deliv- ering current ; all of which will be explained in greater detail in the chapter devoted to that instrument. The Daniell Standard Cell. In the event that a Clark cell is not available, the ancient and honored copper, copper sulphate, zinc sulphate, and zinc Daniell cell can be made up as a standard having no mean pre- tension to accuracy. To make one there is required a glass-containing vessel, usually an ordinary batter jar,- a small porous cup (say two inches in diameter by four inches deep), a rod of commercially pure zinc carefully cleaned with sandpaper and subsequently amalgamated with mercury, a strip of pure electrolytic copper of any convenient dimensions (say one inch broad and five or six inches long), a solution of chemically pure zinc sulphate of a specific gravity of 1.200 (555 parts by weight of zinc sulphate crystals to 445 parts of distilled water will give this density), and a saturated solu- tion of chemically pure copper sulphate in distilled water w th the copper sulphate present in excess. Both the zinc rod and the copper strip must, of course, be provided with suitable terminals for the attachment of the circuit wires. It is advisable to plate the copper strip with a coating of electro- FlG. 16. FIG. 18. 30 ELECTRIC AND MAGNETIC MEASUREMENTS. lytic copper just before using it, either by making it the anode in a regular plating bath or by short circuiting the cell on itself, in which case the copper plate becomes automatically coated with electrolytic copper. The copper strip is placed in the porous cup and the cup is almost filled with the copper sulphate solution. The porous cup is then placed in the glass-containing jar and the zinc solution poured around it until the level of its surface is prac- tically on the same plane as the level of the copper sulphate in the porous cup. The zinc rod is then placed in the zinc sulphate solution, and the cell as a whole is ready for use. Such cells have an E.M.F. of 1.072 volts, and are of extremely low internal resistance so that they may furnish an appreciable amount of current. They do not polarize readily, and have a very low temperature coeffi- cient. With reasonable care in selecting the materials, these cells may be relied upon to be accurate within about one fifth of one per cent. A cell of this kind is shown in section in Fig. 18. Electrostatic Voltmeters. Referring to Fig. 19, if aa be two box-shaped metallic sectors, bb a movable paddle -shaped conductor, and a difference of potential be ap- plied between conductors at- tached to the two, we have the following conditions : The instrument is a con- denser, the double-ended sec- tor, ftfi, forming one coating, the dielectric being air and the outer coating being the stationary sectors, aa. When the difference of potential is applied between the inner and outer coatings, the former, being movable, tends to rotate with a force proportional to the potential about its axis, e, in order that it may place itself in a posi- tion where the capacity of the condenser is a maximum ; FIG. 19. STANDARDS OF RESISTANCE. 31 in other words, to turn until it is completely enshrouded by aa. This force is resisted by the torsional elasticity of the metallic suspension fiber, e, and the resulting deflection is therefore a measure of the applied voltage. Instruments for the measurement of E.M.F., based on this principle, are called electrostatic voltmeters or electrometers. Although they are in somewhat common use abroad they are not as well known or as much relied upon in this country as standards for the measurement of potentials. The deflectional forces are small as compared with those existing in some other types of instruments, so it is necessary to suspend delicately the moving element, and even then they cannot be used for the measurement of very low potentials. On the other hand, they are entirely independent of tempera- ture, can be used on either direct or alternating current, are not influenced by magnetic fields, consume no current, and, in fact, with the exception of the possibility of an error caused by adjacent electrostatic influences (from which, however, it is possible to shield them by a grounded metallic casing), their deflections with a given potential depend only on their geomet- rical dimensions and the elasticity of the suspending fiber. The latter can be made a very constant and reliable quantity by selecting a length of the fiber such that the stress in it, due to its being twisted, is but a small fraction of the limit of elasticity. Electrostatic voltmeters may therefore be made as acceptably reliable standards. Where the voltages to be measured are comparatively low, of, for instance, an order of 100 volts, sufficient deflectional force is obtained by superimposing several sets of charged rotatable vanes swinging between a corresponding number of stationary charged plates. Instruments so constructed are multicellular electrostatic voltmeters, and one of them of a commercial type is shown in Fig. 2.0, this being an illustration of the Kelvin meter. In this, voltage is indicated by a needle that sweeps over a suitably graduated scale, and the indications are damped by a disk attached to the movable portion and moving .'11 a vessel containing oil that is inserted in the lower part of the instrument, as shown by the partially broken away part in the figure. In the laboratory standard type of this instrument, a small mirror is attached to the moving system, and by means of 32 ELECTRIC AND MAGNETIC MEASUREMENTS. a beam of light thrown on it and reflected to a fixed scale, the equivalent of a very long needle is obtained, which enables one to read the indications with a high degree of accuracy. The Board of Trade standard laboratory in London has a set of electrostatic voltmeters of this class, one of which is shown in Fig. 21. These have no numerically divided scales, but only two reference lines, one of which shows the position of the moving element when no current is applied, and the other when a certain potential, such as 100, 500, 1000, etc., volts, is applied. In the illus- tration the metallic hood cov- ering the instrument is shown as removed and placed at one side of the apparatus? To shield against foreign electro- static charges this cover when in place is grounded. The in- dications of this instrument also are damped by means of an oil cup. It is claimed that the electrostatic voltmeters at the Board of Trade laboratory give indications that are accurate within one part in 3000. Volt Balances. From Ohm's law, the current passing through a circuit is di- rectly proportional to the voltage applied, if the resistance of the circuit be kept constant. If, therefore, we take any current-consuming instrument that would ordinarily indicate amperes, having a resistance sufficiently high so that the current drawn would not pull down the E.M.F. of the source to be measured, or to heat the conductors forming the instrument sufficiently to alter its resistance, the indications of the instrument will vary in proportion to the applied voltage, and the scale may be divided to read volts instead of amperes. The Kelvin Centiampere Balance, designed to measure cur- STANDARDS OF RESISTANCE. 33 rents varying in value from .01 to 1 ampere, is frequently used as a standard voltmeter on this principle, by inserting in series with it a properly adjusted known high resistance, that may be obtained from the makers. The value of the re- sistance is made such that the values indicated by the movable rider on the balance indicate volts directly, or else some simple multiple, such as one half, one tenth, etc., of the numerals in volts. The measurement of potentials in this way depends, as above stated, on the assumption that the resistance of the in- strument remains constant during the test. As copper, the material of which the wire coils of the balance are formed, has a resistance that varies quite markedly with a change in tem- 21. perature, it is necessary, where accurate results are required, to correct for such changes of temperature. For this purpose, the temperature is observed by a thermometer, which is inserted as close as possible to the coils. STANDARDS OF CAPACITY. As has been stated on page 4, capacity is the property by virtue of which two electrical conductors, insulated from each other, will store up a quantity of electricity, if a difference of potential be applied to them. The amount of charge depends on the area of the opposing surfaces, on the distance between 34 ELECTRIC AND MAGNETIC MEASUREMENTS. them, and the nature of the intervening medium ; namely, whether this be air, glass, mica, or paper, or any other sub- stance. Such a device for storing up an electric charge is called a " condenser." Condensers that are to be used as standards are often con- structed so that the dielectric intervening between adjacent sides is air, and the spacings between the plates are kept constant by a rigid mechanical construction. The capacity of such standards is determined by measurements involving the ele- ments of current strength and time in one of the ways de- scribed in Chapter VIII, and may then be used for purposes of comparison. The construction of the standard Kelvin air con- denser is shown in Fig. 22. Condensers in which air is the dielectric are bulky because of the mechanical construction, and heavy because the plates FIG. 22. must be made thick enough to support themselves. It is possi- ble to make a form which is as satisfactory as regards perma- nence, and far lighter and more compact, by using mica as the dielectric. The ordinary construction in such cases is to make the conductors of strips of tinfoil with mica plates intervening. However, unless the pressure holding this aggregation of mica and tinfoil assembled together is kept rigorously constant, the capacity will vary, due to the fact that the dielectric between the adjacent tinfoil coatings is a varying thickness of air and mica instead of a constant thickness of mica alone. To minimize trouble OR this score, the condensers are usually well soaked in paraffine, which effectually prevents the entrance of air and makes a more or less solid mass. A much more satisfactory expedient, however, is that used by Mr. Hamilton, in which a thin film of silver is chemically precipitated upon, STANDARDS OF RESISTANCE. 35 and strongly adheres to the mica plates. The coatings on each side of a plate, with the intervening mica, form a condenser of small capacity. By assembling a sufficient number of these small condensers in one case, and interconnecting them, a con- denser of any required capacity may be formed. The final ad- justment is made by utilizing the fact that the sheets of mica vary in thickness, and consequently the capacities of the differ- ent elements are different, together with the principle that series connection of two or more elements reduces the capacity of the whole. Having some extra elements, a few substitutions of thick for thin ones, or vice versa, will bring the capacity at least pretty closely to the desired magnitude, and if the exact value cannot be reached in this manner, it may be reached either by connecting some elements in series or by scraping away a part of the coating from some of the plates. Such con- densers are fully as reliable as the air form, and may be used as standards with equal confidence. It is stated that their accuracy will change less than one part in one thousand, even after taking apart and reassembling. Condensers have temperature coefficients, that is to say, their capacity varies to some extent with changes in temperature, so that in comparison methods of measurement, the temperatures of the standard, and unknown condensers must be taken into consideration. STANDARDS OF INDUCTANCE. As in the case of capacity, inductance is a property of an electrical circuit, which is defined in terms of more funda- mental units, namely, the volt, the ampere, and the second, and standards are prepared by making up a circuit having induc- tance, measuring that inductance by one of the primary methods described in Chapter IX, and afterwards, if desired, using it for comparison purposes when making measurements involving the use of a comparison standard. According to the definition of inductance, this property depends on having the magnetic lines of force which surround a current-carrying conductor cut another conductor or another portion of the same one. A standard that is economical of manufacture, compact, and effi- cient must therefore have its elements arranged so that this cutting action is a maximum. This condition will exist when a 36 ELECTRIC AND MAGNETIC MEASUREMENTS. conductor is wound up into a form of coil, for in that case (see Fig. 23, which shows in section a coil of five turns in which the lines of force surrounding one portion of the first turn are de- picted), the lines of force surrounding each conductor will evi- dently, when generated, cut all of the other conductors, and as inductance is manifested only when current strength is chang- ing, tliis cutting will generate in the portions cut a progres- sive and continuously opposing E.M.F. If we afford a path of less resistance to the flow of the lines of force than that offered by air, the maximum effect is evidently increased, that is, a given coil has more inductance when a good con- ductor of magnetic flux, such encloses the coil. The addi- inductance is, however, not FIG. 23. as iron, wholly or partially tion of iron to increase the permissible in a standard, for two reasons. First, the perme- ability of iron is not a constant quantity, but varies with the density of the magnetic induction. Consequently, the induc- tance, which is proportional to the total magnetic flux divided by the current, is not a con- stant, but is different for each current strength. This alone would be fatal in a standard, but there is a second property of iron, called "hysteresis," or magnetic retentiveness, owing to which the magnetic flux is not always the sams for the same current, but depends, in part, on the preceding magnetic condition of the iron, which furnishes just as potent a reason why the use of iron to increase the induc- tance of a standard is not permissible. FIG. 24. If in Fig. 23 instead of having one coil of five turns this were divided into two sections, one of three and the other of two turns, having the relative positions shown, the inductance of the whole would, of course, be the same. If, however, it were STANDARDS OF RESISTANCE. 37 arranged so that one of the sections could be displaced relative to the other, the action of one part on the other would be in some manner related to the displacement. This fact is utilized in the inductance standard known as the " Ayrton and Perry," one of which is shown in Fig. 24. This consists of an outer stationary coil of wire within which there is the other coil, and the angle that the latter makes with the axis of the former may be varied by manipulating the knurled button. The inductance is at a maximum when the planes of the two coils are parallel, as then the mutual interaction of the two is greatest ; and at a minimum when the planes of the two coils are at right angles, for analo- gous reasons. A dial-shaped scale is provided over which plays a pointer attached to the axis of the movable element, and by calibration in comparison with other standards the scale may be divided off to show directly the commercial units of induc- tance (millihenrys) that are offered by each coil position. CHAPTER III. GALVANOMETERS . THE electric current is imponderable and cannot, therefore, be compared as to weight or dimensions with a standard, as pon- derable masses are, but must be compared with other currents by means of some effect or property of the current which is a measurable magnitude. An electric current may manifest itself in several ways. It may effect chemical composition or decomposition, as in the case of the silver voltameter before mentioned ; its action may be electromagnetic, in that the magnetic field surrounding the con- ductor carrying the current will influence an adjacent magnet and tend to displace it, as in an ordinary polarized telegraph re- lay ; its action may be electrostatic, as in the case of pith balls, which are attracted to or repelled from an electrified glass rod ; or it may be thermal, as in the case where a current passing through a conductor causes the temperature of the latter to rise. Instruments for at least detecting the presence and preferably for measuring the magnitude of one or more of these actions are necessary if we are to have a means of comparing current strengths. Such instruments have the generic name of "gal- vanometers." Galvanometers based on the chemical action of an electric current are in very limited use and need not be enlarged upon here. The great majority of commercially available forms utilize the electromagnetic manifestations of current and may, generally speaking, be divided into two classes ; first, the moving magnet class in which a movable magnet is influenced by the current flowing in a fixed conductor, and the second, the mov- ing coil class, in which the current to be measured, or a known portion thereof, is passed through a movable conductor, usually in the shape of a coil, located within the influence of a magnetic field which may be either that of a permanent magnet, or that of a current-carrying conductor. 38 GALVANOMETERS. 39 In either case one of the elements is fixed and the other free to move against a measurable restraining force, and the extent of the movement of the latter as indicated by suitable means is a measure of current strength. With galvanometers of the first class, those in which there is a movable magnet and a fixed coil, the former is almost invariably a magnetized steel needle or group of needles, usually straight, but sometimes bent double about their centers and taking on the form of a slotted bell (see Fig. 25). In all these instruments the movable needle is suspended from a fiber that offers the minimum possible resist- ance to its turning, the measurable restraining force being that furnished by. an external magnetic field, sometimes that of the earth itself, and sometimes one furnished by adjacent magnets whose positions and distances are adjustable. In high sensibil- ity galvanometers the forces involved are so minute that the delicacy of the suspension becomes a most impor- tant item. It is altogether out of the question to use a pointed hardened steel pivot support engaging in a jewel-bearing, as the friction between the two would be commensurate with the deflectional forces and large errors thus introduced. Great delicacy is obtained by supporting the movable needle on a fiber of cocoon silk of considerable length. Even this, however, is inferior to a suspension formed of a very fine filament of quartz. Such may be constructed by heating a short quartz rod to N s incandescence in an oxyhydrogen blowpipe flame, and having one end rigidly secured to a fixed block, suddenly re- tracting the other end, usually by having it fastened to a miniature form of crossbow in which, when the trigger is re- leased, the end is shot forward with great velocity. The fila- ment is in this manner drawn out to a very small diameter before rupture. As galvanometer sensibility may be increased either by decreasing the amount of restraining force for a given deflec- tional angle or by increasing the number of ampere turns sur- rounding the needle, and as the latter is, from motives of efficiency, made as great as possible in the beginning, the sensi- bility can evidently be further increased only by decreasing the strength of the controlling field. If this is the field due to the earth's magnetism, its directive force may be diminished or, in 40 ELECTRIC AND MAGNETIC MEASUREMENTS. fact, completely annuled or reversed by placing near to the gal- vanometer a magnetized body which sets up a flux opposite in direction to that of the earth's field. If the two were exactly alike and opposite there would evidently be no restraining force except the negligible one of the torsional elasticity of the fiber, and the needle, influenced by the current passed through the coil surrounding it, would assume a position practically at right angles to the plane of the coil with any current strength, no matter how small, and thus fail to act as an index of current strength. When, however, one or the other of the magnetic forces pre- ponderates, there is a directive force which tends to retain the needle in the zero position. The resultant between this and the directive force of the field, due to the flow of the current, deter- mines the position of the needle. Theoretically, therefore, all that is necessary to obtain almost infinite sensibility is an almost infinitesimal difference between the field due to the directive magnet and that of the earth, but this is based on the assumption that the suspension device is f rictionless and absolutely flexible. As a matter of fact, the suspension fiber must be of sufficient size to have the necessary strength for the mechanical support of the needle, and the resultant torsional rigidity or inelastic resistance to torsion is of such magnitude that the directive force must be made quite large in order to render it negligible. In practice, to obtain maximum sensibility with a moving mag- ; net galvanometer, a current is passed through it to cause a deflection, preferably the full scale in amplitude, and the current then cut off to see whether the magnet returns to its initial position. If so, the control magnet is approached a little closer. The operation is repeated until, on opening the circuit, the in- dex showing the movement of the needle no longer comes back to its starting point. It is then evident that the controlling force is too weak, so the magnet must be moved away again, just far enough to insure the return of the index to zero every time the current is cut off. Moving coil instruments may be conveniently divided into two subclasses namely, those in which the coil moves because of the reaction between the current through it and a powerful stationary permanent magnet, and the class in which the reac- tion is between the current-carrying coil and stationary coils GALVANOMETERS. 41 likewise traversed by currents setting up lines of force therein. In movable coil galvanometers, silk and quartz suspension fibers are inadmissible inasmuch as the suspensions are used as a means of conducting the current to be measured to the movable coil. What is ordinarily used, therefore, is a narrow and extremely thin strip of phosphor bronze made by rolling down by successive passages through jeweler's rolls a small diameter phosphor bronze wire. This is, of course, a conductor, and if the movable element be suspended above by one such conductor and steadied below by another, both being held taut, they evidently perform the double function of conductors and opposing springs. 8 FIG. 26. It is also possible to support the movable element by two such metallic strips, both supporting it from above. Another form of construction is shown in 5, Fig. 26. In this construc- tion the metallic strip is coiled helically, and when the movable element deflects, the ordinary spring action of a helically coiled wire is brought into play in place of its torsional elasticity, as in the straight form shown in a of the same figure. At c is shown the movable coil suspended from above by two conduc- tors, as already mentioned. In the forms a and b it is evidently possible to substitute for the lower metallic spring strip a very flexible current-carrying strip, which offers no appreciable 42 ELECTRIC AND MAGNETIC MEASUREMENTS. resistance to motion and at the same time serves as a con- ductor. Such flexible connections are usually made of soft annealed pure silver wires. In the form of suspension shown in a, b, and d, the resistance to turning offered by the suspen- sions can be altered only by changing them. In the form shown in c, however, if the distance between the two suspensions at their upper end is increased, a greater effort will evidently be required to produce the same angular displacement. This bifilar suspension, as it is called, is convenient in some respects but not in very common use in this country. The means employed to indicate the extent of the movement of the swinging member of a galvanometer is also of much importance. As the latter usually rotates about an axis, it is evident that any index actuated by it will have a greater linear displacement over a fixed scale for a given angular displace- ment, the further the scale and the marking extremity of the index are from the axis. This at once suggests the use of a very long hand or pointer, but this is objectionable because of its Aveight, which not only adds very considerably to the inertia of the moving system, and so renders its response to current changes slow, but necessitates stronger suspensions to support it, which suspensions are, of course, more rigid, and therefore decrease the sensibility of the galvanometer. This difficulty is surmounted by using in place of the ponderable pointer a beam of light reflected from a mirror carried on the movable part. This arrangement may assume one of two forms. In the first, a telescope is used, arranged as shown in Fig. 27, where ab is the mirror carried by the moving system, T the telescope, and SS the scale. The telescope is provided with a stretched hair, W, as in a surveyor's transit, which serves as a reference line for the position of the image of the scale markings as seen through the telescope reflected from the mirror. If the moving system, and therefore the mirror, ab, attached thereto, moves through an angle a, the angle between the axis of the telescope and the axis of the ray of light reflected from the mirror is evidently 2 a , the apparent deflection being thus doubled. In order that there may be a minimum loss in illumination due 'to the absorption by the lenses in the telescope, the latter is usu- ally made of the astronomical type, presenting to the eye an image that is reversed and inverted (that is to say, turned GALVANOMETERS. 43 through an angle of 180), while the mirror reverses in the sense in which ordinary printing type are reversed. It follows, there- fore, that a scale, the reflection of which in a mirror is to be observed, must have its numerals reversed, like ordinary printing type, and if they are to be viewed through an astronomical tele- scope, the scale must be placed in the instrument in an inverted position, so that the numerals appear to the direct vision thus J $ '3 ? 3. If an erecting telescope or simple slot be used, the scale is placed in the instrument in an erect position, so that the numerals appear to direct vision thus, Q 5 S I In both cases the numerals will appear in their normal as- pect, 1 2 3 4 5, when seen while making a scale reading. B FIG. 27. On looking through the telescope when current is applied, the whole scale swings across the field or vision, the reference line made by the cross-hair remaining fixed. It is of course possible to use instead of a telescope a small diameter hole or a long narrow slot, but this calls for better illumination, in order to make the scale markings visible, and for good eyesight. This first type of movement-indicating device enables one to make very close readings, as the cross-hair furnishes a sharply defined reference line. On the other hand, it is trying to the eyes, only one of which can be used at a time. It is also inconvenient in that only one party can observe the indications at a given time. - 44 ELECTRIC AND MAGNETIC MEASUREMENTS. In the second plan an actual luminous beam is used. Re- ferring to Fig. 28, L is a source of light arranged with a hood, or otherwise, so that it sends out only a long narrow beam which is reflected by a mirror or prism at M, concentrated by the lens, Z, and thrown on the galvanometer mirror, ab. The latter is made concave to keep the beam concentrated, and the light is thrown from there onto a fixed scale, SS, usually made of ground glass and having pasted thereon an opaque scale divided into millimeters, or other convenient units. This beam falling upon the ground glass scale plate makes a luminous line whose position relative to the opaque scale can usually be read with great ease. Readings can be made to a greater degree of accuracy in the telescope pattern instrument because the lu- minous band has an edge such that it is difficult to say just where it leaves off, but chi the f other hand, the second form is advantageous because sev- eral observers may simultane- J/ ously note the swing, and it is much easier on the eyes. The only remaining argument for the first form is that it can be read in the daylight, the brighter the better, whereas 8 the latter needs darkness, if it is to be shown to advantage. Because the scale, SS, Figs. 27 and 28, is straight instead of being bent into the form of a circle arc about the mirror as a center, the linear displacements shown thereon are proportionate, not to the angle through which the movable element has swung, but to the tangent of twice that angle. Where the angular deflections are but small, the difference between the numerical value of an angle and its tangent is negligible and the linear displacement on the scale may be taken as proportionate to the angular deflection. However, when measuring large deflections, and where accurate results are required, the angles should be calculated from the above relation between them and the linear motion. The following table computed by Dr. Kennelly gives the correction factors to be applied with different distances between the scale and mirror and for varying deflections : J GALVANOMETERS. 45 TABLE II. Reflecting Galvanometer Scale Errors. (A. E. KEXXELLY.) (These corrections are to be subtracted from the observed deflections.) Scale Distance 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 50 0.05 0.05 0. 0. 0. 0. 0. 0. 0. 0. 0. 60 0.05 0.05 0.05 0.05 0.05 0. 0. 0. 0. 0. 0. 70 0.1 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0. 80 0.15 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 0.05 0.05 90 0.2 0.15 0.15 0.1 0.1 0.1 0.05 0.05 0.05 0.05 0.05 100 0.25 0.2 0.2 0.15 0.15 0.1 0.1 0.1 0.1 0.05 0.05 110 0.35 0.25 0.25 0.2 0.2 0.15 0.15 0.1 0.1 0.1 0.1 120 0.45 0.35 0.3 0.25 0.25 0.2 15 0.15 0.15 0.1 0.1 130 0.55 0.45 0.4 0.3 0.3 0.25 0.2 0.2 0.15 0.15 0.15 140 7 0.55 0.5 0.4 0.35 0.3 0.27, 0.25 0.2 0.2 0.15 150 0.85 0.7 0.6 0.5 0.4 0.35 0.35 0.3 0.25 0.25 0.2 160 1.0 0.85 0.7 0.6 0.5 0.45 0.4 0.35 0.3 0.3 0.25 170 1.2 1.0 0.85 0.7 0.6 0.55 0.5 0.45 0.4 0.35 0.3 180 1.4 1.2 1.0 0.85 0.7 0.65 0.55 0.5 0.45 0.4 0.35 190 1.65 1.4 1.2 1.0 0.85 75 0.65 0.6 0.55 0.5 0.45 200 1.95 1.65 14 1.15 1.0 0.9 0.8 0.7 0.6 0.55 0.5 210 2.25 1.9 1.6 1.35 1.15 1.05 0.9 0.8 0.7 0.65 0.6 220 2.6 2.15 1.8 1.55 1.3 1.2 1.05 0.9 0.8 0.75 0.65 230 2.95 2.45 2.05 1.75 1.5 1.35 12 1.05 0.95 0.85 0.75 % 240 3.3 2.8 2.35 2.0 1 .75 1.5 1.35 1.2 1.05 0.95 0.85 o 250 3.75 3.15 2.65 2.25 1 95 1.7 1.5 1.35 1.2 1.05 1.0 H g 260 4.25 3.5 3.0 2.55 2 2 1.9 1.7 1.5 1.35 1.2 1.10 3 270 4.75 3.95 3.35 2.85 2.45 2.15 1.9 1.7 1.5 1.35 1.25 ^ 280 5.3 4.4 3.7 3.15 2.75 2.4 2.1 1.9 1.65 1.5 1.35 a 290 5.85 4.85 4.1 3.5 3.05 2.65 2.35 2.1 1.85 1.65 1.5 - 300 6.45 5.35 4.5 3.9 3.35 2.95 2.6 2.3 2.05 1.85 1.7 310 7.1 5.9 5.0 4.3 3.7 3.25 2.85 2.5 2.25 2.05 1.85 I 320 7.8 6.5 5.5 4.7 4.05 3.55 3.15 2.75 2.45 2.25 2.05 330 8.5 7.1 6.0_ 5.15 4.45 3.9 3.45 3.05 2.7 2.45 2.2 340 9.3 7.75 6.55 5.6 4.85 4.25 3.75 3.35 2.95 2.65 2.4 350 10.1 8.4 7.15 6.1 5.3 4.6 4.1 3.65 3.25 2.9 2.6 360 10.95 9.15 7.75 6.65 5.75 5.0 4.45 3.95 3.55 3.15 2.85 370 11.85 9.9 8.4 7.2 6.2 5.45 4.8 4.3 3.85 3.40 3.1 380 12.8 10.7 9.05 7.8 6.7 5.9 5.2 4.65 4.15 3.7 335 390 13.8 11.5 9.75 8.4 7.25 6.35 5.6 5.0 4.45 4.0 3.6 400 14.85 12.4 10.5 9.05 7.85 6.85 6.05 5.35 4.80 4.3 3.9 410 15.9 13.3 11.3 9.7 8.4 7.4 6.5 5.75 5.2 4.65 4.2 420 17.05 14.25 12.1 10.4 9.05 7.95 7.0 6.2 5.55 5.0 4.5 430 18.2 15.25 1295 11.15 9.7 8.5 75 6.65 5.95 5.35 4.85 440 19.45 16.3 13.85 11 9 10.35 9.05 8.0 7.1 6.35 5.75 5.2 450 20.7 17.35 14.75 12.7 11.05 9.7 8.55 7.6 6.8 6.15 5. R 5 460 22.05 18.5 15.75 13.5 11.8 10.35 9.1 8.1 7.25 6.55 5.i; 470 23.45 19.65 16.8 14.4 12.55 11.0 9.7 8.65 7.75 6.95 6.3 480 24.85 20.9 17.85 15 3 13.3 11.7 10.35 9.2 8.25 7.4 6.7 490 26.35 22.2 18.9 16.25 14.15 12.4 110 9.75 8.75 7.85 7.1 500 27.9 23^55 19.95 17.2 15.0 13.2 11.65 10.35 9.3 8.35 7.55 46 ELECTRIC AND MAGNETIC MEASUREMENTS. We will now proceed to consider commercial forms of galvanometers. MOVABLE COIL OR D'ARSONVAL TYPE. Galvanometers with movable coils through which the current to be measured is passed, and in which the coils rotate in the field furnished by a powerful permanent magnet, are said to be of the D'Arsonval type. An early form of the D'Arsonval galvanom- eter is shown in Fig. 29. The magnet furnishing the field is of the compound pattern made of several U-shaped permanent magnets bolted together and secured vertically to the base of FIG. 29. the apparatus. In the gap, between the legs of the magnet is placed a cylinder of soft iron supported from the rear, which decreases the reluctance of the magnetic circuit and makes the density in the air gap between its face and the magnet faces a maximum, the resultant powerful field giving a maximum re- action for a given current strength. Surrounding the central GALVANOMETERS. 47 cylindrical core, there is a rectangular loop made of many turns of wire supported from above, coaxially with the cylinder by means of a fine silver or alloy strip, as already mentioned. The lower side of the loop is steadied by a similar strip, which in turn is secured at its end to a stiff flat brass spring. The elas- ticity of this spring keeps the strips taut and the coil perfectly centered. The tension on the strips may be varied by means of a suitable thumb-screw, as shown. A small circular mirror hav- ing either a plane or a concave surface, according to the method to be employed in reading the indications of the instrument, is cemented to an upright rod firmly attached to the coil. The current to be measured is led into the coil through the upper metallic suspension, through the several turns of wire com- posing the coil, and out again through the lower strip and flat spring attached thereto. The whole apparatus is kept covered by a glass bell to prevent disturbance by air currents, and .in the bell jar there is provided, a window of very thin clear glass, such as used for microscope slides, through which the beam of light may pass without distor- tion. It will be observed (see Fig. 30 show- ing diagrammatically a plan view of a suspended coil galvanometer) that the D'Arsonval instrument is simply a miniature motor, with fixed permanent magnets for furnishing the field flux, the movable coil, e, forming the armature winding, and the fixed cylinder, c, the armature core. The force with which the coil tends to place itself at right angles to the position shown is thus dependent upon ex- actly the same elements that determine the torque of a motor, that is to say, the strength of the field, the number of turns of wire in the coil, and the strength of the current flowing through that coil. High sensibility may therefore be obtained by using the most powerful possible permanent magnets, and by the em- ployment of the maximum number of turns of fine insulated wire in the loop, at the same time making the restraining frrce of the elastic strips as small as possible. If instead of simply winding the wire into a rectangular coil, it is wound up on a metallic frame, preferably copper or aluminum, because of the good conducting quality of these metals, weight considered, the 48 ELECTRIC AND MAGNETIC MEASUREMENTS. indications of the instrument become " dead-beat," that is, when current is applied, the coil swings at once to the position corre- sponding to the current strength without oscillation around it. When the coil swings, the metallic frame acts like a short-cir- cuited- conductor in a motor armature ; the currents circulating therein require energy for their generation, and that energy is deducted from the momentum of the moving parts, causing them to come to rest almost instantly. In the original form of D'Arsonval galvanometer just de- scribed, the field is not uniform, as the air gap between the cylindrical core and the plane faces of the magnet is, of course, of different depth at different points. As the torsional reaction of the suspension fibers increases in direct proportion to the angle of twist, deflections that are directly proportional to the current strength are obtained only when the coil revolves in a iinif orm magnetic field. A uniform field may be obtained by shaping the poles of the magnet, so that they embrace the central core and leave a uniform air gap, or the same end may be attained by attaching to the magnet poles, iron extension pieces similarly shaped. It is convenient to have an instrument in which the angular de- flections are in direct proportion to the current 'strength, as this greatly facilitates the comparison of different currents with one another. It is claimed by some authorities that the most efficient form of the moving coil is a shuttle shape without a cen- tral core, instead of the rectangular one employing a core. A modern galva- nometer in which this construction is employed is shown in Fig. 31. It will be noted that here the magnet is placed horizontally, instead of vertically, and composed of a large number of com- paratively thin separate magnets stacked one on top of another. Instead of shielding the whole instrument by a glass bell jar, the revolv- ing coil, suspension, and mirror are enclosed in a brass tube, a small glass window being provided opposite the iniiror, through FIG. 31. GALVANOMETERS. 49 which the beam of light indicating the extent of motion may pass. The complete brass tube with its contents may be re- moved from the magnetic structure without disturbing any connection, as contacts are made with the coil through sta- tionary spring plates in electrical contact with the terminal binding posts. Instruments so built may be made of very high sensibility, for instance, one having a resistance of about 200 ohms may be able to show a deflection of the beam of light thrown from a fixed source to the mirror carried by the moving system, and back again to a fixed translucent scale placed 1 meter away from the instrument, of 1 millimeter when 200 megohms are placed in series with the galvanometer, and a potential of 1 volt applied to the free galvanometer and resistance terminals re- spectively. With a coil having a resistance of about 3,500 ohms 1 millimeter deflection can be had through about 1,500 megohms with 1 volt. It must be confessed that these stated sensibilities are some- what misleading, as they are due in part to using a suspension fiber that is so delicate that elastic fatigue will often become noticeable. With such high sensibility instruments it is by no means uncommon to have the light spot on the scale refuse to return to the zero mark after current is cut off, at least until the lapse of a period that may be reckoned in hours, and some- times even days. The low mechanical strength of the suspen- sions introduces another objectionable feature, their great liability to rupture. Means are usually provided for removing the strain on the suspension and then firmly clamping the coil when the instrument is to be transported, but the suspensions are nevertheless frequently broken after the galvanometers are set up, and their replacement is then tedious work. Not only is time required for the delicate operation of replacing the broken suspension, but the calibration, namely, the deflection, given by a stated current must be determined afresh. This is different for different suspensions, not so much because these vary in resistance, for their resistance is generally negligible as compared with that of the coil and the external circuit, but because of the different torsional rigidity of different speci- mens. As the latter are commonly made by flattening a wire of a diameter of about .002 inches in a set of jeweler's rolls, it 50 ELECTRIC AND MAGNETIC MEASUREMENTS. is practically impossible to get the resulting .strips of uniform size and uniform elasticity. One other objection to this sensitive form of D' Arson val gal- vanometer is the fact that the mechanical clearance between the coil and the magnet face is reduced to a minimum in order to reduce the length of the air gap in the magnetic circuit and therefore increase the density of the lines of force flowing there- through. Because of this small clearance it becomes necessary to level the instrument with exceeding care so that the coil may not touch the poles at any point. On the other hand, they are valuable in workshops and laboratories, because they com- bine with high sensibility immunity from disturbance by stray magnetic fields, as the one in which the coil swings is so very strong as to mask any others that are apt to exist at the point of use. A form of D'Arsonval galvanometer that is almost entirely free from the objections to which the sensitive form is open, but which, on the other hand, is of lesser sensibility, is illustrated in Fig. 32. This Chauvin and Arnoux instrument is like the original D'Arsonval pattern, in that a central stationary core is used. The coil consists of a rectangular copper frame around which is wound the moving wire. It does not require the spe- cial leveling screws employed in the high sensitive form, as it is provided with a gimbal interposed between the instrument proper and the wall-plate, which device of course makes the instrument hang perfectly vertical if the plate is screwed upon the wall. The suspension for the coil also differs from those in the high sensibility devices ; it is formed, not of a straight thin strip of bronze, but a strip of very elastic high conductivity alloy wound helically about a mandrel that is about as big as a knitting needle. The toughness of these suspensions is almost incredible, being such that the makers find it entirely superfluous to supply any means of blocking the coil while in transit. They can be shipped around by express, and the writer has even known of one being thrown to the ground with such violence that the mirror became dislodged without caus- ing the suspension to break or to be deformed sufficiently to prevent the coil from swinging freely in its allotted position when the instrument was again hung up. This same suspen- sion is of advantage where mechanical vibration exists at the GALVANOMETERS. 51 point of installation, as it serves to cushion that vibration and greatly diminishes the dancing about of the light spot that is so objectionable in the high sensibility form and frequently renders it impossible to take any readings whatsoever. In. the Chauvin. and Arnoux instrument the support for the scale is arranged to be carried by the instrument itself, and the tele- scope method (see page 43) of making readings is employed in order to render unnecessary the employment of a source of artificial light. It is very light and so small that when FIG. 32. the scale support and scale is removed it may be carried in a coat pocket. With 1 meter distance between the mirror and the scale an instrument having a resistance of about 175 ohms will give a deflection of somewhat over 1 millimeter with 1 volt when about 90 megohms are inserted in series. Com- paring this with the high sensibility form, it will be seen that the sensibility of the Chauvin and Arnoux pattern is less than one half as great. In the D'Arsonval instruments mentioned above, the force 52 ELECTRIC AND MAGNETIC MEASUREMENTS. Flexible FIG. 33. that opposes the motion of the coil is that offered by a strip of elastic metal which is being put under torsion. An interesting variation is where the elasticity of the suspension is made as small as possible and the opposing force supplied by magnetic attraction. Refer- ring to Fig. 33, if the fila- ments attached to the mov- ing coil are conductors, but so flexible that they offer practically no resistance to the rotation of the coil, any current that may be passed would cause the coil to move and assume apposition where its plane is at right angles to the direction of the lines of force in the field between the two magnetic poles. If, however, the wire forming the coil is, as was suggested many years ago (British patent, No. 8,795, of 1887, to Ayrton and Perry), of iron, or is wound on rectangular iron form, the mag- netic flux between the poles will tend to hold the coil so that its plane is parallel to the direction of the lines of force, and the further the plane of the coil departs from this position by rotating around the axis formed by suspension fiber, the greater is the force tending to bring it back again. We therefore have the opposing force furnished by a body that is influenced by the same magnetic force whose reaction with the current causes the coil to move. This tends to pre- serve stability of calibration, for if the strength of the fixed magnet decreases, the reaction between it and a given cur- rent in the coil decreases, but the force opposing the coil motion likewise diminishes as the effort to hold the iron ele- Fio. 34. GALVANOMETERS. 53 ment in line is no longer as great. This form of galvanometer has been reinvented of late by Mr. Weiss, and was described by him in a communication to the French Academy of Science in the early part of 1902. Fig. 34 shows the instrument. The iron element here takes the form of a short bar, M. It is. claimed that the strength of the magnet may vary as much as 20 per cent without changing the calibration. Pivot-borne instruments of this class, for commercial measurements of cur- rent and voltage, have likewise recently been placed on the market in this country. REFLECTING ELECTRO-DYNAMOMETERS. The preceding instruments are suitable only for the measure- ment of direct currents, because the field furnished by the per- manent magnet is constant in direction, so that if the current passed through the movable coil be reversed, the deflecting force is reversed also. The inertia of the coil will not allow it to follow these reversals, so the only effect, if an alternating current is applied, will be a slight trembling of the mirror and the beam of light reflected therefrom. A moving coil galvanometer, which responds to either direct or alternating current, is called an electro-dynamometer, an example of which, well known in this country, is the form designed by the late Professor Rowland. In it the field in which the moving coil swings is supplied by a stationary coil of wire. Through this coil is passed current de- rived from the same source as that flowing through the movable coil. In this apparatus, even if the current be constantly chang- ing in direction, that in the fixed and movable coils is simul- taneously reversed, the resultant, therefore, being a constant effort to turn the coil in one direction. As is shown in the dia- grammatic illustration in Fig. 35, there are two fixed coils, one of fine wire of many turns, and the other of coarse wire of few turns, these being introduced in order to extend the range of the instrument and make its capacity suited to the measurement of both large and small currents. Separate terminals are provided for each winding so that they may be interconnected in any way desired. It is not feasible to make the indications of this class of galvanometers " dead beat " by winding the movable coil on a metallic frame, for if this were done currents would be induced in that frame when alternating currents passed 54 ELECTRIC AND MAGNETIC MEASUREMENTS. through the fixed coil, and the repulsion between these currents would cause a deflection, even if no external current at all were applied to the moving one. The oscillations are therefore damped by mechanical means, a vane of mica being secured to the moving coil and fitted closely in a stationary air-tight box. The sensibility of these instruments is by no means as great as galvanometers of the D'Arsonval type, as the magnetic field furnished by the fixed coils is of far less intensity. It is, however, sufficiently great so that an alter- nating current of .0001 ampere, or an alter- nating potential of .005 volt may be meas- ured. The sensibility for direct current is somewhat higher, but many precautions must be observed in direct current measurements with reflecting electro- dynamometers, in order to eliminate the influence of foreign magnetic fields, nota- bly the earth's field as modified by mag- netic bodies in the vicinity of the appa- ratus. A complete Rowland electro-dyna- mometer is illustrated in Fig. 36. It will be noted that deflec- tions of the moving part are observed with the aid of a tele- scope and fixed scale, as described on page 44. MOVING MAGNET GALVANOMETERS. Galvanometers in which the magnet moved and the coil con- veying the current to be measured was held stationary, formed the earliest type of these instruments. In their elementary form such galvanometers consisted of a compass needle sup- FIG. 35. GALVANOMETERS. 55 ported on a pivot, which was deflected by current passed, par- allel to its length, over and under several times, through a coil of wire. The natural evolution of this form led to an instru- ment in which the needle was suspended by a fine silken fiber which introduced a far smaller error due to torsional rigidity in the fiber than was introduced by the friction between the pivot, and the jewel resting thereon. Of course, the deflection caused by a given current is increased in proportion to the number of times that the current acts on the needle, in other words, by having an increased number of turns in the coil surrounding it TIG. 36. This expedient cannot be carried too far, however, as increased turns mean an increased length of wire, and hence resistance for the current to overcome, and the last turns are necessarily further removed from the needle than the earlier ones, and hence of less efficiency. The next step to increase sensibility is to decrease the directive force tending to hold the needle in a given position. If, as is usually the case, the directive force is that due to the earth's field, its intensity may be diminished by placing a permanent magnet near the apparatus, in such a posi- tion that the field surrounding it is opposite to the earth's field. The magnet is, of course, not adjusted, so that its field and the 56 ELECTRIC AND MAGNETIC MEASUREMENTS. earth's field entirely neutralize one another, as this means no directive force whatsoever. It can, however, be adjusted so that one or the other preponderates but slightly, and the sensi- bility of the apparatus is correspondingly increased. At this point it might be noted that it is possible to make the movable element of a moving magnet galvanometer of a weight the frac- tion of that of the coil in the D'Arsonval type, and hence far finer suspensions are permissible, with a resulting decrease of the force necessary to twist them through a given angle and a corresponding increase of sensibility. As it is not necessary to convey currents to and from the movable element through the FIG. 37. suspensions, only one need be used, and that may be of noncon- ducting material. These features contribute to high sensibility. A prominent moving magnet galvanometer of the above de- scribed type is the " Kelvin instrument," illustrated in Fig. 37. The magnet here takes the form shown in Fig. 38, where three short pieces of watch spring are flattened out and cemented to a mica disk supported by a quartz or silk fiber. This construc- tion is very light and compact. In the Kelvin instrument, the current-carrying coil is divided up into two halves, one of which is movable, so that access may be had to the magnet system, GALVANOMETERS. 57 FIG. 38. and the suspension renewed, if broken. The magnet for varying the sensibility, by neutralizing, the earth's held to a greater or less degree, is not shown in Fig. 37. It is arranged below the apparatus and equipped with a slow-motion screw, so that a fine adjustment of the position of the directive magnet relative to the moving needle is pos- sible. This particular class of Kelvin instrument is objectionable because of its extreme sensi- bility to disturbances due to stray magnetic fields. If the control magnet is adjusted almost to neutralize the controlling effect of the earth's field, any minute variation of the latter due to the presence of magnetic bodies will cause the needle to deflect ; the same effect being, of course, caused by neighboring current- carrying conductors which set up fields modi- fying the influence of the earth's field. This sensibility to magnetic disturbances may be partially overcome as follows : Referring to Fig. 39, if two mag- netized needles of like strength are rigidly coupled together with their ends of the same magnetic polarity pointing in opposite directions, the tendency of the earth's field to keep one needle in a given position is evidently opposite to and neutralized by its tendency to keep the other needle in just the reverse posi- tion. Such a magnetized pair will therefore take up any position freely when in a field as nearly uniform as that of the earth, and is said to be " astatic." An astatic couple for a Kelvin instrument is formed by rigidly joining together in a simi- lar way two of the sets of magnetized watch springs cemented to mica disks used in the plain instrument just described. Both the upper and lower elements are surrounded by wire coils interconnected so that the sum of all the efforts is to cause the element to rotate in a given direction. Each of the two coils is wound in two sections, as in the case of the simpler instruments, and one pair of these is likewise movable, in order that access may be had to the moving part. Fig. 40 shows a four-coil Kelvin S FIG. 58 ELECTRIC AND MAGNETIC MEASURENENTS. galvanometer, the second illustration showing the front coils swung down out of the way and the tube carrying the magnets swung out from the rear coils in order that free access may be had all around it. The mirror, as will be noted, is fastened to the rod joining the two magnetic elements, midway between them. The other cut in Fig. 40 shows the instrument assem- bled and the directive magnet below it. This magnet is closer to the lower set of needles than the upper one, and hence, in- fluences the latter more and furnishes a directive force sufficient to hold it in a given position. The four coils may, of course, be coupled together in series or parallel as desired, or in FIG 40. opposition, namely, differentially, so that the deflection due to the difference between the strength of two currents may be observed. The construction of these instruments is not such that the in- dications are inherently " dead beat," and it is necessary to apply extraneous methods of damping if rapid readings are to be taken. In some forms this is accomplished by attaching to the moving system a thin vane immersed in oil, but it is more common to make the mica disks on which the magnetized watch springs are cemented fit rather closely in a spherical chamber so that the GALVANOMETERS. 59 indications are air dampened. If the hollow chamber has mas- sive copper walls, this also damps the oscillations, as the moving magnet expends energy in setting up currents in the copper and there is, hence, less force available to move it beyond the posi- tion corresponding to the current strength. The four-coil Kelvin galvanometer, notwithstanding the fact that it is provided with an astatic pair of needles, is by no means entirely immune from disturbances by external magnetic forces. This is because it is seldom that such forces are sensibly the same in the regions of both magnets ; or, in other words, that such external fields of force are uniform. It is also exceedingly susceptible to mechanical vibrations and must be mounted with extreme care in order that such vibrations may not affect it sufficiently to throw the light spot off the scale. On the other hand these galvanometers have the highest sensibility attainable. HOT WIRE GALVANOMETERS. When an electric current flows through a conductor, a resist- ance to that flow is encountered, and the work done by the cur- rent in overcoming the resistance heats the conductor. If the conductor is a fine wire and the current is comparatively heavy, the resultant expansion, suitably multiplied and indicated, may be used to measure the current -strength. The use of gal- vanometers utilizing this principle is not general, because their sensibility is not high ; they are sluggish in their indications, owing to the time required for the wire to attain its new temperature when the current strength changes, and it is difficult to compensate for changes in the temperature of the air surrounding them and to shield the wire from slight air currents. On the other hand, they have the great advantage for alter- nating current measurements, that their self-induction and capacity is practically zero, and hence their use does not alter circuit conditions. One of the most sensitive instruments of this class consists of two very fine wires of manganin or platinum silver alloy stretched parallel to one another a short distance apart, their ends being secured to appropriate abutments. These wires are embraced at the center by a very small loop of stiff paper carry- ing a small plane mirror. A microscopic hook at the end of a 60 ELECTRIC AND MAGNETIC MEASUREMENTS. fine light spring is slipped over one of the wires near the paper loop, the mirror in this way being pulled around to a certain angle about the other wire as a center. When current flows through the wire on which this hook is caught, the expansion of the wire due to its heating allows the spring to pull the mirror over still further, the resultant deflection being read off on a suitable scale by the conventional spot of light. For max- imum sensibility to small currents, the wires are made of a material having as high a specific resistance as can be obtained in order to make the heating effect, which, with a given current, varies as the resistance, a maximum. To get the greatest deflection with a low voltage the wires are made of as low resistance as is feasible, in order that a maximum current strength may flow and hence cause maximum elongation. Several galvanometers working on this principle have been brought but from time to time, notably those of Prof. Threlfall and of Dr. Fleming. In this country, a similar instrument is made by Leeds ,nd Northrup. RADIATION GALVANOMETERS. The most sensitive galvanometers for the detec tion of alternating currents seem to be those in which the heating of a wire carrying current is indicated, not by a magnification of the change in length of the wire, but by radiation of its heat to a delicate thermo-couple. The Duddell instru- ment, made on this principle, is diagrammatically illustrated in Fig. 40 A. As will be seen from this, a loop consisting of a single turn of wire is placed in the field of a magnet like that in the conventional D'Arsonval galvanometer. The two ends of the loop terminate in a thermo-couple, which is placed close to the short straight wire through which the current to be measured is led. The heat radiated from the wire causes a current to flow from the thermo-couple through the loop, and that current brings about a deflection of the loop in the conventional manner. The deflec- tions are read off by the aid of the mirror, M, in the ordinary way. According to Duddell, such a galvanometer will show an FIG. 40 A. GALVANOMETERS. 61 apparent scale deflection of 2 millimeters with 1 millivolt difference of potential, at the resistance wire ends. The cur- rents generated by talking into a Bell telephone receiver are sufficient to throw the beam of light entirely off the scale. An instrument having a resistance of 18 ohms is capable of meas- uring a current as low as 160 micro-amperes. REFLECTING ELECTROMETERS. The electrostatic instrument shown in its elementary form in Fig. 19 and described on page 30, may, when suitably designed and provided with a long, delicate suspension and a mirror for taking readings, be made a galvanometer of value for certain alternating and direct current measurements. Its sensibility is by no means as high as that of a very ordinary direct current gal- vanometer or of the galvanometer responsive to both direct and alternating currents just described, but it has the advantage of possessing a practically infinite resistance, no inductance and small capacity. The first of these characteristics is of peculiar advantage in certain direct as well as alternating current meas- ments as the electromotive force measured by the twisting of the suspension as shown by the deflection of the beam of light from its mirror is that of the source under test when it is supplying no current, that is to say, it is the open circuit E.M.F., a value that often requires determintion. In using electrostatic galvanometers, there is a source of possible error which must always be considered. The suspension fiber supporting the movable vane in such instruments must necessarily be a conductor of electricity in order that the cur- rent required to charge the vane may be conveyed to it. The fiber and the vane are almost invariably of different chemical composition, usually phosphor bronze and aluminum respectively, and when two dissimilar metals are placed in contact it is well known that there will exist a difference of potential, usually called a " Contact E.M.F." between them. The movable ele- ment thus always has a small initial charge, and if it is further charged by applying current to the apparatus in such a direction that the new charge assists the initial one, the deflection will be greater, by twice that due to the initial charge, than if the potential of the circuit to be measured were applied in the 62 ELECTRIC AND MAGNETIC MEASUREMENTS. opposite direction. If the instrument is always to be used with direct current, and care is taken to see that the same pole of the applied circuit is always attached to a given binding post, this error may be allowed for in the calibration. If alter- nating current be measured, however, a correction equal to the initial charge must be applied. A reflecting electrometer is shown in Fig. 41. For the very highest sensibilities the suspension for the moving element of an electrometer may be made of a quartz fiber on which is chemically precipitated a very thin, adherent film of gold to render it con- ducting. With a suspension of this sort a sensibility may be obtained such that it is possible to get a deflection of 200 or more millimeters on a scale placed 1 meter away from the mirror with 1 volt. As the deflections of electro- static instruments increase as the square of the applied vol- tage, a very high deflection for a given E.M.F. may evi- dently be obtained by apply- ing a steady initial E.M.F. of some magnitude and then superimposing the unknown one on that. In this way the sensibility of a reflecting electro- meter may be increased enormously. THE TELEPHONE RECEIVER. The conventional telephone receiver is a convenient and simple piece of apparatus often used for the detection of feeble electric currents. Of course, it cannot of itself measure current strength as its indications are audible only, and the human ear cannot evaluate tone volume with any accuracy, but it does form a sensitive means for showing whether a difference of potential does or does not exist. It is naturally necessary to arrange the appara- tus so that the circuit through the receiver may be successively FIG. 41. GALVANOMETERS. 63 made and broken, because it is only on the make and on the break that the diaphragm of the receiver will respond and give forth a clicking sound. A good telephone receiver having a resistance of about 100 ohms will give an audible click when a circuit passing .005 mil- liamperes through it is made or broken. The advantages of a telephone receiver for this kind of work are its low cost, its portability, the fact that it need not be leveled or placed in any definite position, and that it is not affected by stray magnetic fields. CAPILLARY ELECTROMETERS. An effective device for detecting and measuring very small direct current E.M.F.'s is made by enclosing in a glass tube of FIG. 42. very fine Dore, clean, pure mercury and a strong solution of sulphuric acid, the two being in contact with one another. When a potential difference is applied between the two ends of the tube, an action takes place at the surface of contact between the mercury and the acid which causes a change in the capillary pressure. This in turn causes a displacement of the surface of the mercury which, while small, may easily be read with the aid of a microscope. For small differences of potential the dis- placement is directly proportionate to the potential. Obviously, a device built on the above principle may assume many forms. In Fig. 42 is shown the Boley type, in which the mercury is contained in a spherical glass chamber A which 64 ELECTRIC AND MAGNETIC MEASUREMENTS. communicates with the acid solution at e through the fine bore tube t. A relatively large volume of the electrolyte L is pro- vided in order to have a large contact area available between it and the other mercury electrode E through which current is introduced, this large area being desirable to prevent rapid polarization. The level at which the mercury in the fine bore tube t comes in contact "with the electrolyte can obviously be adjusted by varying the air pressure on the surface of the mer- cury in A or by varying the depth of the 'electrolyte in its chambers. The change in level caused by the application of an E.M.F. to the instrument is observed through a microscope, an apparent change of 1 millimeter being shown, with a magnifying power of 100, with a potential change of .0024 volts. The instrument can be read to .0002 volts without difficulty and it is claimed that the changes in level are exactly proportionate to Ihe volt- age up to .01 volts. Capillary electrometers are not in common use as they have unstable zeros, are not portable, and the microscope method of taking readings is very hard on the eyes. GALVAXOMETEK SHUNTS. Plain Shunts. A commercial galvanometer is naturally made of the highest sensibility consistent with its cost and type in order that it may be suitable for delicate and accurate work. For preliminary measurements, the sensibility of an average galvanometer is often too high, however, and in making the first adjustments, currents may flow that will either burn out the windings or injure the device mechanically by deflecting the moving portion too violently against the stops provided to limit the motion. An arrangement of several galvanometers of varying sensibility to be used successively would evidently be both awkward and costly. Devices are therefore supplied, by the aid of which the sensibility of a given galvanometer may be varied from its maximum by successive steps to any desired minimum, and these devices are called " galvanometer shunts." Referring to Fig.43, let G represent a galvanometer of resistance 6r, B the source of the current to be measured, and x a resist- GALVANOMETERS. . 65 ance which may be inserted between the galvanometer terminals. From. the law of divided circuits (see page 93), the resistance of the circuit formed by the galvanometer and the shunt x con- nected to its terminals is -^- and, if the current flowing through the battery circuit is A amperes, the fraction thereof that flows Ax through the galvanometer is -^ . To take a concrete case, if G- is 900 ohms, and x is made 100 ohms, --. zr-c = .1 of the g - G battery current goes through the galvanometer and the same current from the battery that would cause a given deflection with no galvanometer shunt will cause but one tenth of that deflection with the shunt attached, provided, of course, that the gal- vanometer is of a pattern in which the deflections are proportionate to the current. It is usual to supply a set of shunt resistances like x in the figure, all built into one case and having suitable bind- ing-posts for the attachment of the various wires. Such shunts are usually made 1, gL, and -Q-$ of the galvanometer resistance, reducing the sensibility to respectively .1, and .01, and .001 of the normal. One of them is illustrated in Fig. 44. In order to have the simple decimal relationship between the value of the deflections when such shunts are used, it is evidently neces- sary to have the shunt resistances accurately adjusted to work with the given galvanometer. A separate shunt-box is there- fore required for each instrument. B FlG - 43 - Compensated Shunts. It will be noticed that with simple shunts of the character just described, the combined resistance of the galvanometer and shunt will vary with the shunts of different values. This is a feature that is often objectionable, because with a given source of E.M.F. the current through the galvanometer circuit will 66 ELECTRIC AND MAGNETIC MEASUREMENTS. vary with every step. It is therefore evident, if we have a given E.M.F. which produced a given deflection with the one tenth shunt in, this deflection is not one tenth of that which would have been given with the same E.M.F. and no shunt, but differs by an amount dependent on the resistance of both shunt and galvanometer. To correct this, compensated shunt-boxes are made, in which, when the movable plug is shifted to insert any ratio shunt, there is inserted at the same time an auxiliary resistance in the galvanometer circuit, which offsets the changed resistance of the whole, and keeps the effective resistance be- tween the battery terminals con- stant. The way in which this is done can be seen from inspection of Fig. 45. Owing to the greater amount of work involved in ad- justment, these compensated*shunts are far more costly than the type described before, and c o n s e- quently are in less common use. The Ayrton Shunt. As above stated, galvanometer shunts of the types just described are open to the objection that each must be separately adjusted to work with the galvanometer with which it is to be used. This is a disadvantage not only in that it necessitates the purchase of as many shunts as the user has instruments, but because if a gal- vanometer should be injured and require rewinding, its shunt would have to be readjusted too, thus adding considerably to the expense. Such shunts are also objectionable in that, while correct for a steady current, the indications of the gal- vanometer with which they are used are not correct when meas- uring current impulses that exist only momentarily, as in measuring capacity. The proof of this need not be given here, although it may be of interest to note that the tendency is to make the galvanometer read too low.- The universal shunt devised by Ayrton and Mather escapes FIG. 44. GALVANOMETERS. 67 these objections. This shunt is universal in that it need not be adjusted to any particular galvaonmeter but can be used interchangeably with all, and the results are accurate whether the current flow is continuous or only momentary. The principle of the Ayrton and Mather shunt can be understood from Fig. 46. Here Q- is a galvanometer of resistance 6r, TT' the resistance which is connected to the galvanometer terminals and forms the shunt proper, B a source of current, C the current (total) flowing through the battery circuit, c the current flowing through the galvanometer cir- cuit, and R the resistance of the conductor, TT. f From the law of divided circuits the current that flows through the galvano- meter is C = r = -^ ^ When the contact of the source of current is made at the extremities, TT' of the shunt, the current fl o w i n g through the galvanometer is evi- ~D dently c =__ . If, there- fore, r be made -^ of R, only -J-g- of the battery current goes through the galvanometer, and the deflection for a given bat- tery current is reduced to y 1 ^. If r be made 01 of R, only T -J-g. of the battery current goes through the galvanometer, and the sensibility is reduced to that amount. A commercial form of Ayrton and Mather shunt is illustrated in Fig. 47. Here there are four steps giving sensibilities of 1, - 1 and of FIG. 45. the normal with two additional steps, one short circuiting the galvanometer when no current is on, and the other opening the galvanometer circuit itself. By means of the small hard rubber handle shown, the contact carriage maybe quickly moved along the line of contacts, the galvanometer being watched at 68 ELECTRIC AND MAGNETIC MEASUREMENTS. the same time, until a sensibility is reached which gives a good deflection. ERECTION AND CAKE OF GALVANOMETERS. Generally speaking, the higher the electrical sensibility of a galvanometer, the more it is subject to the influence of mechan- ical vibration, and, if placed on an ordinary work-bench or table, it is out of the question to use one in a workshop ; for the trembling of the mirror causes the spot of light to jump over the scale in such a manner that no readings can be taken. A frequently adopted plan to overcome this annoyance is to build a heavy brick or stone column, capped with a slab of soap- stone or slate, on which the galvanometer may be placed and leveled for use. In order to prevent the communication of the vibrations of the building thereto, this masonry pier must be carried clear down into the ground, and must be ept free throughout its whole length from contact with any part of the FIG. 46. building. This expedient, of course, is expensive, and local conditions are sometimes such that even it does not afford a complete remedy ; moreover, the construction of such a pier for use in the upper stories of a building is out of the question. In most circumstances, as good or better results can be secured at a less expense, by mounting the galvanometer on a heavy timber or stone shelf built solidly into the walls of the building, provided the machinery foundations are separate from the foundations of the walls. With a reasonably well-built structure, and not too much moving machinery on the floors, good results may be obtained some stories from the ground. In cases where this plan does not give a sufficiently steady support, the galvanometer may be mounted on a platform hung GALVANOMETERS. 69 from springs, and provided with suitable weights. The proper adjustment of the weight, with respect to the strength of the suspending springs, is the principal feature in making a success of the method. The springs should be rather long, moderately strong, and should then be loaded down so as to stretch them well. Thus adjusted, the natural period of oscillation of the apparatus, as regards vertical displacements, is large, so vertical tremors of a comparatively high frequency are, practically speaking, completely damped out. High frequency disturbances in a horizontal plane are still more completely gotten rid of. FIG. 47. Should there be a tendency for the apparatus to oscillate in its natural period, pendulum-wise or vertically, it can be overcome only by the use of dash-pots or their equivalent. These may be arranged to damp either a vertical or horizontal oscillation. Another good way to damp horizontal movements of long period is to fasten rubber bags below the platform, in such positions that they may be brought into contact with the under side of the platform by inflating them with air. This will stop the long period movements, while the bags are not sufficiently rigid to communicate short period movements. Fig. 48 shows a double platform. On the upper shelf is 70 ELECTRIC AND MAGNETIC MEASUREMENTS. placed the principal weight, while the galvanometer is placed on the lower shelf. The weights and springs should be so ad- justed that the natural periods of the two shelves are incom- mensurable, which still further tends to damp out vibrations of all frequencies. This arrangement is, however, necessary only under exceptionally unfavorable circumstances. The scale on which the deflections of the beam of light from y//////////////////^^^^^ FIG. 48. the galvanometer mirror read off is placed on a separate support, as, in the case of the pier or shelf arrangement, a support large enough to contain both would be too costly, and, in the case of the spring suspension form, both bulky and offering a chance of trouble if the scale should be accidently touched by the observer, as this would then set the whole apparatus in vibration. A GALVANOMETERS. 71 small vibration on the part of the scale is of little importance, as it is not magnified in the same way that the light beam motion is, and the scales are, therefore, usually mounted on a simple standard at the proper distance from the galvanometer, or, in special cases, may be supported from overhead. In that form of reading device in which a telescope is em- ployed, the only requisite is that the general illumination on the scale be sufficient to make the scale markings, as reflected in the mirror, and viewed through the telescope, readily visible. In the pattern where a beam of light is thrown on the galva- nometer mirror, and reflected from there by a translucent scale, the apparatus must, of course, be placed in a room, which, while it need not be absolutely dark, must have but a low illumination in order that the position of the line of light on the ground glass may be readily discerned. The source of the beam of light may be an oil lamp or a gas jet, inclosed by a metal chimney, having a fine slot in one side through which the ray emerges. This is condensed by a lense and thrown on the mirror, the latter being concave to prevent disper- sion, and makes a sharp line on the scale. In order to obtain a darkened galvanometer room, hangings are usually used, which interfere with the circula- tion of the air, and the room is apt to become stuffy, if gas or oil flame is employed. It is therefore still better to use an incandescent lamp as the light source where possible. The lamp should not have a filament of the coiled form, but one of the old plain U shape, and the shield around the lamp arranged so that the light from the straight portion of one of the halves of the U is what is allowed to fall on the mirror. Some foreign makers go so far as to construct a special incandescent lamp for this work, in which one leg of the filament is made absolutely straight. An example of this is illustrated in Fig. 49. Few general instructions can be given in a work of this kind as to the care of a galvanometer, because the constructional details vary in instruments of different makes, and where com- plete instructions are not supplied with the apparatus by the builders, the application of common sense will remedy the defect. FIG. 49. 72 ELECTRIC AND MAGNETIC MEASUREMENTS. Those not accustomed to handling such work will have their patience sorely tried, when a suspension breaks and must be re- placed, but they must console themselves with the reflection that even experienced users break many a new suspension when replacing an old one. CHAPTER IV. POTENTIOMETERS. SLIDE WIRE TYPES. THE potentiometer is an instrument of precision for electri- cal measurements that is sufficiently important to warrant devoting an entire chapter to its uses. With its aid, and that of certain auxiliary appliances, measurements of potential may be made in terms of the E.M.F. of a standard cell, covering a range of from a very small faction of a volt to several thousand volts, and of currents from a fraction of an ampere to many thousand amperes. It may also be used for the accurate com- parison of resistances, and therefore indirectly for the meas- urement of temperatures varying from below freezing to 1,200 C. The principle of the ordinary potentiometer may be under- stood by reference to the accompanying Fig. 50. Here MN is a straight wire of convenient length and as high resistance as possible consistent with mechanical durability. To its ends are attached leads from a battery, B, usually a storage cell giving a potential of about two volts, in circuit with an adjustable resist- ance, R, by means of which the difference in potential between the points M and N may be adjusted to any desired value lower than the cell potential. To the point M there is also connected a wire running to one pole of a double-throw switch, D. By means of a suitable device, 6 y , contact may be made at any desired point along the wire, MN. The connection running from the contact, (7, passes through the galvanometer, 6r, to the other pole of the double-throw switch, D. When D is thrown to the position shown in the figure, it connects the wire terminal attached to one end of the wire, MN, with one pole of a standard cell, S, and the adjustable contact, (7, with the other pole of that cell. When the switch, D, is thrown to its other position, the same points are connected with the unknown E.M.F. to be measured. The standard cell has a resistance, r (usually about 10, 000 ohms), 73 74 ELECTRIC AND MAGNETIC MEASUREMENTS. connected in series .therewith, which resistance may be short cir- cuited by the switch shown, and the galvanometer is provided with a shunt, $, which may be cut in or out by means of its switch. When a potential measurement is to be made, the switch, D, is thrown so as to couple in the standard cell, the resistance, r, being in the standard cell circuit, and the shunt, S, across the galvanometer terminals. If the wire, MN, has an adjacent scale divided into 2,000 equally spaced divisions, and the E.M.F. of the standard cell at the temperature at which it is being worked is 1.434 volts, the contact, (7, is placed 1,434 divisions away from J/, and the rheostat, 72, varied until the galvanom- FiG. 50. eter shows no deflection. The shunt, $, across the galvanometer terminals is then cut out so as to increase the sensibility, and if the galvanometer then shows a small deflection, the rheostat, R, is further adjusted until that deflection disappears. As -the strength of the current from the battery, B, through the wire, MN, is now such that it causes between 1,434 of the 2,000 spaces in which that wire is divided, a drop of potential of 1.434 volts, the difference in potential between M and N is evidently two volts. If therefore the switch, D, is thrown over, so as to apply to the points, M and <7, an unknown potential, which POTENTIOMETERS. 75 must, of course, be less than two volts, and the contact, (?, is moved along the wire until the galvanometer shows no deflec- tion, the E.M.F. of the source to be measured is given directly by a number of the divisions between M and (?, each of which divisions represents .001 volt. In actual practice the length of the wire, MN, is usually made about one meter. If it is longer the apparatus becomes awkward to handle, and if much shorter it is extremely diffi- cult to read its scale, with 2,000 divisions, without straining the eyes. A more practical form of potentiometer is diagrammatically shown in Fig. 51. It will be noticed that this differs from the ele- mentary one in that the resistence between the points M and JVis FIG. 51. no longer composed of a single straight wire, but of fourteen coils of wire, each provided with an appropriate terminal, plus the straight wire. The resistance of each of the coils is the same as that of the straight wire, MN' , and both of the wires running to the multithrow switch terminate in contacts which may be moved along the resistance, MN. In this form, if the rheostat R, be adjusted so that the difference of potential between M and N is 1.5 volts, the fall of potential between the terminals of each of the fourteen coils is one tenth of a volt, and if the wire, MN, be divided into 1,000 divisions, the difference of poten- tial between each will be YoJo"o f a volt; in other words, the arrangement is made ten times as sensitive as the elemen- 76 ELECTRIC AND MAGNETIC MEASUREMENTS. tary form by the addition of supplementary coils. The length of the wire, MN 7 , may be made somewhat less than a meter, but if the apparatus is to be used for considerable periods at a time, the length should not be less than two feet, because of the strain on the eyes of the observer, due to the fineness of the divisions. The modified form has an additional advantage over the ele- mentary, in that the resistance between the points M and N is far higher, and there is therefore less current drawn from the battery B, with a consequent less liability of change in strength of that current. In both it is essential that the straight wire be of uniform resistance throughout its length, in order that the drops across equal portions thereof may be uniform. Calibration of the Slide Wire. As the accuracy of a slide wire potentiometer depends funda- mentally on the assumption that the wire is of uniform resistance throughout its length, and as the results given by it are erone- ous unless this holds rigorously correct, it is well that a user should know how to investigate this point for himself. Accurate checking is at best a tedious process, the following being probably the most convenient method : First, two stand- ard resistance coils of a value which may conveniently be in the neighborhood of one ohm each are selected, and these must then be adjusted so that their resistances are exactly alike. This is usually accomplished by shunting the higher resistance one with a plug resistance box and altering the box resistance until the two are shown by any convenient one of the methods de- scribed in the chapter on resistance measurements to be exactly the same. That fine adjustments are possible in this manner is evident from consideration of the fact that if the box has a resistance of as low as say 2,000 ohms, and this is placed in 1 x 2000 shunt to one ohm, the combined resistance becomes ohms, or approximately, .9995 ohms, a variation of .05 per cent. Having by such means obtained two exactly equal resistances, adjust one of them so that its resistance differs from that of the other by a very small but definite amount, which it may be assumed is obtained by shunting it with 1,000 ohms. If each of the resistances were originally x ohms, the one shunted by POTENTIOMETERS. 77 1,000 ohms becomes -JTTTJTJ and the difference between them, x ^. - ohms. The two coils differing by the known J.UUU -]- X amount, derived from the above formula, are then used as the coils A and Bin the arrangement shown in Fig. 52, which figure will be understood to be merely diagrammatic. In the same figure ab form the terminals to which the extremities of the wire under test are secured and e and/, terminals for another bare stretched wire, whose resistance per unit of length need, however, not be uniform. A battery and a galvanometer are also provided as shown. The galvanometer contact G- is now moved along the wire ef, until the galvanometer shows no de- flection, with the contact Q kept constantly at position 1 ; this point is noted, and the coils A and B interchanged. The gal- vanometer can again be brought back to zero by moving C to the point 2. The distance between the points 1 and 2 of the wire under test is then the difference of the resistance of the coils A and B. The coils A and B are now put back in their origi- nal positions, and being kept at the point 2, the contact 6r shifted to another position, 6r r , on the wire ef, where balance is restored. This evidently forms a fresh starting point, and the resistance of the section 2-3 of the wire under test may be found in terms of the difference between the resistances A and B. The process is repeated until the whole wire ab has been divided up into sections of equal and known resistance. If these coincide with the scale markings on the potentiometer as secured from the maker, it may safely be presumed that the wire 78 ELECTRIC AND MAGNETIC MEASUREMENTS. has been properly tested for and adjusted to uniformity, or else that the scale has been drawn to allow for inequalities in the wire. When calibrating a wire that has not been checked before, it is usually advisable to make the above test more than once, using fresh values of difference in resistance between A and J9, in order that the measurements will include practically every section of the wire length. A rougher test of the uniformity of resistance of a slide wire may be made by passing a continuous current of an appropriate constant strength through it and then by means of a pair of contacts held rigidly spaced at a small distance apart, observ- ing whether the deflections of a galvanometer attached to the contact terminals are the same wherever on the wire length the contact may be applied. If they are, the wire is ^evidently electrically uniform. Contact Devices. The device used to make contact with a potentiometer wire must be carefully constructed in order that its position with reference to the fixed scale may be accurately read off and that the operator cannot mar the wire when making contact, and thus destroy the uniformity of its resistance. The form of contact used in the old model Crompton potentiometer, which instrument is built on the principle illustrated by Fig. 51, is illustrated in Fig. 53. Here S is the extremity of a long weak spring, which tends to press downward the wedge-shaped block secured to the end of the spring. The down- ward tendency of S is more than FIG. 53. overbalanced by the upward pull on it exerted by the button-shaped head of the plunger, P, beneath whose shoulder there abuts a spiral spring. P is the knob that is depressed by the operator when it is desired to make contact with the wire and the exertion of considerable pressure on the knob, P, will not increase the pressure of the contact on the wire, as P simply releases the weak spring that carries S, and the pressure on the wire is determined solely by the elasticity of that spring. The knurled-headed screw pro- POTENTIOMETERS. 79 jecting from the end of the contrivance works a micrometer screw to make very fine adjustments. An even more elaborate form of contact is shown in Figs. 54 and 55, this being one designed by Callender and Griffiths for use with their labora- tory standard bridges. It is made in two parts, one of them, ABA', sliding against the non-graduated guide bar that is placed parallel to the graduated scale, and the other against the graduated bar. The first part is steadied by means of springs, placed as shown, that keep it in contact with its guide, and the second piece in a similar manner has a flat spring between it and the first. To the section ABA' is attached a bracket carrying the screw S, which is used to make fine adjustments. When this is turned, the inner block, E, alone moves, as its pressure against the graduated bar is only that due to the spring at EE', whereas the pressure of the outer portion against the guide bar on which it slides is the pressure exerted by the spring EE', plus that of the springs at AA'. The wire, W, FIG. 54. FIG. 55. is brought into contact with the sliding wire itself, and the one parallel to it attached to the galvanometer terminal by turning the screw, O, and forcing the slide and galvanometer wires down on one running at right angles thereto. By this means a very definite point of contact may be obtained. It is very difficult for a careless operator to injure the potentiometer wire with this form of bridge, for if it were attempted to move it without releasing the screw, O, the outer block, ABA', would simply move relative to the inner one without tearing or deform- ing the wire. In commercial potentiometers where laboratory accuracy is not required and the item of cost comes into consideration, it is becoming more common practice to use a simpler form of con- tact in connection with the slide wire. This device is continu- ally in contact with the wire, and is simply slid along from one position to the other when readings are being made. Such con- 80 ELECTRIC AND MAGNETIC MEASUREMENTS. tacts usually take the form of rather blunted knife edges at right angles to the wire length, being pressed against the slide wire by a weak spring and supported by a rigidly guided block. The spring tension must be adjusted with great care to avoid the wear on the slide wire that would ensue if it were too great, and the uncertain contact that would exist if it were too small. The spring adjustment is usually fixed by the maker of the in- strument and no means are provided by which the user can change it later on. With the constantly engaged form of contact it is necessary to be particularly careful to see that both the wire and contact are OAQ OO OcQ FIG. 56. perfectly clean, as any grit would cause rapid and, of course, un- even wear, which would destroy the uniformity of the resistance of the wire, and hence the accuracy of the whole device. In the present type of the Crompton potentiometer, which is probably the best known of the slide-wire type instruments, the wire itself, as well as all other moving contacts, are, as is shown by Fig. 56, completely enclosed and shielded by plate glass. In one form of the Leeds and Northrup instrument, shown in Fig. 57. the slide wire is exposed on the surface of the marble drum about which it is wound in a manner that renders it easily POTENTIOMETERS. 81 accessible for cleaning with a soft cloth, or fine tissue paper. In both instruments it is necessary to keep the wire coated with a thin film of vaseline or parafrme oil, as this is found to eliminate the otherwise troublesome thermal E.M.F's set up at the point of contact and, of course, diminishes the wear. In a later design of the Leeds and Northrup potentiometer, the marble drum is covered by a cylindrical shield to protect it from dust. All potentiometers of the slide-wire type are somewhat objectionable in that their necessarily low resistance means that FIG. 57. a fairly heavy current is required from the working battery, a condition that involves more rapid polarization with a conse- quent change in the drop along the wire. To check up the cor- respondence of the wire and its scale is further, as is evident from what has before been said, an extremely tedious operation, and one calling for auxiliary apparatus of a kind that is not always available. On the other hand, the low resistance poten- tiometer is better suited for making measurements of very small potentials, and being continuously adjustable, has an infinite number of steps in contrast to any step by step design. 82 ELECTRIC AND MAGNETIC MEASUREMENTS. RESISTANCE COIL POTENTIOMETERS. Potentiometers having a relatively high resistance may be made by substituting for a straight wire a set of resistance coils electrically connected in series, and with their terminals attached to contact plates or buttons. If it be desired to work to the fourth or fifth decimal place the number of coils that would be required, if a separate one were provided for each step, would be prohibitively large, one thousand, for instance, being needed to replace the slide wire alone if the wire scale of the Crompton instrument was to be duplicated. To avoid this a modification of the Varley slide, which is analogous to the vernier used in mechanical measurements, is used. Referring to Fig. 58, in which the apparatus is diagram- matically illustrated, between the points A and C tbfere are .10, 10 Ohm Coils: \ FIG. 58. fourteen coils, each of 1,000 ohms resistance, connected to the terminal contacts shown. Between the points and J5, 10 resistances of 10 ohms each are similarly connected. Between E and F there are 9 coils, each of 1,000 ohms resistance, and between G- and H, 9 coils, each of 10 ohms resistance. The terminals of EF and Grff are connected to a pair of contact points, 3M~ and M f M f , respectively, rigidly coupled together by means of an insulating piece, and held separated by a distance equal to the space between the contact buttons of the coils com- posing A C and CB respectively. Referring first to section A O of the apparatus, the drop of potential between the buttons under MM is evidently that due to the flow of the current through a circuit composed of 1,000 ohms resistance shunted by 9,000 ohms, namely, a circuit of 9000x1000 POTENTIOMETERS. 83 As this drop is that between j^and F, which in turn is com- posed of a series of nine equal resistances, the drop between any two buttons on EF is evidently that due to the cur- rent flowing through a resistance of one ninth of 900 ohms, namely, 100 ohms. In an exactly similar way the drop be- tween the contact buttons of the resistance forming the series GrH, is that due to the current flowing through 1 ohm. In other words, if adjustable contacts be made to slide over EF and GrH, the total drop may be varied in four steps, the unity steps being caused by shifting the contact, 1, along GrH, the tens steps by shifting MM along GB, the hundreds steps by shifting J along EF, and, finally, the thousands steps, by shifting MM along AC. The total range is made to take in 1,500 units in order that the value of the E.M.F. of the standard cell to be used for comparison 'purposes may be set off directly to steps corresponding to a resistance of 1,434 ohms if the Clark cell is used, or 1,019 ohms if the Weston cell is used, whereupon any E.M.F. to be measured in terms of the standard cell could be read directly by steps of .0001 volt each. The resistance of the contracts at MM, M'M', J, and I intro- duce errors that are inappreciable. Taking, for instance, the case of the contacts M'M', if these had a resistance as high as 0.1 ohm, the 10-ohm coil, to whose terminals connection is made, is shunted by 90.1 ohms instead of 90 ohms, and the resultant resistance is -^ = 9.001 ohms instead of 9 ohms, which 10 + 903 is an error of only about .01 of 1 per cent. As the resistance coils entering into the construction of this type of potentiometer are all of either ten or one thousand ohms value, it is a very simple matter to check the adjustment at any time as almost every testing installation includes apparatus by means of which resistances of this order may be compared with a high degree of accuracy. Each contact button usually has a hole drilled in it at some convenient point and is provided with a set screw, so that it is easy to attach wires to the terminal of each individual coil to measure its resistance. It should be noted that it is not essential even that standard resistances of 10 and 1,000 ohms respectively, be available, as all that is necessary in order to have the apparatus read correctly 84 ELECTRIC AND MAGNETIC MEASUREMENTS. is that all the 1,000 ohm resistances shall be alike and all the 10 ohm, resistances alike, and equal to one one-hundredth part of the nominal 1,000 ohm resistances. Any one of the coils may, therefore be used as the standard of comparison, and if the others agree with it the apparatus is in proper shape. Leeds and Nbrthrup Potentiometer. A potentiometer of the step by step type using the Varley slide, is shown in plan view in Fig. 59, the connections of the same being illustrated by Fig. 60. It will be observed that the series of coils in the right-hand side of the figure, that is to say, between and B, is provided with a slide on a slide, thus in- FIG. 59. creasing the number of readable steps to 15,000. A feature of great convenience in this potentiometer is the arrangement for throwing in the standard cell for making the initial adjustment of the rheostat R in the working cell circuit and of allowing the checking at any instant of the fact that the current sent through the potentiometer by the working cell has remained unchanged, both without necessitating a resetting of the five radial switch arms to the positions corresponding to the standard cell voltage. This is accomplished as follows : In Fig. 60 the resistance of the fifteen 1,000-ohm coils between A and (7, one of which is always shunted by 9,000 ohms, is 14,900 ohms, and of the ten 10-ohm coils in CB, as shunted by the double slides, 99.9 ohms, a total of 14999.9 ohms. POTENTIOMETERS. 85 Now, assuming that a non-saturated solution Clark cell is to be used as the standard, the maximum temperature at which this will be employed would hardly exceed 32 C., at which point its E.M.F. would be, according to the formula before given, 1.4355 volts. Now, if the standard cell were at E and the double pole- switch 7 in the position shown, the various slides would have to be set to positions making the drop at the cell terminals, that is, across 14,355 ohms, in order that when the working cell cur- rent was adjusted by the rheostat, R, so that there would be no FIG. 60. deflection of the galvanometer, G-, when the key, FJ was closed, the drop per readable point on the potentiometer should be exactly .0001 volt. By simply shifting the double pole-switch, Z7, to its other position, however, it will be seen that no matter where the slides may be placed (with a single exception to be noted presently) the resistance across which the cell terminals is connected is AC (13,900 ohms), plus CB (99.8 ohms), plus K, which latter is made 355.1 ohms, a total of 14,335 ohms, or just what is required. To allow for the increased E.M.F. of 86 ELECTRIC AND MAGENTIC MEASUREMENTS. the standard cell with decreasing temperatures, the series of coils between T and S is added, the value of each coil being made such that when the plug shown in the diagram as at Tis shifted to another position, stamped as shown in Fig. 59, with the different temperatures that the cell may have, the total resistance between the terminals of S is added to sufficiently to effect the necessary compensation. The one position of the slides at which the resistance of the series AC is not 13,900 ohms, is when the slide for that series spans the first coil, Aa. To avoid its being necessary for the operator to make inspection each time to see that the slide is not in that position when making a standard cell setting or check, the coil ac is divided into two sections, ab of 100 ohms, and be of 900 ohms. The small single pole-switch shown at that point and clearly illustrated also in Fig. 59 is mechanically interlocked with the slide arm lever in such a manner that when the latter is at the position Aa it connects the standard cell to 5, and when the slide is at any other position it connects the cell to a. Of course, when the standard cell is of a type having some voltage other than that of the non-saturated solution (Clark) the value of the resistance at K, and, if necessary, the point of attach- ment of #, is appropriately changed at the time that the appara- tus is built. If the cell has no temperature coefficient, the coils TS are omitted. Other potentiometer constructions which maintain a constant resistance of the working cell circuit and at the same time allow a shifting of the points at which contact may be made along that circuit are feasible, and, in fact, in some use, but 'the two above described are the most common and the best suited to ordinary requirements. Before leaving the general subject of the potentiometer method of measurement, it may be well to point out that one reason for the great accuracy attainable thereby is that it is a zero method, that is to say, the results are obtained when a galvanometer shows an absence of current rather than when it gives a certain deflection. In this way errors due to varia- tions of magnetic force when measurement is going on, to alterations in resistance of the galvanometer circuit because of temperature changes, to an alteration in the restoring force POTENTIOMETERS. 87 of the galvanometer system, to a change in potential of the standard cell due to drawing too great a current from it, and to varying contact resistances, are all eliminated. The Lorenz apparatus for the determination of resistance in terms of the fundamental units, as described on page 6, is an example of the potentiometer system of measurement as is likewise the method of plotting the wave forms of alternating currents described on page 259. Other applications are numerous. MEASUREMENT OF E.M.F. WITH A POTENTIOMETER. The method of measuring the difference of potential between any two conductors led to a potentiometer is fairly obvious from the foregoing descriptions of this class of apparatus. The procedure involves, first, the establishment of a known difference of potential per step, if the potentiometer is of the step by step type, or per scale division, if of the slide wire type, by adjusting the strength of the current supplied by the work- ing cell until the standard cell voltage is exactly balanced by the drop over the number of steps or divisions equal to its voltage. The unknown E.M.F. is then applied to the series of resist- ances by manipulating the sliding contacts until a point is found where no current flows through that branch circuit, whereupon it is known that the difference of potential between the ends of the circuit is the same as that existing across that number of steps of the potentiometer. Volt Boxes. It is obvious that none of the potentiometers so far described is suitable for the measurement of potentials in excess of 1.5 or 2 volts. To measure higher ones, devices called " volt boxes " are used, which are simply coils of wire of high resistance hav- ing terminals attached so that one half, one tenth, one one-hun- dredth, or any other desired fraction of the total E.M.F. between the volt-box terminals exists between the one end of the volt coil and the lead selected. Where the potentiometer is to be used to cover a wide range of measurement, the volt box is made to contain several coils, often having a resistance of 50, 88 ELECTRIC AND MAGNETIC MEASUREMENTS. 50,400 and 9,500 ohms respectively, connected in series as shown in Fig. 61. From this figure it is evident that if the leads to the potentiometer be attached at a and 6, a difference of potential as high as 300 volts may exist between a and e with- out making the E.M.F. applied to the instrument come above its maximum capacity of 1.5 volts, in other words, the volt box is at that step a multiplier of 200. If the potentiometer connection be made at a and c the potential difference between a and e may be as high as 150 volts without exceeding the potentiometer's capacity, and the volt box acts as a multiplier of 100 ; similarly, the step ad forms a multiplier of 20, permitting the measure- ment of potentials up to 30 volts. When the voltage to be measured is over 1.5 and less than 3 volts, the range of the potentiometer itself may be temporarily Applied E.M.F 50 a) 50 a) 400 a} 95OO a> (VWVK^A/V^^ <*> '6 \c \d, |c 1 I J .__ TO Potentiometer FIG. 61. doubled by using two standard cells in series instead of one, and two working cells in series instead of one, the value of the potential difference per scale division being thus doubled. This, however, means the passage of a current of twice the normal strength through the potentiometer, and it should first be ascer- tained whether the device can safely withstand that overload. CURRENT MEASUREMENTS WITH THE POTENTIOMETER. Currents are measured with the aid of the potentiometer by determining, in terms of the E.M.F. of a standard cell as usual, the drop in potential across a known standard resistance, traversed by the current whose strength is to be ascertained, and then calculating the current from Ohm's law. Such standard PO TEN TIOMETERS. 89 resistances must, of course, be selected to have a value which will give a sufficiently large drop when traversed by the cur- rent to enable this to be accurately read, and must also have a section large enough to carry that current for a sufficient time to make the test, without heating to an extent that appreciably increases the resistance. While such standard low resistances, or shunts, as they are sometimes called, are usually purchased by a user as a finished piece of apparatus, it may not be out of place to point out some of the precautions that must be observed in their proper design, as these have some bearing on their use. Moreover, it is some- times desirable to extemporize a shunt, as can readily be done by taking a suitable resistance and calibrating it by measuring its value in terms of any of the sizes of shunts already on hand i / i I y/'/li j \ j i ' / / / i ////,' '//I! d i j I i ' / / / / * !,'////: i , j i i f / / ,'-. D V \ \ * ' > ' =M \ j i i i :Yjij 1 1 1. 1 -',''\\\ \d\ '//I I j I i ; y ji j! w i j FIG. 62. by the potentiometer resistance measuring method to be de- scribed presently, and in that case a failure to observe the pre- cautions is apt to make the results inaccurate. Standard Low Resistances. Standard low resistances, then, may not consist of a simple sheet of resistance metal through which the current to be measured is passed and between any two equidistant points on which the drop is taken, unless the points of attachment of the main and potential wires are always the same. This is because the current flowing through a sheet will distribute itself differ- ently with different points of attachment of the terminal wires. Fig. 62 illustrates this point. Here A is a resistance sheet into which the current is lead by a terminal, a, secured to the 90 ELECTRIC AND MAGNETIC MEASUREMENTS. upper left-hand corner, and out again through the upper right- hand corner, b. B shows the same plate with the current led in and out through diagonally opposite corners, and (7, the same thing again, but with the current conducted through it by con- ductors attached to the center of the plate at each end. The curves in the figures are lines connecting the points of equal potential as found by actual measurement with a galvanometer and exploring points, and are credited by Mr. Fisher to Mr. A. C. Keep. The author has made similar tests which substantiate these. The proper current distribution in the plate is attained only by working along the lines shown in D of the same figure, where there are heavy terminal blocks, either of another mate- rial than the resistance sheet, or else heavy masses of the .same material. Even with this form care must be taken in propor- tioning the terminals, for if their size be insufficient or^ the re- sistance of the attached lugs too high, the distribution may be affected to an appreciable degree. Another important consideration is the location of the con- tact points where attachment is made to the potentiometer or other apparatus for measuring the drop due to the current flow. In shunts for commercial indicating instruments where the highest accuracy is not required, it is not uncommon to attach these drop studs to the terminal blocks, as by this means a maximum drop is obtained and a saving in material is effected. This location is not only apt to bring the drop studs to a position where the equipotential lines are disturbed when cur- rent is led into and out of the terminal blocks at different angles but to introduce thermoelectric potentials, which, whether they be opposing or assisting the drop due to the current, of course introduce errors. These foreign potentials are generated for the following reasons. The material of the resistance strip is ordinarily different from that of the terminal blocks, the latter being usually of copper and the former of some resistance alloy like manganin or German silver. If the temperature at the junction between the resistance plate and one terminal lug be the same as that at the junction between the plate and the other lug, the thermoelectric E.M.F. between one of them and the resis- tance sheet is equal and opposite to that between the resistance sheet and the other lug, and hence there is no difference of potential between the contact points on the lugs due to that POTENTIOMETERS. 91 source. If, however, as is often the case, one of the junctions be hotter than the other, due, perhaps, to imperfect soldering between the resistance sheet and the lug, or perhaps to a poor contact between the lug and the wire which carries the current, the heat generated thereby being conducted by the lug to the junction generates an E.M.F. The potential between the sheet and one lug becomes, therefore, greater than that between the sheet and the other lug, and the algebraic sum of these poten- tials, namely, their arithmetical difference, represents a foreign difference of potential that will exist between the points of attachment of the measuring instrument. The author has known of instances in which these potentials amounted to fully 5 per cent of the difference in potential between the drop studs, due to the full capacity current flow. The objection can be overcome by the simple expedient of at- taching the drop stud to the resistance sheet, as indicated at 6?, Fig. 62, instead of the outer lugs. This is at the expense of increased weight and bulk, but safeguards against errors that are large enough to be objectionable when making measure- ments of any accuracy. RESISTANCE MEASUREMENT WITH A POTENTIOMETER. The method of comparing resistances with the aid of a potentio- meter is very simple ; it consists of coupling together in series a standard resistance and the one under test. A current of suitable strength is sent through these resistances and the drop in potential across them is measured by means of the potentio- meter. The resistances, since the current in both is the same, are, according to Ohm's law, in direct proportion to the drops. For such resistance work it is very desirable that the multi-throw switch of the potentiometer be provided with at least three pairs of contacts for making connection with external circuits, one pair being for standard cell, as usual, one for the standard resis- tance, and the third for the unknown resistance. In this way a simple movement of the switch arm throws in the resistance to be measured, while the drop readings may be taken in such qnick succession that there is but an inappreciable chance of any change in the current during the operation. This system of resistance measurement is capable of a very high degree of accuracy, results that are correct within one 92 ELECTRIC AND MAGNETIC MEASUREMENTS. part in 1,000 being attainable with very ordinary care. When the resistance to be measured is of a very different order from that of the available standard, the measurements are preferably made indirectly, by lirst constructing a secondary standard hav- ing a value of one tenth, or ten times, as the case may be, of that of the primary one, and working from that, or even a tertiary standard adjusted from it in a similar way. Another method of accomplishing the same end consists in taking the drop from the unknown standard through the volt box already mentioned, and leading only a fraction thereof to the potentiometer. If, for instance, we have a resistance to measure approximately .01 ohm in value, and our available standard is 1 ohm, the two may be joined in series and the terminals of the 1 ohm stand- ard connected to the volt box. If, then, those potentiometer terminals of the volt box are selected that give the ijatio of one one-hundredth, the drop across these with a given cur- rent flowing through the standard is one one-hundredth of the drop across the terminals of the standard itself, and the same as the drop that would be given when the same current trav- ersed a resistance of .01 ohm value. It is evident that tests made as above are best suited for comparatively low resistance work. CHAPTER V. THE MEASUREMENT OF RESISTANCE. RESISTANCES of different ohmic value must be measured by using different tests if the results are required to be determined to a high degree of accuracy. While there is no hard and fast line of demarkation, resistances may be conveniently divided into three groups, namely, medium resistances, this including those lying between .1 ohm and 1 megohm ; low resistances, under 1 ohm ; and high resistances, over 1 megohm. Before considering the various methods and appliances for resistance measurements, it will be best to glance briefly at the laws determining the resistance of electrical conductors grouped in various combinations, as the measurement of such combina- tions or networks is a very common problem. When we have several conductors connected in series the fact that the combined resistance of all is the sum of the individual resistances is almost axiomatic. When the conductors are connected in parallel their combined resistance can be calculated by the formula derived as follows : Referring to Fig. 63 let R^ be a conductor having a resistance designated by M l and R 2 a second conductor having similarly a resistance R^ the two being joined in parallel as shown ; let the current through R l be designated J t and that through R^ by 1^ the total current being I. According to Ohm's law we now have V V J i = J? and J 2 = 75- R l ^2 V being the difference of potential between the junction points A and B. Let now R be the combined resistance of the two conductors in parallel, that is to say, the resistance that we desire to ascer- tain. We then have . or as I = ^ 4- 1 2 , -= + or i = -L+.l R R^^ R^ R R I jR 2 93 94 ELECTRIC AND MAGNETIC MEASUREMENTS. Where more than two conductors are connected in parallel, their combined resistance may be ascertained by first determin- ing the resistance of one pair from, the above formula, finding the combined resistance of this pair and the next succeeding conductor by substituting the value of the pair resistance for that of a simple one, and so on throughout. As all systems of conductors must be connected either in series or parallel, or combinations of the two, any resistance can be calculated if that of its elements be known, by the application of the above simple principles. However, although the princi- ples themselves are very simple, their practical application to networks of conductors may sometimes involve the solution of complicated equations.* MEASUREMENT OF MEDIUM RESISTANCES. THE WHEATSTONE BRIDGE. The Wheatstone bridge is a network of six conductors, inter- connected as shown in Fig. 64. Four of them, lettered A, B, and X respectively, contain resistances only. In one of the remaining branches there is a galvanometer, and in the other a * An interesting example of the foregoing is the calculation of the resistance of the network of five conductors shown in the marginal figure, between the points + and . At first glance it would seem as if this should be given by a simple expression, but actually the formula, calculated by Townsend Wolcott is : (R R (R (R ^ (^) Q) y O~~ @> OJ200 1 ?oo ^> C TT IT ^ 5 1 20 /o 20 /OOO 2000 T ances ^4. and .5, commonly termed the " ratio arms " of the bridge and the variable known resistance (7, commonly called the " rheostat arm," are geometrically arranged in a different manner from that shown in Fig. 64, in order to economize space; the electrical connections, however, remain the same. Post- Office Pattern. The arrangement of Wheatstone bridge coils still in most com- mon use is called the " Post-office pattern," it being the form THE MEASUREMENT OF RESISTANCE. 97 adopted by the British Post-office many years ago. A plan view of a Post-office bridge is given in Fig. 65, the wiring connections being shown by the heavy lines. As will be noted, keys are in- serted in the battery and galvanometer cir- cuits, in order that these may be manipulated at the will of the operator. The separate re- sistance coils forming the bridge and rheostat arms are made as nearly non-inductive as pos- sible, by making each one of a loop of wire, that is, a wire doubled on itself before wind- ing. After being adjusted to the proper resistance the terminals of these loops are soldered to heavy brass^ blocks, as is shown in Fig. 66. Taper plugs may be inserted, that fit snugly be- tween the members of each pair, which when in place short circuit their respective coils and offer a negligible resistance. To insert given resistance in circuit, therefore, the plug making connections between the two terminals is simply re- moved. It is common to give the resistance coils the value in ohms indicated by the numerals in Fig. 65. As can be seen by in- spection of this figure, resistances of from 1 ohm to 11,110 ohms, varying by steps of one ohm at a time, are attainable in the rheostat arm, by pulling out the proper plugs, and the ratio arms may be adjusted from a given value of the B divided by A ratio, of 100 to 1 to a value of same ratio of T ^, thus making the theoretical range of the instrument from 1,110,000 ohms to .01 ohms. In the original Post-office pattern bridge, the galvanometer, the battery, and sometimes even the galvanometer and battery keys form separate pieces of apparatus. These, plus the bridge itself and the necessary connection wires, form an assemblage of apparatus that is too bulky and awkward to use for ordinary commercial work, particularly when the devices have to be transported from place to place. Combination sets in which the battery, galvanometer, and keys are all built into a common carrying case, and the various wiring connections between them permanently made, are the favorites to-day, except for labora- tory work. An instrument of this class is shown in Fig. 67. Here the battery power is furnished by six dry cells arranged in 98 ELECTRIC AND MAGNETIC MEASUREMENTS. a separate compartment at the right, and cords are fitted in such a way that any number of the cells, from one up to six, may be used at will. The galvanometer is of the class in which the moving system is supported by pivots instead of suspension fibers, and the indications given by a needle playing over a scale, instead of a beam of light, as in the reflecting form. This, while not as sensitive as the other pattern, is sufficiently so to enable readings to be made to a fraction of a per cent when measuring resistances falling within the favorable range of the bridge (.1 ohm to 100,000 ohms). It is compact, does not require accurate leveling, and is sufficiently robust to withstand ship- ping. A plug-reversing switch lettered AXBll in the figure is inserted in the bridge arm circuit. By means of this the con- nections of the bridge arms to the rest of the network may be FIG. 67. reversed. In the present instance this extends the multiplying value of the bridge ratios so as to take in the values 1,000, 100, 10, 1, .1, .01, and .001. As space is such a valuable consideration in these portable bridges, provision can seldom be made for securing specially high insulation of the terminals and key contacts, the hard rubber cover on which all are mounted being supposed to give insulation enough. When measuring high resistances on damp days, however, particularly when a high E.M.F. from some outside set of batteries is being used, to give higher sensibility, the rubber must be very carefully cleansed and dried before making readings, as otherwise the leakage errors may become considerable. THE MEASUREMENT OF RESISTANCE. 99 Decade Pattern. Wheatstone bridges, in which the ratio arms and rheostat values are altered by withdrawing or inserting a plug for each coil, are open to the objection that, small as is the resistance of each individual contact, the total may be comparatively high, particularly after the plugs become slightly tarnished, and the further objection that the continued withdrawal and insertion of a plug tends to loosen, not only the blocks between which it wedges, but the neighboring ones as well, thus making it neces- sary to go over a whole row each time that a plug is moved, to make sure that the others have not been affected. There is also such 'a large number of plugs that it becomes a very easy matter to mislay one or more of them when making a test. It is possible to overcome these drawbacks to a considerable FIG. 68. extent by using a " decade " type of bridge in which the rheostat arm resistances are arranged, as shown in Fig. 68. Here, as can be seen, a resistance is cut in by inserting instead of withdraw- ing a plug, and there is only one plug with its corresponding contact, to each unit, ten, hundred, or thousand numeral in the total. In addition to this, the decade arrangement is convenient because it is formed of groups of coils, in which each member of a group has a resistance which is the same as that of all the other members of the group, and if terminals are provided so that leads may be attached to these resistances, the various coils may be intercompared without its being necessary to have re- course to outside standards. 100 ELECTRIC AND MAGNETIC MEASUREMENTS. The plan calls for a greater number of coils than the " Post- office " one, with a consequent higher manufacturing and selling cost. In spite of this it is now rapidly superseding the old arrangement, as the greater rapidity of working and the higher accuracy of the results attained more than offset the difference. A portable pattern of the decade type of set is shown in Fig. 69, Fig. 70 giving the wiring connections. In the latter the block marked " Galv." is so connected that when a plug is inserted between it and the block " Int." the gal- vanometer indicated in the figure is connected into the bridge network, and used in obtaining a balance in the regular way. FIG. G9. When the plug is transferred to the gap between u Galv." and the other block, the gap at Gr is substituted for the galvanometer in the set, and as the gap has binding-post terminals, an outside high sensibility galvanometer may be there attached, and used for more accurate work. The block marked " Loop" is arranged so that when a plug is inserted between it and the block " V&B," the connections of the set are such as to form a regular Wheatstone bridge, the unknown resistance to be measured being inserted at X. When the plug is changed to its other position, the connections become those for making the " Murray Loop Test," for the location of faults, as described on page THE MEASUREMENT OF RESISTANCE. 101 Any number of the five cells contained in the box may be uti- lized by the aid of the connector on the end of the flexible chord coming up through the rubber top between the ratio arms, or that connector may be left free, and an outside source of E.M.F. applied at B, whichever the user may desire. The keys BK and GrK, for the battery and galvanometer circuits respectively, are su- perimposed, so that when the upper one, BK, is depressed, first the battery and then the galvanometer circuits are completed, as is the desirable procedure in the general run of tests. The end of the key, GrK, is extended beyond that of BK, however, and provided with a separate button, so that if desired the galvanometer circuit may first be closed. As this set measures FIG. 70. but 10 inches by 6 inches by 6| inches, it evidently forms a convenient, portable device for covering a large range of measurements. Radial Arm Patterns. It is possible to dispense entirely with plugs in bridges, by using sliding contacts. In this case the decade system of coils is usually employed, the contacts being arranged in a circle over which sweeps the end of a contact brush. Such bridges are extremely convenient to manipulate, but very careful design and a higher grade of workmanship than for a plug bridge are neces- sary, as a brush sliding over a flat surface cannot cause the same intimate contact as a taper plug forced into a hole reamed to receive it between two heavy blocks, and variable contact re- sistances are fatal to accuracy. Crompton & Co. make " dial 102 ELECTRIC AND MAGNETIC MEASUREMENTS. switch " bridges, as they call this type, with the contacts under plate glass, similar to the scheme used by the same concern in their potentiometer shown in Fig. 56, page 80. The brushes are flat and rather light, and are turned by a hard rubber knob coming up through the glass. In the Wolff bridges, one of which is shown in Fig. 71, the contact blocks are massive pieces of brass, and the brushes that bear on them are formed of a series of bronze blades fastened to the radial arms that carry them at an angle of 45 degrees. In being moved from one position to another, such brushes automat- FIG 71. ically wipe the surfaces, and if these are kept slightly moistened with a refined light mineral oil, as directed, they will be found most durable and extremely satisfactory. Tests have been made on such bridges which showed a total resistance of all five sets of brush contacts in series of less than .008 ohms. SLIDE-WIRE BRIDGES. As was demonstrated on page 95, it is not necessary that the actual values of the resistances of the coils A and B be known, in order to determine X in terms of (7, but only that their ratio be known. THE MEASUREMENT OF RESISTANCE. 103 If, therefore, we select a fixed value of C and vary the ratio of A to B, the resistance of X can be determined by application BC of the formula X = . Devices for resistance measurements yi. in which this variable ratio arm and fixed rheostat arm plan are employed are geiierall ycalled "slide- wire bridges" and are con- structed as follows : In Fig. 72 MN is a wire having as high a resistance per unit of length as is consistent with mechanical strength, and whose ends are secured to heavy brass or copper bars. A third bar, Q, is provided, gaps being left between its ends and the adjacent terminals just named, the said gaps being designed to be bridged by a standard resistance, (7, and the unknown re- N. FIG. 72. sistance, X, to be measured respectively. Current is put through this network, from a battery whose terminals are attached as shown, and a galvanometer, 6r, is likewise provided, inserted in a circuit starting from the point, (J, and terminating in the sliding contact, $, which may be moved along the wire, MN. There is, further, a scale beneath MN, that is uniformly divided and serves to measure the distance between the contact and the points of attachment of the bridge wire. It will be observed that the arrangement of the various elements is exactly the same as that of the diagrammatic Wheatstone bridge shown in Fig. 64 and as like parts are similarly lettered, the relationship X = BC 1 In contradistinction to the orthodox holds good. Wheatstone bridge, however, in the slide-wire form, the rheo- stat arm, (7, is constant and the ratio of the A and B arms to 104 ELECTRIC AND MAGNETIC MEASUREMENTS. one another is varied until a balance is obtained, this being accomplished by sliding S along MN. Fig. 72 is simply diagrammatic. In the commercial form of slide-wire bridge there are at least two other air gaps in and P that can be bridged over with copper straps when desired, and there is also a wire stretched parallel to the slide wire proper and connected to one terminal of the galvanometer, so that the sliding contact, &\ makes connection between the two, and the use of a loose wire between /S'and the galvanometer, 6r, is made unnecessary. A slide-wire bridge differing in these particulars from the diagrammatic figure is shown in Fig. 73. Accurate results are seldom obtained from a single reading with the simple form of slide-wire bridge above mentioned, as --+;/\>O T" o.()o. -W- 1 V [ I ||l[!lli|lll!|llll[llN|llll|llll[lll!|!lll|llll[!ll!|!i!l|llll]!lllJllll}lllljllll|lll|i N p _J : L_J FIG. 84. P is then, from Ohm's law, the resistance of that part of the bar, $, included between M and 7V, for the same current flows through both, as they are connected in series, and the drops in potential are alike, as the galvanometer shows no deflection. The resistance of the battery leads, of the wire joining the two resistances and at the points of contact of these with the bars, do not enter, as they are not in the measuring circuit and merely affect the current strength. The resistance between the con- tacts, Af, TV, (?, and P, and their resistance bars, do not enter either, as they are negligible in comparison with the high resist- . ance of the galvanometer. As the accuracy of results obtained by this method depends on having a galvanometer that is truly differential, the instru- THE MEASUREMENT OF RESISTANCE. 117 ment should be tested for that quality before use. To do so, connect the two coils in series, but in opposition, and pass a very weak current through them, whereupon there should be no deflec- tion. The coils should then be coupled in opposition but in parallel, and current again applied; if there is still no deflection, the coil resistances are alike. The latter test is the one actually determining the fitness of the apparatus for use in making this test, as while if it shows no deflection the instrument may still not be truly differential, any error due to that cause is offset by a difference in coil resistances. The galvanometer should also be tested to see that its two ~v * FIG. 85: coils are insulated from one another so that no current can flow between them. MEASUREMENTS WITH AN AMMETER. Low resistances of nearly the same value can be measured with the aid of commercial ammeters of the type in which the shunts are separate from the instruments themselves, provided that the resistance of their shunts is known. For instance, referring to Fig. 85, A represents the ammeter, S its shunt, X the unknown resistance, and B the source of current. The same current flows through $ and X, as they are connected in series ; and if the ammeter A be one in which the angular deflec- 118 ELECTRIC AND MAGNETIC MEASUREMENTS. tions of the needle are proportional to the current strengths, or even if this be not so and the scale be divided so as to indicate current strength, X may be found in terms of S, from the fact that, as will be evident on consideration, the drop across S is to the drop across X as the resistance of S is to the resistance of X. For instance, if the current through S gives a deflection of ten scale divisions on the instrument, A, and that across X, when the terminals of the instrument are shifted to take up the position shown by the dotted lines be twenty scale divi- sions, then X is twenty tenths, or two times 8. A few manufacturers make the drop of all of their shunts uni- form, for instance, 50 millivolts when worked at maximum load. From this data the resistance of the shunt between the points at which the connection to the instrument is U^CX^^N T T' c c H ^|ii"|""|""|"'1'i"|""h'l'"'|i4't"'l'H'H""l""l'"'l'H l "t4 I [ K f I v ^z^^*r f FIG. 86. made is easily figured; that of a 100 amperes hunt on the 50 millivolt basis being .005 ohms, and that of a 1,000 ampere shunt .0005 ohms, etc. If in this example the current strength supplied by B be such that the instrument, A, gives a reading of ten scale divisions when its terminals are at- tached to a shunt of 100 amperes capacity, S, a resistance, X, in series with S, the drop across which causes one scale divi- sion deflection, will have a value of .0005 ohms, or generally, if the resistance, X, give JV scale divisions deflection, it has a value of .0005 N" ohms. The resistance of A is usually sufficiently high so that the resistance of the contacts between its leads and the S and X resistances is negligible, and such work as measuring the resistance of armature coils can therefore be rapidly and accurately conducted with inexpensive apparatus. THE MEASUREMENT OF RESISTANCE. 119 THE THOMSON DOUBLE BRIDGE. The Kirchhoff bridge necessitates the use of- a differential galvanometer, and this instrument is not often available. Lord Kelvin devised a modification of this bridge, which renders it possible to use an ordinary galvanometer, the connections being as shown in Fig. 86. The leads from the standard and un- known resistances are, as is seen from the figure, connected, so that the E.M.F.'s at their terminals are opposed, and when these are equal the galvanometer of course gives no deflection. The standard bar >S is divided up, so that fractions of its length, and hence resistance, may be read off, as in the Kirchhoff bridge ; and when the sliding contact, (7, which is adjustable along its length, reaches the point where the galvanometer gives no de- A C 1000 100 10 10 IOO ' - / ""^---oS T , and then to those of X ; whereupon the result is at once obtained in a manner analogous to that mentioned on page 117. No correction need be made in this instance for the resistance of the device that indicates the potential, as this is infinitely high as compared with the resistance of the objects under measurement. A Thompson or D'Arsonval ballistic galvanometer can be used in place of the electrostatic instrument by charging a condenser first from the drop across $, discharging it through the galvanometer and noting the throw, and then by Repeating the operation with X, in which case the throws are, in the ratio of the resistances. EVERSHED OHMMETER. This is an instrument for measuring moderately high resist- ances, which shows directly from the position of a needle swing- FlG. 103. ing over a calibrated scale the value in ohms of the resistance under measurement. It consists of two coils arranged with their axes at right angles to each other, one of which coils is connected in series with the source of current and the resistance to be measured, and the other, like a voltmeter, across the line from which current is supplied. At the point of intersection of the coil axes there is suspended, so as to be freely movable, a THE MEASUREMENT OF RESISTANCE. 137 short magnetized steel needle. If the resistance be infinitely high, no current will flow through the series coil of the instru- ment ; the needle will be influenced by the potential coil only and assume a position at right angles to its axis. If, on the other hand, the resistance be zero, and the current obtained from a source whose internal resistance is fairly high, current will flow through the series coil only, there will be practically no difference of potential between the points of attachment of the potential coil, and therefore the needle will assume a position parallel to the axis of the series coil. With finite resistances the needle is evidently influenced by the joint action of the fields of the two coils, tending to swing toward the infinity FIG. 104. mark when the current is low and the potential high and vice versa. In the actual apparatus the source of current is a small hand- driven dynamo having permanent magnet fields, namely, a mag- neto which when driven at a reasonably constant speed sup- plies rectified alternating current at potentials of from 100 volts, in the case of instruments designed to measure resistances up to about 5 megohms to 500 volts for meters measuring up to 500 megohms. Theoretically, the calibration of this ohm meter can be calculated from the geometrical dimensions of the appa- ratus, the number of turns of wire, etc., but practically it is better to graduate the scales empirically by comparison with resistances of known value. A diagram of the connections of the instrument is shown in Fig. 104. In the early form of this ohmmeter, the moving needle was of steel magnetized as above mentioned, but this was open to the objection that the needle was readily influenced by comparatively 138 ELECTRIC AND MAGNETIC MEASUREMENTS. feeble stray magnetic fields, even those of the hand generator which supplied the current. In the more modern form of appa- ratus a soft iron needle is employed, which, while resulting in a shorter scale because the zero must be placed in the center in- stead of at one end, enables the user to eliminate the effect of stray fields, by reversing the current and taking the mean of the observed indications. The current reversal is readily effected by turning the crank in an opposite direction, thus reversing the direction of the rotation of the magneto armature. SPECIAL CONDITIONS. The foregoing outline of methods of measuring resistances of FIG. 105. different values treats only of the measurement of simple cir- cuits, such as the resistance of a metallic body, or a poor con- ductor in which no disturbing factors, such as local E.M.F.'s exist. In practice, however, disturbing E.M.F.'s are frequently present, being either existent before the measurement is at- tempted, as in the case of a- battery, or being set up by the passage of the current employed in measuring the resistance, as in the case of an electrolyte. These E.M.F.'s tend to cause currents to flow in the network of conductors, which are ordinarily nec- essary in measuring resistances, and make the indications of the galvanometer or telephone receiver, used as the current detector, erroneous. In the following we will take up the methods of measuring the resistances of circuits which contain these dis- turbing elements and are frequently met with in practice. THE MEASUREMENT OF RESISTANCE. 139 RESISTANCE OF ELECTROLYTES. Any liquid not a melted metal, such as mercury, fused lead, etc., which is a conductor of electricity, is an electrolyte, and all electrolytes are decomposed when current flows, the decomposi- tion setting up an E.M.F. opposing that of the source that forces the current through it. This fact makes it impossible to meas- ure the resistance of an electrolyte with the ordinary Wheat- stone bridge arrangement, lief erring to Fig. 105, if the X arm of the elementary Wheatstone bridge shown in the figure con- tains in itself a source of E.M.F. the correct value of jS, which must be inserted to make the ratio -^ = -^ hold good, is no .o ^A. longer attained when the galvanometer shows no deflection, as, where an ordinary resistance would keep the difference of potential between the junctions of AB and SX alike, a source, X, that contains in itself a source of potential difference will cause a flow of current through the bridge network under the same circumstances and show a galvanometer deflection. Kohlrausch Bridge. Tn measuring the resistance of an electrolyte, one way of overcoming this point is to use, instead of the direct current which calls forth the counter E.M.F. of the electrolyte, an alter- nating current with the current reversals succeeding each other so rapidly that decomposition at either pole is immediately re- composed and the disturbing E.M.F. set up in one direction, off- set by an immediately following and opposite one. Kohlrausch first suggested the above method and used for the measurement of the resistance of electrolytes an ordinary slide- wire bridge of the type shown in Fig. 72, obtaining the current applied to the slide wire terminals from the secondary winding of an induction coil actuated by a battery. If the induction coil core be of hard iron, or even steel, the secondary current becomes very nearly a pure alternating current with smooth, symmetrical waves, a feature that is necessary to secure good results. The ordinary Thompson or D' Arsonval types of galvanometers cannot be used as current detectors with this form of bridge because they respond only to direct current. Their place is usually taken by a telephone receiver and when 140 ELECTRIC AND MAGNETIC MEASUREMENTS. the sliding contact is moved along until a point is reached where the receiver no longer gives forth a humming sound, the value of the resistance of the electrolyte can be calculated or read off exactly as in the case of the same instruments used with direct current for the measurement of ordinary resistances. The frequency of the alternating current used must be high, because if the current reversals follow one another too slowly, polarization may take place. With the frequency obtainable with the interrupter of an ordinary induction coil, fairly good results are obtainable, but it is claimed by Duddell that the frequency must attain, at least, FIG. 106. 10,000 alternations per second if polarization errors are to be entirely eliminated. No orthodox Kohlrausch bridges are made in this country, but the Hanchett-Sage ohmmeter described on page 107 is often used for such work. A special model of this instrument with the induction coil for supplying the alternating current permanently fastened in the cover, and with the wiring con- nections self-contained, is shown in Fig. 106. The galvanometer shown as built into the instrument, responds to direct current only, and is used for other tests, it being possible to throw either it or the telephone receiver into circuit to act as the current detector by means of a switch provided for that purpose. Secohmmeter Method. A galvanometer which responds to direct current only can be used when the direction of the current flowing through the elec- THE MEASUREMENT OF RESISTANCE. 141 FIG. 107. trolyte is being continuously reversed, if the connections to the galvanometer be simultaneously reversed. The apparatus for bringing about these two reversals simultaneously is the secohm- meter illustrated in Fig. 107. The device consists of a commu- tator, rotated by hand by means of a crank, and having bearing thereon, contact brushes through whose aid the direction of the current flowing through both circuits is con- tinuously re- versed. It is necessary to rotate the handle at a high speed, as the current reversals must, as before ex- plained, succeed each other with sufficient rapidity to annul the polarization effect. The galvanom- eter movement must be heavy, so as to possess inertia sufficient to prevent its swinging back and forth in an attempt to keep step with the pulsations of the current. With these conditions fulfilled, the resistance of an electrolyte may be measured by the Wheatstone bridge method, and a secohmmeter with the same ease as that of any metallic circuit. Stroud and Henderson Method. This is entirely different from any of the foregoing, and con- sists of an ingenious modification of the ordinary Wheat- stone bridge. Referring to Fig. 108, T^ and T 2 are two tubular vessels containing the electrolyte, similar as to diameter and nature of terminals, but differing in length by a known amount. P and circuited conductor in a motor armature, and, as stated before, consumes energy which is subtracted from that due to the inertia which tends to swing the needle beyond the position of equi- librium. The strength of the cur- rents that can be passed through the winding of an instrument of this descrip- tion is very small as com- pared with those used in most commercial work, as the springs, which serve also as conductors, become over- heated and lose their proper elasticity if a very small cur- FIG. 119. rent flow through them be exceeded. In order to render the apparatus available for the measurement of large currents, the same expedient is used as that employed in the case of reflecting galvanometers for decreasing their sensibility, and incidentally increasing the amount of current that may flow through the- galvanometer circuit without injury, that is, by using a shunt and diverting the major portion of the current through that by-path. The remarks made on the subject of shunts for use with the potentiometer when measuring current strengths (see page 89) also apply to shunts for such am- meters. An ammeter made by the Whitney Electrical Instrument Com- pany differs from the conventional d'Arsonval form, in that, 158 ELECTRIC AND MAGNETIC MEASUREMENTS. among other things, there is only one gap in the magnetic circuit, instead of the usual two, arid that the coil of moving wire is not symmetrical to the axis about which it rotates. Fig. 120 illustrates the mechanism of this type of instrument, the outer pole piece of the magnet being shown as transparent in order that the coil arrangement may be seen more clearly. As in the case of the Weston meter, the indications of the Whitney device are made " dead beat " by winding the active- wire on a spool of copper or aluminum, the currents generated in the spool tending to bring it rapidly to rest. However, the action is not as efficient as in the other form, because in order to balance the moving element mechanically, so that a small dif- ference in the angle to the horizontal at which the meter is used will not introduce an appreciable error, a counterweight is added FIG. 120. on the side of the supporting shaft opposite the coil, and the in- ertia of this carries the needle slightly beyond the position corresponding to the new current strength, when that current is applied, and time must elapse before it can swing back again and indicate the true value. On the other hand, the construc- tion is advantageous in affording very perfect shielding against disturbances due to neighboring magnetic fields, and also in that it allows the use of a greater clearance between the coil and pole pieces. The Kennelly ammeter is shown in Fig. 121. In this as in the Whitney instrument it will be seen that there is but a single air gap in the magnetic circuit ; the moving conductors, however, instead of being wound into the form of a loop are distributed radially on a flat disk, and the disk itself is made of a good conductor, such as aluminum, which damps the swing MEASUREMENT OF CURRENT. 159 of the indicating needle, not as in the case of the two preceding instruments, by setting up currents as in a short-circuited turn of motor or generator armature, but by the eddy currents gene- rated. There is a considerable amount of inactive wire in the moving element of this class of instrument, because, in order to avoid leading the current back through the same magnetic field, which would render it inoperative, the turns must be carried around the periphery of the disk for a considerable portion of its circumference before they can again be led back to the center and the two ends connected to the flat spiral FIG. 121. springs, to which electrical connection is made with the outside line, and which exert the force opposing the motion of the disk. A somewhat similar instrument is the Thompson ammeter, shown in Fig. 122. In this as in the Kennelly meter the moving wire is mounted on a flat disk, but instead of having the individual conductors follow along separate radii, they are bunched and flow along a single diameter, being symmetrically divided into halves, the return halves of each portion being led along opposite semi-circumferences. The form of stationary magnet, which furnishes the magnetic field necessary for the operation of the instrument, is also different from that in the Kennelly instrument. There are two of these magnets placed with their poles of unlike signs adjacent. While the necessity of two magnets enhances the first cost, their use has the advan- 160 ELECTRIC AND MAGNETIC MEASUREMENTS. tage that, if the instrument be placed in a powerful magnetic field, whatever additional field strength is caused by this between the poles of one of the magnets is offset, so far as the action on the movable coil is concerned, by the weakening of the magnetic field of the other magnet. In other words, the instrument is astatic. This point, however, is of more theoretical than prac- tical importance, as the Whitney form is practically as immune from external influences, and any of the meters described may be so effectively shielded, for commercial purposes at least, by FIG. 122. placing them within an iron casing that no further protection is needed. The three types of moving-coil instrument mechanisms that have been briefly mentioned above were selected in order to emphasize what has been mentioned in a preceding chapter, namely, that coil instruments for the commercial measurement of direct current are nothing more or less than special electric motors, in which the field magnet is stationary as usual and the armature allowed to rotate against the constantly increasing resistance of a spring until the point of balance is reached. MEASUREMENT OF CURRENT. 161 J., Fig. 123, makes it clear that the original d'Arsonval form of instrument, as exemplified by the Weston ammeter, is a small motor with a permanent magnet field, having a stationary armature core and a section of armature winding of the con- ventional series or drum wound type as moving element. B of the same figure shows that the Whitney form of ammeter is likewise a small motor with a permanent magnet field, a sta- tionary armature core, and one section of armature coil of the Gramme pattern as the movable element ; whereas the cuts O in the same figure show that the Kennelly and Thompson in- fl \ N Illllllll 1)))' ii(((t .... . i i ' ^^ u B FIG. 123. struments are motors having armatures of the radially wound form. In each case the opposing force may be that furnished by a flat spiral spring or springs ; gravitational attraction is sometimes employed when the apparatus is placed in a favorable position, or magnetic attraction on an iron needle (see page 52) may be used. It is usual to conduct the current to and from the moving coil through the springs, but separate flexible con- ductors may be used if the springs be absent, or if it is desired to electrically reinforce the capacity of existing springs. In all of the forms it is impossible to pass all of the current to 162 ELECTRIC AND MAGNETIC MEASUREMENTS. be measured through the moving coil unless the current be of very small value, and recourse is had, therefore, to shunts for diverting the major portion of the current, as already mentioned in connection with galvanometers in Chapter III. Shunted ammeters of the types so far described have two great advantages : first, their scales are equally divided, which means that when used to measure the output of constant potential generators or the load on such circuits, the percentage of full load being carried may be estimated at a glance from the angular position of the pointer, much as time is casually read off from a clock from the relative position of the hands without looking at the numerals on the dial. Second, and more impor- tant, the amount of current needed by the instrument itself to produce full scale deflection is so very small that it is easily carried by light flexible conductors, the shunt leads, with the result that the instrument may be placed in any convenient position, irrespective of the location of the bus-bars, the shunt only, carrying the predetermined remaining part of the current, being inserted in the main circuit. On the other hand, it is rarely the case that a shunted am- meter will give as accurate results as an instrument in which the whole current to be measured is passed through the instru- ment windings. First of all, there are the temperature errors. In order that the windings of commercial shunted ammeters may have the requisite sensibility they are of necessity composed largely of copper wire, a material whose resistance changes about 1 per cent for every 5 Fahr. change in temperature. Therefore if the shunt is of a material having a practically zero temperature coefficient, the changes in resistance of the instru- ment windings become important. The temperatures at which instruments are used commonly cover a range of from 40 to 100 Fahr., which if the calibration were effected at 70 Fahr. means a variable error of 6 per cent, which cannot properly be designated as falling within allowable limits. If the shunt be made of copper so that its resistance increases in the same ratio as that of the instrument, the ratio of the two thus remaining the same, we encounter the fact that instruments and their shunts are very seldom of the same temperature, the former being usually on the front of a switchboard where the temperature may be taken, as about 80 degrees on an average, and the latter, in the rearsur- MEASUREMENT OF CURRENT. 163 rounded by current-carrying conductors, rheostats, and the like, often boxed in so as to be at a temperature of 120 Fahr., or more. This would mean an error of 8 per cent if the instrument and shunt were calibrated at the same temperature. It would not be safe to assume that the shunt will always be at a point where the temperature is higher than that at which the instrument is located, either, as it is not uncommon to find switchboards erected in galleries where their rears, and hence the shunts mounted thereon, are exposed to direct blasts from open win- dows in winter, their fronts, where the instruments themselves are located, being at the same time subjected to the hot air of the interior of the station. The compromise that leads to the minimum value of the greatest error possible under these varying conditions is to make the shunt of a material having a temperature coefficient one half of that of the instrument circuit formed by the instrument windings with the attached flexible leads. The error is in this way halved, but even then we have possible variations of 3 or 4 per cent from the normal from this one cause alone, a figure which, while it would have no earthly effect on the operation of 99 per cent of the plants in existence, would, if known, be protested against in holy horror by the majority of the operators who have heard tales of accuracies of one half or even one fifth of a per cent for so long that they actually expect to be able to count on this being attained in ordinary practice. Another very common source of error in shunted ammeters is the resistance at the point of contact where the shunt leads are attached to the instrument and the shunt. For convenience in constructing the switchboard the leads are usually made de- tached from both instrument and shunt, and the connections are finally completed by securing the lead ends under screw heads and washers at each end, making a total of four of such joints. Now, metallic surfaces become corroded and screws often work loose where there is vibration, with the result that such joints become of very uncertain resistance and the instru- ment readings are correspondingly thrown out. Cases have frequently come to the notice of the author in which brighten- ing the surfaces and retightening the screws has caused a difference of 25 per cent or more in the indications with the same load. Such errors can obviously be minimized by careful 164 ELECTRIC AND MAGNETIC MEASUREMENTS. periodic inspection of the contacts, and where such instruments are installed this practice should be faithfully followed. The error pointed out on page 89, due to leading the current into and out of the shunt at a different set of points than those used when calibration was effected, seldom enters as a con- siderable factor with well-built switchboards, but the errors due to thermo E.M.F.'s, mentioned on page 90, may be larger than good practice will permit. One manufacturer avoids the difficulty by the expedient mentioned on the- page referred to, that is to say, by placing the points of attachment of the shunt leads inside of the distribution terminals of the shunt. Another uses the following special plan : Referring to Fig. 124, A and B are the shunt terminals, D the resistance strip, made of a different metal from the terminals, E, a conductor, of the same material as D and C, a terminal of the same material as A, secured to A in such a manner tkat the thermal contact is good, but the two are electrically insulated. If, now, the block B is at a higher temperature than the block A, due, for instance, to a poorer contact be- 124. tween B and its bus-bar, there will be a lesser thermo electric E.M.F. at the junction between A and D than at the junction between .B and D, and if the values of these E.M.F.'s are 1 millivolt and 2 millivolts re- spectively, there would be a difference of potential of 1 milli- volt between A and J9, due to that cause alone which would be added to or subtracted from that due to the drop in potential across the shunt terminals because of the current flowing through it, and would hence introduce a corresponding error in the indications of the instrument if the leads were attached at these points. If, however, one instrument lead is attached to J., and the other to (7, as shown in the figure, the equal and opposing E.M.F.'s at the junctions between A and D and C and E cancel one another, and the E.M.F. between A and (7, being then that due to the drop of potential because of the current flowing only, thus becomes in direct proportion to MEASUREMENT OF CURRENT. 165 FIG. 125. the current strength. A shunt of this kind is illustrated in Fig. 125. AMMETERS FOR BOTH DIRECT AND ALTERNATING CURRENT. THE KELVIN AMPERE BALANCE. As was pointed out in the chapter on laboratory standards for the measurement of current, the Kelvin ampere balance works equally well, whether the current be direct or alternating, as, in the latter event, the current in the ^ various coils reverses simul- taneously and the resultant effort is always to urge one end of the balance up and the other down. This instrument, however, hardly belongs in the class of apparatus for the commercial measurement of current strengths as its bulk, weight, and cost, the length of time required to obtain a reading, and the fact that it is not direct reading, render it unsuited for all except laboratory work. SIEMENS.' DYNAMOMETER. This familiar instrument, illus- trated in Fig. 126, consists of two conductors, each wound into coil form, one of them being sta- tionary and surrounded by the other, their axes being in line, but their planes at right angles. The outer coil is suspended by a/fine silken fiber or a steel pivot resting on a jewel bearing, and has secured to its upper side one end of a spiral spring whose otiier extremity is made fast to what is called a " torsion head." This torsion head is a button which can be manually rotated about its axis and which carries FIG. 126. 166 ELECTRIC AND MAGNETIC MEASUREMENTS. a pointer that sweeps over a scale divided into degrees. Attached to the outer coil itself there is another pointer coming up to the same scale, but whose motion is limited by two closely adjacent stops. Current is conducted to and from the outer coil, through mercury cups secured to the frame of the appa- ratus, and the electrical connections between the two coils are usually so made that the current to be measured has to flow first through one and then through the other, they being con- nected in series. When current flows in this way, the suspended coil tends to turn so that its plane is parallel to that of the stationary coil, something that is not possible because of the stops which limit the play of the so-called zero needle attached to it. To bring the zero needle back to the position from which it started, and which is generally called the zero mark, the knurled button secured to . the spring is rotated until coinci- dence is shown. The torsion spring is now subject to a stress which is equal to the reaction between the fixed and moving coils, and the amount of the said stress, as indicated by the pointer attached to the torsion head and showing the amount that the spring has been wound up, gives the current strength, as each apparatus is provided with a set of curve sheets, from which the ampere value corresponding to any scale degree may be read off. The Siemens instrument can be made more permanent, so far as its accuracy is concerned, than the direct current devices before described, as the uncertain element of the strength of the permanent magnet entering into the construction of the D.C. instruments is eliminated and, as the single spring does not carry current, there is no danger of having its elasticity modi- fied by being overheated from that cause. On the other hand, the mercury contacts are a nuisance, as the cups must be drained before the instrument can be transported, and the con- stant reference from scale reading to curve and back to note- book is very trying, when numerous observations are to be made. They also share the same objection to which a large majority of alternating current instruments are open, that is, that the field furnished by the stationary coil is but weak, and neighboring fields may form a considerable percentage thereof. This makes no difference when alternating currents are being measured, as what the foreign field adds to the instrument coil MEASUREMENT OF CURRENT. 167 field when current flows in one direction, is subtracted when the current flow reverses. When measuring direct current, however, this favorable condition does not exist, and if accurate results are to be had, it is necessary to pass the current through the instrument first in one direction, noting results, and then, with the minimum possible delay, reversing the connections and noting the new result. The true value may safely be taken as the arithmetical mean, namely, one half the sum of the two observations. ELECTROMAGNETIC INSTRU- MENTS. Kohlrausch Instruments. One of the earliest, if not the earliest, form of electrical meas- uring instruments is that in which the current to be meas- ured is passed through a hollow coil of wire, that is, a solenoid, and its force measured by the attraction exerted on a mag- netic body suspended within the core. The simplest ex- ample of such an instrument is the Kohlrausch, shown in Fig. 127. The solenoid in this in- strument surrounds a long thin iron wire which is suspended from above by a coiled spring similar to that in the ordi- nary spring balance. A pointer FlG - 127 ' secured to the iron wire, or a prolongation thereof, moves ver- tically over a scale, empirically graduated to show current strengths. Such an instrument will work, whether the current flowing through the solenoid be direct or alternating, but care must be used in the design if accurate results are to be at- tained when the instrument is used with both kinds of current, because if the iron be hard, or of too large a mass, the indica- 168 ELECTRIC AND MAGNETIC MEASUREMENTS. tions will not be correct for both, unless separate scales be drawn. For ammeters, the best design calls for the use of a very fine iron wire for the moving element, as this eliminates to a great degree the error due to varying frequencies, and also has the advantage of making the scale of more convenient divisions. The latter holds good, because of the fact that the attraction of a solenoid on an iron core varies as the square of the strength of the current until the core is magnetically sat- urated, after which time the attraction becomes directly propor- tionate to the current strength. With a very small core, there- fore, the part of the scale in which the divisions are of unequal width is a very small one, in fact, it is possible so to design the apparatus that, from 10 per cent of full capacity upward, the scale divisions will be practically equally spaced for equal current in- crements. In voltmeters, the iron core is usu- ally made more massive, in order that the law of squares may hold good throughout a good part of the range, as this gives more open divisions at the part of the scale where readings are usually taken. Atkinson Instrument. The Kohlrausch electromagnetic in- struments are not in common use in this country, but find their greatest popularity on the continent of Europe. In England a modification thereof is used to a limited extent. The instrument referred to is the "Atkinson," diagrammati- cally illustrated in Fig. 128. In this the solenoid surrounds a vessel containing a fluid in which floats a sealed hollow glass cylinder with a graduated stem, very similar to a hydrometer. The iron wire is placed inside of this float, so that the pull exerted by the current flowing through the solenoid is against the buoyant effect of the liquid on the more or less submerged float, instead of a coiled spring. This modified Kohlrausch FIG. 128 MEASUREMENT OF CURRENT. 169 instrument gives indications that are much more "dead beat" than those of the original form, but this is at the expense of simplicity and portability. One of the best, and to-day most widely used forms of elec- tromagnetic ammeters, retains the feature of a very fine iron wire suspended in the center of a current carrying solenoid, but instead of having the extent of motion of this wire indicate directly the current values, the motion is first translated into that of a pivoted pointer that swings over a graduated circle arc. Fig. 129 shows the construction of such an instrument. The iron wire is suspended from an arm rigidly secured to an axle Counterbalance far Needle. Weight W FIG. 129. whose ends are pointed and rest in jewel bearings, and the same axle carries a pointer and a weight, W, which, as the needle moves, offers an increased resistance to its displacement. The figure is so nearly self-explanatory that it is needless to go into the construction at further length. If the swings of the needle of electromagnetic instruments like this be damped, either by a suitable air vane moving in a nearly closed box, or by a piston fitting very loosely in an open ended cylinder nearly filled with viscous oil, we have a form of apparatus that is exceptionally well suited for use on a switchboard of an industrial plant. The accuracy can be made more than sufficient for commercial purposes, by proper design and careful selection of the iron ; moreover, there are no parts 170 ELECTRIC AND MAGNETIC MEASUREMENTS. liable to change through age, the force opposing the needle's swing being that due to gravitational attraction, and there being no springs or permanent magnets. Furthermore, the apparatus is available for either direct or alternating current. Kelvin Ampere Granges. Lord Kelvin, one of our foremost authorities on matters per- taining to electrical measurements and electrical measuring apparatus, has, within the last few years, put the seal of his approval on instruments of this class, by redesigning and putting on the market, under his name, the Kelvin ampere gauges, one of ^hich is shown in Fig. 130. As may be seen from this illustration, the dead beating is effected by an oil damper, the mova- ble element is supported on hooks which allow of a rol- ling motion, and the opposing force is that of gravity. The extreme reliability of these instruments has led to their wide adoption abroad, and the author expects to see similar types extensively used in this country before the lapse of many years. The station engineer will be far better satisfied with an ammeter that is accurate to only one or one and a half per cent, when installed, but which will retain that accuracy unchanged for an indefinite period, than with a meter of a questionable quarter or half per cent error on erection, that may become an unknown amount greater in the course of a few months, because of magnet or spring strength changes, varying lead resistances, etc. The accuracy of a solenoid ammeter is, moreover, for all practical purposes, abso- lutely independent of temperature, whereas shunted ammeters FIG. 130. MEASUREMENT OF CURRENT. 171 may, as before explained, have temperature errors that may be as great as 1 per cent for a change of 5 degrees. In large capacities, solenoid ammeters are not inexpensive, as the construction of a coil, even of but one or two turns, to carry heavy currents is a costly mat- ter. They are, also, expensive to install, as it is, of course, necessary to pass the entire current to be meas- ured through the meter, and this means extensions and complicated rearrangements of heavy copper bus- bars. To meet this last objection, Lord Kelvin places the solenoid with its accompanying core on the bus bars themselves, and runs a light cord from the core to an arm actuating the swinging needle, enclosed in a FlG 131 conventional case and swinging over the usual' graduated scale. In such case it is necessary that the indicating portion of the instrument be located vertically above the actuating part, but the indicating portion is still free to assume any form, usually either the type shown in Fig. 130, or the so-called edgewise type, shown in Fig. 131. Thomson Inclined Coil Instruments. The Thomson inclined coil ammeter is an electromagnetic instrument extensively used in this country for the measure- FlG. 132. ment of relatively small currents. In it, as will be seen from Fig. 132, the stationary coil of wire is placed at an angle to the 172 ELECTRIC AND MAGNETIC MEASUREMENTS. axis of the staff of the indicating needle and the staff carries a strip, or bundle of strips, of iron, which, when no current is passing, are held so that their plane is nearly parallel to the plane of the coil. When current is put on, the bundle of strips, of course, tends to take up a position such that the reluctance of the magnetic circuit of the solenoid is reduced to a mini- mum, and in so doing, of necessity rotates the iron and with it the shaft to the position shown by the dotted line. The force with which it tends to rotate is in proportion to the current strength, so that the amount that it winds up the volute phos- phor bronze spring which opposes its motion, as indicated by the attached needle, indicates the current strength. The arrange- ment of parts in this instrument results in a large angular motion of the needle, without necessitating the use of any FIG. 133. multiplying devices, such as levers, gears, or pulleys. When properly designed and built, this instrument is capable of a very satisfactory degree of accuracy and reliability. Magnetic Vane Instruments. Another form of electromagnetic ammeter, called the " mag- netic vane type," and in extensive use in this country, is dia- grammatically shown in Fig. 133. Here the current passes through a solenoid, whose axis is at right angles to the face of the instrument. Permanently secured inside of the solenoid spool is a strip of soft iron which when unrolled is triangular in shape, the base MEASUREMENT OF CURRENT. 173 of the triangle being bent out at right angles, as the figure shows. Also within the solenoid core is a steel staff or shaft whose pointed ends rest in appropriate jewel bearings, and which carries, in addition to the indicating needle, a flat rect- angular strip of soft iron, which is parallel to the bent in stationary piece when no current is on. When current passes through the wire coil, the stationary and movable strips are, of course, similarly magnetized, so that the like poles of the magnets so formed are adjacent ; they there- fore repel each other, and in so doing the movable one carries with it over the scale the indicating needle. This form of instrument has many modifications, differing in more or less important details. The force opposing the motion of the needle is sometimes that offered by a flat spiral spring, and sometimes the attraction of gravity on a weighted arm. Like other electromagnetic instruments, this type is operative with either direct or alternating current, and its motions are damped, preferably, by means of the air vane or the oil dash pot. Electromagnetic instruments in which a portion of the iron used is stationary, are open to certain objections, experiment showing that there are errors, when a fixed plate of magnetic material is present, that exist to a much less extent when such a plate is not used. This error is mainly due to the following cause : Referring to the chapter on magnetic hysteresis (see page 380), the flux through a magnetic circuit, composed wholly of iron, has different values for the same magnetizing force, according to whether the magnetizing force be increasing or decreasing. When, on the other hand, the iron is removed, the flux is the same, no matter how any given current value has been reached, that is to say, air is non-hysteretic. In a composite magnetic circuit, formed partly of air and partly of iron, such as that in the instruments in question, the hysteretic influence of the iron decreases as the percentage of the total magnetic circuit formed by the iron decreases. In the magnetic vane type of instrument, therefore, involving stationary as well as movable iron, the error due to hysteresis is thus increased, so that there is a greater discrepancy between the values of a rising and falling current of the same strength. The character of the iron entering into the construction of all 174 ELECTRIC AND MAGNETIC MEASUREMENTS. electromagnetic instruments is of great importance, as the hysteresis losses vary widely in different specimens of the metal. While careful design and a proper selection of the iron may result in an instrument in which the difference in indications between a rising and falling current of the same strength is no greater than one half of one per cent, poor design and poor iron may cause an error of 5 per cent, or over. It is advisable, therefore, carefully to test electromagnetic instru- ments intended for use in direct current work, before assuming that they are correct and, moreover, to repeat the checking at intervals, because iron ages magnetically, and has a higher hysteretic coefficient, after being subject to changes in the intensity of its magnetization for extended periods. The effect of aging is negligible in some brands of iron, and can be reduced in all by proper preliminary treatment, although this fact does not seem to be appreciated by all instrument makers. '\Vhere electromagnetic instruments are used for the measurement of alternating currents, the first source of error, namely, the dif- ference in indications between a rising and a falling current, does not exist, by reason of the continuous, automatic reversal that is going on and which was present when calibration was effected. HOT WIRE INSTRUMENTS. When an electric current flows through a conductor, the energy expended in overcoming the conductor's resistance is manifested in the form of heat. The energy consumed varies as the square of the current strength, and the temperature varies proportionately, so that, as a body brought to different temperatures expands and contracts, these variations, suitably indicated, may be utilized as a means of measuring current strengths. The amount of elongation of a heated conductor depends on the temperature rise, the length of the rod or wire, and the material of which it is composed. Cardew Instruments. In what is, perhaps, the earliest commercial form of hot wire instrument, namely, the Cardew, the conductor is a platinum silver wire, about seven feet in length, arranged as shown in MEASUREMENT OF CURRENT. 175 Fig. 135. It is coiled back and forth over ivory pulleys in order to decrease the length of the instrument, and the motion is amplified by a gear wheel and segment, or a pulley and cord, so that the needle traverses an arc of over three hundred degrees. To prevent air currents from cooling the wire, the whole is enclosed in a case, the wire and lower pulleys being shielded by a brass tube. As the coefficient of expansion of the brass tube and the platinum silver wire are not identical, it is evidently not feasible to attach the bearings for the pulleys over which the wire passes, to the tube, for, if this were done and the instrument placed where the temperature was not that which existed at the time when the instrument was calibrated, the difference between the expansion of the tube and that of the wire would cause the needle to move. The pulleys are, there- fore, mounted on a framework built up on a com- bination of brass and iron rods, with the lengths of these respective metals so selected that the whole expands and contracts with changes of temperature at the same rate as the platinum silver wire. Fig. 136 shows the complete meter. The Cardew instrument should not be used with the tube in a vertical position as air cur- rents are then set up within it by the heated wire, and the cooling effect of these currents on other portions of the wire causes an appreciable error. The tube is, therefore, always placed horizon- tally, when possible. While abundantly able to satisfy the require- ments existing when it was devised, the Cardew instrument, as just described, does not compare favorably with modern hot wire types. The errors introduced by the friction of the bearings of the numerous wheels it contains, the disturb- FlGt 135 * ing effect of air currents set up in the tube by the heated wires, and the generally unsatisfactory result of leading a wire around the sharp bend of a pulley when the expansion of its whole 176 ELECTRIC AND MAGNETIC MEASUREMENTS. length is to be utilized, render its indications too inaccurate for present day demands. The electromagnetic and moving coil instruments that have been developed since its time are much better and, because but little work was done on apparatus util- izing the hot wire principle for a considerable period, the preva- lence of these other forms has led many to believe that the principle itself is inherently defective. Such, however, is not the case, as hot wire measuring instruments when properly designed, are capable of making a showing that is fully satisfac- tory as compared with that of the other types. Hartmann and Braun Instruments. Not only is the length of the Cardew instrument objection- able, but the wire therein must be run at such high tempera- tures, in order to obtain a sufficient linear expan- sion to work the indicating gear, that the amount of energy consumed renders its use impossible for the measurement of small currents when the allow- able drop in E.M.F. in the meter is small, or for very large currents where the potential necessary to force the current through the instrument is ob- tained from the drop across the terminals of a resistance placed in the main circuit, that is, it cannot be used as a shunt ammeter. The Hartmann and Braun hot wire instruments overcome these disadvantages, to a considerable degree, by the em- ployment of a somewhat different principle. It is well known that, if a wire strand be stretched be- tween two fixed points, the amount that it will sag at its center, when the strand is slightly stretched, is many times the elongation of the strand itself. Referring: to Fig:. 137, AS is the FIG. 136. ... ,, & TT expansion wire in the Hartmann and Braun in- strument, which, when current flows through it, stretches and allows its center to sag. At the center is attached one end of a wire, CD, secured to a fixed point at D. When the distance between O and D lessens, because of the sag of the hot wire, CD is itself pulled aside by the spring attached to its center, by an amount that is as much greater than the sag of AB, as the sag MEASUREMENT OF CURRENT. 177 of AB is greater than the elongation of A B. At the point, E, in the center of CD, there is attached a cord, 6r, which passes around a pulley fastened on an axis carrying an indicating needle, and this cord is kept taut by the spring, 8. In this way a very short hot wire elongates sufficiently with a reasonable rise in temperature to cause readily readable needle deflections. The terminals of the hot wire are attached to a common metallic framework, but are electrically insulated therefrom. The metal of the framework has the same coefficient of expansion as the wire, so that changes in the temperature of the surround- ing atmosphere affect both equally, and do not give rise to erroneous indications. It is claimed that with a voltage as low as 300 millivolts at the terminals of conductors attached to A n B tfH-^/wvw-^ s E rJ> FIG. 137. and B, sufficient current will flow through the wire to cause it to expand to an amount that will make the indicating needle traverse full scale. This drop is one that is readily attainable with a shunt whose size and cost are not prohibitive, and which does not call for an unreasonable drain of energy from the circuit. The end A of the expansion wire is secured to a special terminal part as shown. This is provided in order that the zero position of the needle may be adjusted by varying the tension of AB, should this at any time be necessary. A complete Hartmann and Braun hot wire type instrument of the kind made in this country is shown in Fig. 138. The device having the shape of a wheel with opposite segments indented, attached to the axis of the pointer, is of thin sheet aluminum, and moves between the pole faces of the permanent magnet, 178 ELECTRIC AND MAGNETIC MEASUREMENTS. the eddy currents set up in the aluminum when the needle swings assisting in bringing it rapidly to rest and making the indications dead beat. Roller Hot Wire Instruments. The principle on which these instruments operate is dia- gram matically shown in Fig. 139. Referring to it, a wire, a, of high resistance, low temperature coefficient and non-oxidiz- able metal is secured at one end to a plate, c^ passed around a pulley, d, secured to a shaft, e, and its free end brought back again and mechanically, though not electrically, attached to the same plate, c. Plate, j ^AAY^AAAAAAAA E are, 215 216 ELECTRIC AND MAGNETIC MEASUREMENTS. of course, straight and parallel to the axis. It is evident that whatever instant is chosen, the product of a b and a c remains the same. The case of alternating current is shown in the suc- ceeding figure. Here the horizontal axis again represents time, the curve, /, 7, the values of the current at any instant, and JE, E, the potential values at any instant. The reversal of current direction is indicated by drawing the curves below the horizontal axis for such length of time as they are opposite to the initial direction. If the circuit is non-inductive and without capacity, the current varies with and in phase with the potential, and the curves therefore have the relative position shown in Fig. 165. In such circuits the effective watts can be FIG. 165. calculated by simply multiplying together the effective volts and effective amperes. If, however, the circuit is inductive, the current no longer varies in phase with the voltage, but its changes in value lag behind it, the relative position of the two being dependent on the relative value of the inductance. Fig. 166 shows the current and potential curves under these circum- stances. Here it is evident that the product of the effective volts shown by the voltmeter and the effective amperes shown by the ammeter no longer gives the effective watts. Take, for instance, the point a on the time line. Here the current has the value indicated by the height of the ordinate a c, but the potential value at that instant is zero, so that their product is zero. The maximum product at any period is no longer the product of the maximum values of the current and voltage but that at some instant, n, where neither is it at its maximum. As MEASUREMENT OF POWER. 217 algebraic signs must be taken into consideration, we might, theo- retically, even arrive at the case given in Fig. 167, where the potential and current curves are in opposing phases throughout, so that their product is zero, although the voltmeter would show FIG. 166. the normal effective voltage and the ammeter the normal effects ive amperage. The measurement of the displacement between current curves is by no means easy, and even if it were it would be necessary FIG. 167. to make calculations to determine energy from volt and ampere readings with alternating current on an inductive circuit. Fortunately there are available means of constructing instru- ments which will give the watts direct without this necessity. 218 ELECTRIC AND MAGNETIC MEASUREMENTS. DYNAMOMETER WATTMETERS. The Siemens ammeter described on page 165 may be con- verted into an instrument that will measure the watts in any circuit by constructing the stationary 'coil of comparatively few turns of large diameter wire connected so that all of the current to be measured flows through it, and making the movable coil of many turns of fine wire with its terminals connected directly, or through the interposition of a resistance, across the line like a voltmeter. When this is done the field set up by the station- ary coil is evidently proportionate to the effective amperage, and that by the fine wire coil to the effective E.M.F. If the current and voltage do not attain their maximum values simul- taneously, that is to say, if they are out of phase with one another, the reaction between the two fields will diminish* with increasing phase difference, and the instrument indications will be true watts instead of volt amperes. THE WATT BALANCE. The Kelvin balance described on page 18 may likewise be utilized as a wattmeter if one of the sets of coils is made to carry the total current flowing and the other is connected across the line, so that the current through it, and hence the magnetic field that it sets up, is proportional to the voltage. As in the case of the dynamometer wattmeter, the fine wire or " potential winding " is used for the movable coils, as the current to be carried to them through the suspending ligaments is then very much less. WHITNEY WATTMETER. This is an instrument whose principle is the same as that of the dynamometer wattmeter, but the construction is modified to make the apparatus portable and hence more suitable for com- mercial measurements. As can be seen from Fig. 168, the heavy current winding is formed of two coils supported on suitable frames, which inclose instead of being inclosed by the fine wire coil. The latter is mounted on a shaft with pointed ends resting in jeweled bearings, and the spring effort which MEASUREMENT OF POWER. 219 balances the turning effort of the coil, when the button pro- jecting through the top of the instrument case is rotated, is that of a pair of volute springs of flat strip phosphor-bronze, instead of a spirally wound round wire. The current is led into and out of the movable coil through the volute springs, so that the mercury cups used in the Siemens form are done away with. The scale over which the needle attached to the torsion button moves is divided so as to indicate watts directly instead of degrees from which the watts must be calcu- lated by referring to tables or curves. The needle that is FIG. 168. attached to the shaft carrying the potential coil, and which is brought back to a reference mark on the dial by turning the torque button to obtain a reading, is allowed a somewhat greater range of movement than the corresponding needle in the Siemens form. A short scale is drawn on both sides of the reference mark, so that the instrument can be used to read watt- ages differing slightly from those indicated by the needle attached to the torsion head. For instance, if the torsion head needle was pointing to the 50 watt division with a given cur- rent flowing, but the other or zero needle was pointing, not to the reference mark, but to the division to the left thereof corre- 220 ELECTRIC AND MAGNETIC MEASUREMENTS. spending to 10 watts value, the true reading is 60 watts, as the divisions of the short scale are so spaced that it would be necessary to turn the torsion head until its attached needle pointed to 60 watts on the principal scale in order to bring the zero needle to its zero line. Similarly if the zero needle pointed to the 10 watt mark at the right of the reference line, the true reading would be 40 watts. The short scale is convenient in lamp testing, as the torsion needle may be set to the average wattage that the lamps are supposed to take, and the amount in ex- cess of or less than this may be read* off at once from the short scale. A better idea of the scale and general appearance of such an instrument may be had from Fig. 169. WESTON WATTMETERS. A still further modi- fication of the Siemens wattmeter is the Wes- ton instrument shown in perspective in Fig. 170 and diagrammati- cally in Fig. 171. Here the heavy wire coil is likewise stationary and surrounds the circular potential coil, the latter being supported on steel pivots resting in jeweled bear- ings and having the current lead to and from it through volute springs. However, no torsion head is used, and the potential coil, instead of being maintained at practically the same position for every value within the capacity of the apparatus, rotates about its axis over an angle of about eighty degrees. As in the case of the spring controlled voltmeters and ammeters, the opposing force that increases in proportion to the deflection of FIG. 169. MEASUREMENT OF POWER. 221 . FIG. 170. the needle is supplied by the volute springs, so that, as the reaction between the currents in the two coils is nearly directly proportional to the watts, the scale divisions are nearly equally spaced. This form of instru- ment has an advantage over the dynamometer types, in that no manip- ulation is necessary and the needle points at once to the scale mark show- ing the watts. On the other hand, as the angle between the planes of the current and potential coils is variable, the mu- tual induction between the two varies with different positions of the needle. For any given difference in phase between the potential and current the apparatus may have its scale divisions drawn so that the indications are cor- rect. If, however, the power factor varies, this varying mutual induction in- troduces an error that cannot be compen- sated for, and can be allowed for only when the phase dif- ference is known. The error from this source is mini- mized by making the mutual inductance of the windings as small as possible, and with proper design can be made negligible for much commercial work where the power factors do not cover too wide a range. However, it is not safe to assume that such an instrument will give correct FIG. 171. 222 ELECTRIC AND MAGNETIC MEASUREMENTS. indications when making measurements on both unity and very low power factors, such as an incandescent lamp load and the energy consumed by the primary winding of an open secondary circuit transformer, for instance, as with the best design there will be a difference in accuracy of at least two or three per cent under such circumstances. INDUCTION WATTMETERS. A wattmeter suitable for the measurement of watts on alter- nating current circuits only, may be made following along the lines of an induction motor. Referring to Fig. 172, if D is a disk of good conducting metal, such as aluminum or copper, and BAB a series of sheet-iron stampings assembled to- gether and surrounded on the B extensions with fine wire windings and on the A extension by a coarse wire winding, and these coils are connected in circuit like the fine and coarse coils of a dynamometer watt- meter, the disk will be subjected to a torque pro- portional to the watts flowing. Briefly, the reason for this is that the alternate ing current through the coarse winding produces currents in the disk whose paths are as shown by the concentric circles in the figure and of a strength proportional to the cur- rent. The current flowing through the fine wire coils sets up a magnetic flux in the legs B, B, whose strength is proportional to the E.M.F., and the reaction between this and the current in the disk urges the latter to rotate with a torque proportional to the product of the current and the potential, i.e., the watts. The magnetic circuit for the lines of force flowing is made of less FIG. 172. MEASUREMENT OF POWER. 223 reluctance by the addition of the set of stampings C placed below the disk. Having thus an apparatus in which an element is urged to rotate with a torque proportionate to the watts, all that is necessary to convert it into an indicating wattmeter is the attachment of an index to the disk D, a calibrated scale over which this needle may swing, and a spring for oppos- ing the disk torque. The indications of the needle of induction instru- ments are usually dampened or made " dead beat " by adding a permanent magnet between whose polar extrem- ities the conducting disk rotates, the resultant eddy currents supplying the neces- sary retardation. The Westinghouse indicat- FIG. 173. ing induction wattmeter is shown in Fig. 173. The conducting disk here takes the form of a cylinder, but the principle being the same as that of the above wattmeter, the operation may be readily under- stood without going into further details. HOT WIRE WATTMETER. A simple and ingenious wattmeter utilizing the expansion of wires heated by the passage of current and proposed by Bauch is diagrammatically illustrated in Fig. 175. Here a and b are the two hot wires, S being a shunt inserted in one current carrying conductor, and c a resistance inserted between the junction of the two wires and the other conductor. Starting from the assumption that the elongation of a heated wire is proportionate to the heat that it is called upon to dissipate, it can be shown (see ^Industrie Eleetrique, Sept. 10, 1901) that the difference between the elongation of two wires interconnected as shown in Fig. 175 is proportional to the watts dissipated in the circuit L,L. 224 ELECTRIC AND MAGNETIC MEASUREMENTS. A mechanical arrangement for indicating the difference in the elongation, and hence pull of the two wires, is shown in Fig. 176. Here c and / are solid levers, d and e flexible liga- B S FIG. 175. ments taking the place of pivots, and h an arm with a bifurcated end for actuating the needle as in the hot wire volt and am- Resistance 'hunt Generator FIG. 176. meters described on p. 178. When a difference of potential exists between k and /, but no current flows through the shunt, the wires a and b are heated alike, as the resistance of the shunt MEASUREMENT OF POWER. 225 is negligible as compared with the rest of the circuit so formed. The lever h will therefore move vertically only and fail to rotate the needle. A similar reasoning applies when current flows through the shunt, but there is no difference of potential between k arid I. If there is both a difference of potential and a current flow through the shunt, b is heated more than a, the lever / rocks, and the arm h urges the needle up the scale. Its excur- sions are proportionate to the watts. CONNECTIONS OF WATTMETERS. The way in which the current and potential coils of the dynamometer type wattmeters and their equivalents are con- nected in circuit has a considerable influence on the accuracy of the results obtained. Such connections may be made in FIG. 177 FIG. 178. either of the two ways indicated by Figs. 177 and 178 respec- tively. In the former, the potential coil is connected across the terminals of the circuit whose watt consumption is to be measured, the current coil being cut in before it ; whereas, in the second case, the potential coil is across the supply line and the current coil inserted further on. With the first arrange- ment the current flowing through the series winding is evidently that demanded by the load and by the potential coil, and in the second case, while the current is that demanded by the load alone, the potential indicated is not that at the load terminals but that due to the drop across the currenkconsuming apparatus plus that across the current winding. To see the effect of these two plans it will be instructive to take an actual example in each case. Considering first the results with connections as in Fig. 177, let the load be a 16 C. P. incandescent lamp, and the potential of the supply mains 120 226 ELECTRIC AND MAGNETIC MEASUREMENTS. volts ; assume also that the resistance of the potential coil E is 4,000 ohms. The current through the lamp may be taken as .5 amperes and that through the potential coil $-$$ = .03 amperes. The current demanded by the potential winding and which passes through the current coil is therefore six per cent of the current required by the lamp, and the instrument indica- tions are that percentage higher than the wattage expended in the lamp alone. Such an error is, of course, entirely too great even for the roughest commercial work. If the connections are as in Fig. 178, the results would be as follows : The current flowing through the series coil is now only that demanded by the lamp, but the potential applied to the FIG. 179. lamp is less than the 120 volt line potential by the amount of the drop across the series winding. Let the resistance of the latter be taken as .2 ohms, a fair value. With one half ampere flowing, the drop is therefore .1 volts, and as the instrument takes account of the line voltage only, the resultant indications are less than one tenth of a per cent high. This error is less than in the preceding case, but if the cur- rent demanded is large and approximating the maximum capacity of the series winding, and the potential applied is low, it also may become appreciable, although seldom as great as in the first case. For accurate work -it -is therefore necessary that the resistance of both windings of the instrument be known in order that proper corrections may be applied to the results MEASUREMENT OF POWER. 227 obtained. In almost all cases it is desirable to use the second scheme of connections. COMPENSATED WATTMETERS. If certain connections of a wattmeter are made permanently inside of the case, so that it is assured that the circuits will be as in Fig. 177, the error due to the current drawn by the potential coil can be compensated for in a simple manner. Referring to Fig. 179, which shows diagrammatically the internal connections of a wattmeter and the way in which it is attached to the line, it can be seen that in addition to the regular potential coil and the non- + inductive resistance placed in series there- with to adjust the calibration, turns of wire convey the po- tential circuit cur- rent around the spool carrying the series coil. The number of these turns is made equal to the number of turns in __ the movable coil, the result being that the additional fixed coil field due to the additional current flowing through it demanded by the potential winding is exactly neu- tralized by the back turns of the same current carried around the same number of times through this compensating winding. An instrument so equipped will therefore indicate the watts expended on the receiving circuit without requiring the appli- cation of any correction factor. THKEE-VOLTMETER METHOD. The watts expended in any given circuit may be determined by using three voltmeters or making three successive measure- ments with one voltmeter in accordance with the following plan: Referring to Fig. 180,72 is a non-inductive resistance connected in series with the inductive resistance included JL_. FiG. 180. 228 ELECTRIC AND MAGNETIC MEASUREMENTS. between b and o in which the power to be measured is expended. Three voltmeters are then attached, one to show the potential between a and 5, another that between b and c, and the third that across the line ac. It is not within the scope of this volume to give a demonstration of the correctness of the conclusion, but it is a fact that the watts in be are, under these circum- stances, represented by the formula 2E To obtain maximum accuracy, R should be chosen so that the potential across it is as nearly as possible equal to the difference in potential between the terminals of be. As R is in series with be, and the drop across it should be practi- cally the same, it is evident that this method of testing calls for the presence of a testing voltage double that demanded for the normal oper- ation of the device inserted between b and - (T * 7" 2 T ?\ 2 v 3 i 2 ) In contradistinction to the three-voltmeter method, the three- FrG 181 MEASUREMENT OF POWER. 229 ammeter one does not call for an increased potential for testing purposes, but it does demand increased current. On the other hand, while with the three-voltmeter method it is possible to arrange a switch by means of which connections may be rapidly shifted so that one voltmeter may be used for reading all three potentials, a similar plan is not practicable with the ammeters, owing to the heavy currents involved and the necessity of keeping the circuits intact and their resistances unchanged, so that three meters are essential. Both the three-voltmeter and the three-ammeter methods have the very serious drawback that a very small percentage error in the accuracy of the indications or the observations of the indi- cations of any of the instruments introduces a very large error in the results. Neither is used in modern practice unless it becomes absolutely necessary to make a test when voltmeters or ammeters alone are available, and every precaution is then ex- ercised to have the readings as exact as possible. POWER CONSUMPTION OF MULTIPHASE CIRCUITS. The various instruments for and methods of watt measurement above described are all suitable only for use on simple direct or alternating current circuits involving two conductors only. Where the case involves multiphase currents the conditions become essentially different. If the line on which measurement is to be made is a four- wire two-phase one, watts are measured just as one would measure them in two independent alternating current circuits, a separate wattmeter being used in the conventional way with each, and their indications arithmetically added. With three- phase three-wire systems two wattmeters must likewise be em- ployed if the results are to be accurate, whether the loads on the different phases are like or unlike. These instruments are to be connected in the circuits, as in Fig. 182, the current coil of one being inserted in one line, the same coil of the other in another line, and the potential coils of each bridged across between their respective lines and the third conductor. The sketch shows the connections of the receiving apparatus as being in delta, but the connections of the wattmeter are made the same if they are 230 ELECTRIC AND MAGNETIC MEASUREMENTS. arranged in Y. The total watts absorbed is given by the algebraic sum of the indications of the two wattmeters. When the power factor of the load is over 50 per cent the algebraic sum is the arithmetical one, but when less than 50 per cent it is the arithmetical difference, so that the indications of the lower reading wattmeter must be subtracted from the higher reading one to get the correct result. It is essential that the potential coil connections be made as in Fig. 182, as otherwise the results obtained may be erroneous. This caution is necessary because approximately the same poten- FiG. 182. * tial difference exists between a and b as between a and 2 , in which D Y is the first deflection. For maximum accuracy, the capacity of the standard should be made as nearly as possible equal to that of the condenser of unknown value. Bridge Methods. Condenser capacities may be compared when they are intercon- nected by a network of conductors arranged like those in the Wheats tone bridge. This method has the same advantage that exists in the measurement of resistances with a bridge ; that is, it is a zero one, and errors due to reading the galvanometer deflections are thus avoided. It is further possible to eliminate practically all errors due to inductance. In the simple bridge method, the standard condenser F l and the unknown one F 2 are connected as shown in Fig. 191 ; ad- justable resistances 7^ and R^ a galvanometer, a battery and a special contact key, a, 5, being also employed. When the a end of the key is depressed the condensers are evidently being charged by the battery, and when the b end is depressed they are being discharged through the resistances and the galvanom- eter. To make the test, a is first depressed for a brief inter- val and then raised for its full height, so that the condenser discharges as stated. If this results in a deflection of the galvanometer, the ratio of R l to R 2 is altered and the trial again made, b being kept depressed until then, in order that the condensers may be kept discharged. When a ratio of R l to R 2 MEASUREMENT OF CAPACITY. 241 is finally attained such that no galvanometer deflection ensues r> TT when a is raised and b depressed, the relation = _ 2 holds # 2 Jf\ good. This is so because if the galvanometer does not deflect when the condensers discharge, the potentials at its points of attachment to the network are equal; being charged by the some potential, the quantities of current stored by the con- densers are proportional to their capacities, and these quantities are in inverse proportion to the resistances R 1 and R 2 in the circuits leading to them. In this, as in all other capacity measurements involving the employment of adjustable resistances, it is essential that the latter be absolutely without capacity and without inductance. Such coils are purchasable on the open market, and are best made as follows : Each resistance unit is made up of two wires connected in parallel, each having twice the resistance of that desired for the coil, and each of the two coils is wound into a flat and very thin spiral. The two spirals are placed, theii flat faces touching and connected so that the currents flowing through them run in opposite directions. Being now connected in parallel, the opposing windings make the coil non-inductive as the current flows in reversed directions in parallel conductors 242 ELECTRIC AND MAGNETIC MEASUREMENTS. for a like distance. The capacity of such a unit is negligible, as it forms a condenser in which the potential between its two surfaces is but half of that between the innermost and the out- side convolutions, and the distance between the surfaces is that between the wires forming these convolutions. Such construc- tion is necessarily expensive, but must be employed if reliable results are to be had. Modified Bridge Method. If the connections in Fig. 191 are modified to those in Fig. 192, the galvanometer and battery positions being interchanged, FIG. 192. we have another method of measuring an unknown capacity in terms of a standard. The keys in the battery and galvanometer circuits are manipulated so that the condensers are charged by the battery and subsequently discharged through the resistances and the galvanometer in a way analogous to that in the preced- ing method. The values of the resistances are likewise to be varied until no galvanometer deflection results when the con- densers are unloaded by depressing the galvanometer key, whereupon the capacity F 1 is to F 2 as R 2 is to R^. This follows because the condensers, connected in series, must each contain a like quantity, and the discharge from F^ through R^ times the potential difference between the terminals of R l must equal the MEASUREMENT OF CAPACITY. 243 discharge through R 2 times the potential difference across R 2 . We therefore have the relation .B, Thompson Method of Mixtures. This method, so called because it involves mixing the opposed charges of two condensers so as to determine whether or not J t ^^aAr^ FIG. 193. they are equal, is an acknowledged standard, particularly for the measurement of cable capacities, and is also a favorite when the capacity of one condenser is to be accurately determined in terms of that of another. In making it, connections are arranged as in Fig. 193. In making a test, the two center buttons of the special key L are first depressed so that the condensers are charged by means of the battery with the potential differences that exist between the terminals of the resistances R } and R 2 . After this has been done the keys are released, making contact with c and d respec- tively, which places the two condensers in parallel and allows 244 ELECTRIC AND MAGNETIC MEASUREMENTS. the charges to mix. If these charges were equal and opposite when the key E is depressed, there will be no galvanometer deflection, as there is no current to cause it. If there should be a deflection, the charges were not alike, and the resistances R 1 and R 2 must therefore be varied until this condition is attained. When it is, the ratio F t is to F 2 as R 2 is to R 1 evi- dently holds. When the capacity of a cable is being measured, the point of junction of the resistances R l and R 2 must be connected to earth, as the earth forms the one coating of each condenser. If the results obtained are to be comparable with others, some standard time of charging must be used, which time may con- veniently be chosen as five seconds. The value of the capacities FIG. 194. should also be as nearly alike as possible. The key L is a special device known as the Lambert capacity key, one of which is shown in Fig. 194. CAPACITY BY LOSS OF CHARGE. If the terminals of a charged condenser are left connected together through a known resistance, R, for a period of T sec- onds, its capacity can be calculated from the formula T F= - . 2.303 R (log D! - log Z> 2 ) in which D 1 is the deflection of a ballistic galvanometer caused by the discharge through it of the condenser after it has first been electrified and before the resistance is attached, and D 2 the same after it has been freshly electrified and then left dis- MEASUREMENT OF CAPACITY. 245 charging through the resistance R for T seconds. If R, the resistance, is in megohms, the capacity, F, is in microfarads. If the condenser under test is of the type in which paper is used as the dielectric, its own internal resistance is frequently sufficiently low to enable the above test to be made, it being, of course, in that event necessary to determine the condenser resistance by one of the methods described in that section of Chapter V treating of high-resistance measurements. If the condenser is of the mica-insulated type, its resistance is or- dinarily too high to allow of this, and an external resistance of 20 or 30 megohms must be connected across its terminals. A modification of this test is made by connecting up the condenser, battery, galvanometer, resistance coil, and key, as K FIG. 195. shown in Fig. 195. With the apparatus so arranged the key is depressed and the steady deflection of the galvanometer noted. The key is then raised and the deflection given read after the expiration of T seconds. If the initial deflection is designated by D^ and the subsequent one by _Z> 2 the capacity may be calculated by the same formula given above. In both the foregoing, if the condenser resistance is inter- mediate between the low value which allows of its use as the resistance through which the charge is dissipated and the high value which makes its figure so high as compared to the one connected to its terminals that the current flow througl it is negligible, the value of R in the formula must be calculated from the law of divided circuits, page 94, the true resistance being that of the external one and that of the condenser con- nected in parallel. 246 ELECTRIC AND MAGNETIC MEASUREMENTS. CONDENSER ABSORPTION. The majority of types of condensers have, to a greater or less degree, a property of their dielectric by virtue of which they will receive a quantity of electricity in excess of that due to their electrostatic capacity. This excess charge is taken up more slowly than the condenser charge proper, and the phe- nomenon, known as condenser absorption, must be allowed for in all capacity measurements. The absorption of a given condenser may be measured as follows : A condenser, F^ whose absorption is to be measured, is connected up with a standard condenser, F^ and resistances and a galvanometer, all as shown in Fig. 192. A balance is obtained in the same way that is employed in measuring capacity, but when obtained, it does not indicate that F l \s to F^ as R^ is to R^ as a portion of the charge, Q, that has been put into F 2 has been absorbed. If the quantity absorbed is designated by , the potential at jF 2 's terminals is that caused by the charge Q q. To determine q the battery key K.^ is "closed and the ratio of the two resistances adjusted, so that when the key 7T 2 is depressed the galvanometer gives a small deflection. If .ffj is then opened and a few seconds are allowed to elapse, a deflec- tion will be observed on closing J?T, which deflection should be opposite to the former one. By further adjusting the ratio R^ to R 2 , the two deflections can be made equal, whereupon q is the quantity of electricity that would cause either of the de- flections. The value of q may then be readily determined by the direct deflection method. CHAPTER X. MEASUREMENT OF INDUCTANCE. As has been previously noted, inductance, or more properly, the coefficient of inductance, may be either that of a given conductor or that between a plurality of conductors. The electromotive force set up in any circuit because of its induc- tance is the product of the coefficient of induction L and the rate at which the current flowing changes. If, with an alternating current whose intensity and direction vary according to the sine law, we take the instant at which the current strength is a maximum, we have chosen a time when the strength is neither increasing nor decreasing, and the E.M.F. of self-induction is therefore zero. If the time is that at which the current is passing from a positive to a negative sign, the rate of current change is a maximum, and the E.M.F. of induction likewise maximum. Analogous conditions hold for the whole cycle of current changes, the result being that the E.M.F. caused by induction follows the shape of the current curve, but differs from it in phase, in that the E.M.F. is zero when the current is a maximum and vice versa. As the E.M.F. so set up opposes any change in the E.M.F. that causes the energizing current to flow, a lesser current will evidently pass through a given inductive circuit if the current is alternating, that is, constantly changing in value and direction, than if it is direct and has a constant value and direction. The resistance in the latter event is a purely ohmic one which may be measured by any of the methods described in Chapter V. The resistance to the flow of an alternating current may likewise be measured by observing the amount of current that is passing and simultaneously reading the drop across the coil terminals by means of a static voltmeter. With this value and the true ohmic resistance known, the induction can be calculated, as is evident from the following : As by Ohm's law, the E.M.F. causing the flow of current through an ohmic resistance must change with any current 247 248 ELECTRIC AND MAGNETIC MEASUREMENTS. change, the E.M.F. and current for this component of the total resistance or " impedance " offered by the coil are in phase. On the other hand, as above explained, the E.M.F. due to the induc- tance of the circuit is a maximum when the current strength is zero, that is, it is one quarter of a period, 90 degrees, or a right angle behind the current. The effects of the two may therefore be graphically represented by two sides of a right-angled tri- angle, as in Fig. 196, in which Rl is drawn of a length possess- ing the number of scalar units equal to the drop in E.M.F. due to the ohmic resistance, and Leo I to the same scale represents the drop due to the inductive resistance, while the length of the re- maining side of the triangle represents the total impedance. R I may be determined by measuring the ohmic resistance with direct current flowing, and the hypothenuse of the triangle, which is, of course, equal to + L 2 a) 2 by measuring the current that passes when alternating Lu)f current is applied and the drop across the coil terminals, simultaneously. In j?iu. mo. ^ both R is the ohmic resistance, I the current, and L the coefficient of self-induction. is equal to 2 TT times the frequency of the supply circuit. The value of any two sides of the triangle being known, that of the remaining one may be readily calculated. INDUCTANCE BY THE BRIDGE METHOD. In this the coil whose inductance is to be measured, a gal- vanometer, a set of non-inductive resistances, a battery, and ballistic galvanometer are connected up as shown in Fig. 197. All of the resistances must be of the type described on page 241, free from inductance and capacity, and R^ must be capable of very exact adjustment which, if necessary, may be accomplished by shunting it with a second adjustable resistance. The re- sistances of the ratio -arms of the bridge A and B are made alike, and the value of the rheostat arm R } adjusted until the galva- nometer shows no deflection when first the battery key and then the galvanometer key are closed. Thereupon the galvanometer MEASUREMENT OF INDUCTANCE. 249 key is first depressed and then the battery key, which will cause a deflection or rather throw D l of the galvanometer due to the inductance of & This deflection is noted. The value of \ is then changed by a known amount, and the steady deflection, which we will designate as Z> 2 that is then given when both battery and galvanometer keys are kept closed, is noted. If now the time of vibration of the movable element of the gal- vanometer determined as described on page 234, be called T, and X is the logarithmic decrement of the instrument, and if the differ- FlG. 197. ence between the initial and final values of H l is r, the induc- tance can be calculated from the equation In the above, D^ is the galvanometer throw first observed, and D the second one noted under like conditions. MAXWELL S METHOD. In this the inductance is found by comparison with the capacity of a standard condenser. Connections are made as shown in Fig. 198, in which Q is the inductive coil anu S a standard condenser. The resistances in the arms /*, 7?, and S must be without inductance and without capacity. To make a measurement, the value of P is first varied until the galva- nometer shows no deflection with the battery key and its own 250 ELECTRIC AND MAGNETIC MEASUREMENTS. key kept closed. The battery circuit is then made and broken, whereupon it will be found as a rule that the galvanometer gives a throw each time. The resistance R is then varied until the battery circuit may be interrupted without producing a galvanometer throw, and the key again closed and held in order to see whether there is any steady deflection of the galvanometer needle. If there is, the process must be repeated until such values of P and R are reached that there is no galvanometer deflection under either FIG. 198. condition. The value of the inductance is then found from the equation or L=QRC. Modified Maxwell Method. In this method, proposed by Russell (see London Electrician, May 4, 1894), the connections are the same as in the original Maxwell one, but the condenser 8 is of the adjustable pattern, by means of which varying known capacities may be inserted. P is varied so that the galvanometer shows no deflection with a steady current flowing, and the battery circuit is then made and broken with its key in the regular way. If the condenser MEASUREMENT OF INDUCTANCE. 251 is now attached and its value varied, it will be possible to find two values of condenser capacities, the one of which will give a throw in one direction on opening or closing the battery circuit and the other in the reverse direction. By interpolation be- tween the extent of these throws we can calculate the value of the capacity which would reduce the deflection to zero. Call- ing this value (7, the inductance L may be calculated from the formula L = QRC. COMPAEISON METHODS. The value of an unknown inductance may be determined in terms of a known one by using the connections and apparatus FIG. 199. shown in Fig. 199. In this the galvanometer need not be of the ballistic pattern. /S\ is the known coil, and S z the one whose inductance is to be measured. Auxiliary resistances, R l and R 2 , are connected in series with each, and these groups are inter- connected with other resistances, a battery and a battery key, a galvanometer and a galvanometer key, as the figure shows. Keeping B and R^ alike, and of fairly high value, say 1,000 ohms each, the ratio of A to R^ may be varied, so that the gal- vanometer shows no deflection whether its key and the battery key are kept closed or the former closed and the latter tapped. V 7? When this adjustment is reached, S 2 = ^ . 252 ELECTRIC AND MAGNETIC MEASUREMENTS. SECOHMETER METHOD. The secohmeter is a mechanically driven commutator, illus- trated in Fig. 200, which is provided with two pairs of brushes, one of which makes contact with the terminals of a galvanometer and the other with the source of E.M.F. under measurement. When the commutator is set in rotation, it reverses the direction of the battery current through the circuit and simultaneously reverses the connections of the galvanometer to the circuit, so that the effort on the galvanometer needle is always exerted in one direction and a steady deflection maintained in spite of the current reversals through the circuit under test. With the aid FIG. 200. of this piece of apparatus, an unknown inductance can be measured in terms of a known one by the following method (due to Maxwell). In Fig. 201, S is the standard inductance, A^ the unknown inductance, and R and R } two adjustable non- inductive resistances. When the secohmeter handle is turned, the battery circuit being closed, the ratio of R to R^ may be adjusted until the galvanometer shows no deflection. If the same adjustment is such that there is no galvanometer deflec- V7? tion when the secohmeter commutator is at rest, S =. l - R MEASUREMENT OF INDUCTANCE. 253 INDUCTANCE WITH ADJUSTABLE STANDARDS. If the variable standard self-inductance described and illus- trated on page 36 be used in place of the single value standard S in the preceding paragraph, the measurement becomes simpli- fied, since after adjusting R and R^ so that there is no galva- nometer deflection with a steady current it is only necessary to set the secohmeter in operation and turn the button on the adjust- Gal. FIG. 201. able standard until the galvanometer is again at zero, whereupon the unknown inductance may be calculated from the formula Cf T> = already given. INDUCTANCE BY CALCULATION. In a few instances, with suitably shaped coils, inductance may be obtained with a fair degree of accuracy by calculation. The simplest case is when the inductance is in the shape of a con- ductor coiled up to make a solenoid whose diameter is small as compared with its length. With such a coil the value of the inductance is 4 7T 2 n z r* 254 ELECTRIC AND MAGNETIC MEASUREMENTS. in which n is the number of turns of wire, r is the mean radius of the turns in centimeters, and I the over-all length in centimeters. This formula is theoretically applicable only to solenoids of infinite length, but the error introduced when applying it to solenoids having a length of at least ten times their diameter is negligible for many practical purposes. MUTUAL INDUCTANCE. NICHOLS METHOD. The quantity of electricity that is momentarily discharged through a circuit connecting the terminals of a coil inductively influenced by a neighboring current carrying coil, varies in direct proportion to the strength of the current through the influencing coil and inversely as the resistance in its own circuit. FIG. 202. It is also dependent upon the mutual inductance between the coils ; in other words, the relationship is Q = - where Q is H the quantity of electricity momentarily flowing through the influenced coil, R the resistance of that coil, I the current that has been caused to flow through the other coil, and M the co- efficient of mutual inductance. To measure mutual inductance utilizing this formula, con- nections are made as in Fig. 202. Here P is the coil through which battery current is passed, and 8 the one in which current is induced when the strength of that in the former is varied. The value of Q in the formula must be determined from the characteristics of the galvanometer employed. These character- istics are preferably found by charging a condenser of known capacity with a standard cell and then discharging this through the instrument, as before described. / is measured by an ordinary direct current ammeter, A, inserted in the primary MEASUREMENT OF INDUCTANCE. 255 circuit as shown, and the value of the current is adjusted at will with the aid of the resistance D. R in the formula is the resist- ance of the whole secondary circuit, including the galvanometer and adjustable resistance r, and may be measured by any of the conventional methods already described. The ammeter, A, for measuring the current in the primary circuit should be of low range ; in fact, if the current values OffffTOT JWSUL --dscMtkU- FlG. 203. employed are reckoned in milliamperes the results will be in millihenrys, which is the unit usually employed. MAXWELL S METHOD. This involves the use of a standard of mutual inductance, and the test is made as shown in Fig. 203, in which 72 and R l are adjustable resistances and M the standard pair of coils. The values of the resistances are varied until the galvanometer shows no deflection when the battery circuit is rapidly made and broken, at which time the ratio M : M l : : R : R^ holds good. In making this test great care must be taken to separate the standard and unknown inductances by a distance sufficient to prevent any possibility of mutual interference by their own mutually inductive actions. CAREY-FOSTER METHOD. If a pair of coils whose mutual inductance is to be determined, a pair of adjustable resistances, a galvanometer, an adjustable condenser, a battery, and a key are interconnected as shown in 256 ELECTRIC AND MAGNETIC MEASUREMENTS. Fig. 204, we have another method of measuring mutual induc- tance. The ratio of R to R^ and the value of the capacity, (7, must be adjusted until there is no galvanometer deflection whether the battery circuit is held closed or whether it is being FIG. 204. rapidly made and broken. When this condition is attained, the mutual induction may be calculated from the formula M = C Rr, where r is the resistance of R^ plus that of e. (See Phil. Mag. Vol. XXIII, p. 121.) CHAPTER XL MISCELLANEOUS DETERMINATIONS. WAVE FORMS. THE determination of the curves depicting the rate of variar tion in strength and direction of the E.M.F. and current from an alternating source is often of considerable importance, par- ticularly as affecting the design of auxiliary appliances. Such curves are not obtainable from apparatus ordinarily forming part of an engineer's equipment, but may be derived in the following ways: Contact Methods. One method of obtaining the E.M.F. curve of a given alter- nating current dynamo is to rigidly attach a disk of insulating material, as diagrammatically shown in Fig. 205, to the armature shaft, so that it rotates at the same speed and maintains a fixed b FIG. 205. position relative to the armature windings. On the periphery of this disk there is located a metal block connected to the windings, and a brush arranged to bear on the disk makes con- tact with the block once in every revolution of the armature. If the brush is held fixed, the difference of potential between it and the other terminal of the armature winding is, at the instant of contact, that generated by the coil when it is in the position 257 258 ELECTRIC AND MAGNETIC MEASUREMENTS. relative to the pole pieces corresponding to the brush position. As this potential is applied to the brush several times per sec- ond with machines of the usual commercial frequencies, and always in the same direction, its value may be read off from the indications of an ordinary direct current voltmeter connected between the brushes a and &, in Fig. 205. By rotating the contact brush to different angular positions around the armature shaft, the E.M.F. values may there- fore be determined for any position of the armature con- ductors and the values thus obtained plotted so as i^o give the curve required. A convenient de- vice for making con- tact at various angu- lar positions of the armature is the Fes- senden portable con- tact maker, shown in Fig. 206. This consists of a hard rubber disk provided with a pointed spindle which is pressed against the end of th armature shaft like an ordi- nary tachometer. The handle shown is secured to the frame carrying the brushes and terminals, and the angle at which con- tact is being made is read off from the position of the scale relative to the pointer-like end of the rod carrying the heavy steadying bob. In order that the indications of a voltmeter used with a de- vice like the foregoing may be rigorously correct, it is necessary that the same be of a type which does not draw current from the circuit, a fact which at once suggests the use of a FIG. 206. MISCELLANEOUS DETERMINATIONS. 259 potentiometer method, that is to say, balancing the unknown potential against an opposing known one. To do this with a regular potentiometer, a contact maker, and the necessary accessories, and to plot the observed readings on section paper, is, however, a tedious procedure ; in fact, it may require some hours if the current being investigated is not of a smooth wave form. The following instrument was devised for the purpose of minimizing this objection. Rosa Curve Tracer. The plan employed in the Rosa curve tracer is shown in Fig. 207, the apparatus being in this case connected up to record a current curve. AB is a non-inductive resistance of known value FlG. 207. connected in series in the line under test, CM is a contact maker, MN is a resistance wire wound on and supported by an insulating cylinder, P is a contact brush sliding over NM, and Q is a permanent connection to B, the galvanometer Gr being inserted in that circuit. Current is supplied by a battery B having a potential that is indicated by the voltmeter Vm. The frame carrying the sliding contact P, by means of which contact may be made at any portion of the wire resistance forming the coil MN, carries also the point J 7 , which makes the record. D is a drum to which the record chart is secured. 260 ELECTRIC AND MAGNETIC MEASUREMENTS. With any given load on the circuit under test, the contact P may be placed at some point on the wire MN where the galva- nometer G- will show no deflection. At this time the difference of potential between P and Q is evidently the same as that be- tween A and B, and is therefore the instantaneous value of the impressed current with the position of the contact brush that at the time of making the reading. If the brush angle is now changed, P must be moved in order to bring the galvanometer FIG. 208. to zero once more, and this operation must be repeated for each angular position of the brush. For that portion of the current curve in which the current is flowing in a reversed direction through AB, P must be placed on the other side of Q from that shown in order to obtain a balance. The pointer F does not bear continuously on the chart, but is struck against it by means of a bar, and thus makes a dot for each reading. When the lever that operates the bar is being returned to its first position, it works a ratchet that rotates the paper drum the proper distance ahead, and at the same time closes a circuit that energizes an electromagnet forming part of the contact maker, which in that MISCELLANEOUS DETERMINATIONS. 261 way has its contact brush advanced a corresponding amount, leaving everything ready for the next reading. The operation is therefore reduced to the simple act of moving the contact along until the galvanometer shows no deflection, raising and lowering a lever, and repeating. It is claimed that twenty points a minute can be printed by an experienced op- erator. The curve tracer is shown in Fig. 208. The crank at the right is turned to cause the contact P to travel along its wire, FlG. 209. and the lever at the left is the one used for printing, etc. The contact maker is shown in Fig. 209. Instead of using a potentiometer method, the instantaneous values of a fluctuating current at various points on the curve may be satisfactorily determined with the aid of a contact maker, a condenser, and a galvanometer. Referring to Fig. 210, the E.M.F. at the instant of contact is used to charge the condenser C of known capacity. Subse- quently the key JVis depressed, and the deflection of the gal- vanometer G- noted. The throw of the galvanometer is of course proportional to the condenser charge, and the latter to the charging E.M.F., so that the throws are proportional to the instantaneous potentials at the different positions of the contact brush. The Blondel contactor shown in Fig. 211 simplifies making this test. An inspection of the figure will show that if the disk D rotates in synchronism with the source of supply, contact is first made so that the condenser is charged by the E.M.F. at the point of rotation of the armature determined by the setting 262 ELECTRIC AND MAGNETIC MEASUREMENTS. of the brush, and that the condenser is immediately afterward discharged through the galvanometer. The impulses thus sent FIG. 210. follow one another with such rapidity that the galvanometer deflection becomes a steady one, and there is therefore nothing FIG. 211. to do but set the contact maker at different angles, and observe the deflections due to each in order to obtain the relative values of the ordinates at different points on the curve. MISCELLANEOUS DETERMINA TIONS. 263 Duddell Oscillograph. This instrument, illustrated by Fig. 212, is one in which one or more strips of conducting material traversed by the currents whose wave forms are to be determined are placed in an ex- tremely powerful magnetic field. The latter is furnished by a circular electromagnet having its poles shaped so as to give a very nar- row and intense field, and energized by several separate sets of coils, in order that by intercon- necting them in different ways the necessary ex- citing current may be obtained from circuits of different E.M.F.'s. In the apparatus illustrated there are three mirrors similar to those used in ordinary galvanometers, but smaller and lighter. One is stationary and furnishes a reference line. Each of the other two is attached to a pair of metal strips electrically connected at their lower extremities, and held in tension by the adjust- able spring arrangement shown projecting above the rest of the instrument. The path of the current is up one and down the other strip of a pair in each case. Owing to the tension of the strips the time required for a complete oscillation of a mirror is exceedingly small, namely, about .0001 second. When current is sent through either of the pair of strips, the reaction between that current and the field causes the attached mirror to deflect an amount 264 ELECTRIC AND MAGNETIC MEASUREMENTS. proportional to the current strength, and because the period of vibration is so small, the mirror position may continuously vary with a changing current strength, and follow it exactly. If the beam of light from the mirror were simply projected on a trans- lucent scale plate, the visible result would be merely a straight luminous band on the plate. When, however, the light beam is first thrown on a mirror that is oscillated by a cam synchron- ously driven, and whose axis is at right angles to that of the oscillograph, the ray traces on the surface to which it is re- flected, a curve which is, of course, the current curve. Owing to the rapidity with which the successive values in each curve are repeated and follow one another, persistence of vision causes the observer to see on the screen a curve which is the current curve. As the fixed mirror shows a straight line under the same conditions, we have all the information that is necessary in order to be able to observe the character of any current. Where records of this are to be kept, it is a simple matter to substitute a photographic plate for the screen. The object in having two sets of strips each with its attached mirror is to enable one instrument to show on a scale or record on photographic paper, simultaneously, the varying values of both the potential and current curves of any circuit. This form is called the " Double Oscillograph." HotMiss Oscillograph. In this instrument the stationary magnetic field is furnished by a powerful laminated permanent magnet, and instead of having movable strips through which the current flows, station- ary coils are provided inside of which again there are located minute soft iron needles suspended by quartz fibers. It is plain that this instrument is merely a special form of Thompson gal- vanometer, just as the Duddell oscillograph is merely a special form of d'Arsonval galvanometer. The dimensions of the movable iron needles in the Hotchkiss device are so small that the period of oscillation of the systems formed of these and their respective mirrors is about the same as the moving system of the Duddell device, that is, .0001 second. MISCELLANEOUS DETERMINATIONS. 265 One of the double oscillographs of this pattern is shown in plan and elevation by Fig. 213, the two moving systems being, as shown, in two independent magnetic fields instead of one common one. The rectilinear deflections of the mirrors are translated into curves showing the current strength variations, by using a synchronous motor driven mirror, as in the Duddell oscillograph. FREQUENCY METERS. Hartmann and Braun Frequency Meters. If an electromagnet be excited by an alternating current, and a tuning fork is presented to one pole of this magnet, the FIG. 213= successive attractions will set the tuning fork in vibration if the period of the fork is the same as that of the alternations, but the fork will not respond if this sympathy does not exist. The Hartmann and Braun frequency meter takes advantage of this fact. Referring to Fig. 214, showing a switchboard pattern of such a device, the twelve white rectangular patches appearirg in the two openings cut in the dial plate are the ends of steel strips or reeds bent over at right angles to the length of the strips proper and painted white to make them more conspicuous. Opposite each reed there will be noticed a numeral, 100.5, 101, 266 ELECTRIC AND MAGNETIC MEASUREMENTS. 101.5, etc., these being their respective vibration rates in alter- nations per second. Between the two rows of reeds is a lami- nated core electromagnet (not visible in the illustration) through whose windings is passed the alternating current whose fre- quency is to be measured. Evidently now if, as shown by the cut, the end of reed 98.5 vibrates over its full amplitude, the ninety-eight and ninety-nine reeds at the same time vibrating slightly, the current impulses follow one another at intervals corresponding to the vibration period of reed 98.5, that is to say its frequency is 98.5 alternations per second. Instead of visually noting which of a series of reeds of differ- ent periods is vibrating over a maximum amplitude, the accous- FIG. 214. tic properties of such strips may be utilized, provided that their rate is one giving a note that is audible to the human ear, namely between fifty and one hundred and fifty vibrations per second. A Hartmann and Brauii instrument of this kind, with its outer casing removed to show the arrangement of the mechanism, is illustrated in Fig. 215. The various reeds, in this case of peri- ods from 79 to 110 inclusive, are arranged on a circular frame- work which may be rotated by means of the central handle so as to successively present them to the magnet system. This system is composed of two magnets which when brought MISCELLANEOUS DETERMINATIONS. 267 together by means of the handles shown act as one. The double magnet arrangement is convenient in that, after the fre- quency of the circuit under test has been determined by rotating the central button until a note of maximum volume is heard, the magnets may be separated and the otherwise continuous sound which might De annoying, stopped. They still perform a useful service, however, as if the fre- quency of the circuit should either increase or decrease, one or the other of the magnets would set its corresponding reed in vibration and the note then heard serves as a warning of the change. In both the visual and acoustic types of meters the range of FIG. 215. measurement may be doubled, or rather each reed may be made to respond to a frequency double that of its normal one by add- ing either a few turns of direct current exciting winding or by inserting a permanent magnet to polarize the reeds. This follows, as a non-polarized strip is evidently attracted by each current impulse irrespective of direction of the alternating current flow, whereas if a strip be polarized magnetically the current flow in one direction attracts and that in the reverse direction repels it, and there is hence required double the original frequency to give the same number of attractive efforts. 268 ELECTRIC AND MAGNETIC MEASUREMENTS. The accuracy of these instruments is extremely good, and their simplicity and the absence of what in the accepted sense of the term are moving parts commends them for general ser- vice. /Schmidt Frequency Meter. Another acoustic device for measuring the frequency of alternating currents is that due to K. E. F. Schmidt. In it the current under investigation is passed through a telephone receiver and the diaphragm of that receiver placed before the open end of a tube about one inch distant there- from. The tube is about one inch in diameter and two or three feet long, and has within it a piston which may be moved backward and forward by means of a handle so as to vary the effective tube length. The vibrations of the receiver diaphragm tend to set the air imprisoned in the tube into vibration also, and if the piston is moved in and out, a position can be found where the tone emitted by the tube is of a maximum volume. The vibration periods of the diaphragm and the air column are then alike, and hence the frequency may be read off directly from a scale properly marked on the piston rod. Manzetti Frequency Meter. In this instrument there is a moving system which consists of a copper disk mounted rigidly on the same axis with a parallel- epiped of laminated iron. This element is either pivoted or carried by a quartz fiber, and the copper and iron used therein are acted upon by separate sets of coils. The two sets of coils are connected across the circuit with a resistance in series with each pair. When current flows, the turning effort exerted on the iron is independent of the frequency, while in the copper disk it is a function of the frequency. If, therefore, the two sets of coils are adjusted so that at the standard frequency the torques exerted by them are equal and opposite, there will, of course, be no deflection, but if the frequency changes, a deflec- tion will be produced because of the different torque then exerted by the copper disk. This torque can be measured either on the dynamometer principle mentioned on page 165, or may be used to urge a needle over an appropriate scale against a constantly increasing spring pressure. In the latter event the scale may be calibrated so as to indicate frequencies directly. MISCELLANEOUS DETERMINATIONS. 269 WestingJiouse Frequency Indicator. This instrument is illustrated in Fig. 216, and consists of two voltmeter movements so connected together mechanically that they tend to move the pointer in opposite directions. In series with one of the movements there is a non-inductive resistance, and in series with the other, a resistance that is highly inductive. If the frequency changes, the torque exerted by the two wind- ings will therefore become unbalanced, that of the inductive winding being relatively decreased, and if, as is the case, the construction of the apparatus is such that when the needle swings in either direction, the torque of the member tending to swing it in opposite direction is increased, it will evidently move until the two forces are again balanced. The scale is empirically graduated by passing currents of known frequency through the device and marking on the scale the different posi- tions assumed by the needle. The indications of these instru- ments are influenced by wave form as well as frequency, and they are hence correct only on the wave form for which they are adjusted. PHASE INDICATORS. Two alternating currents of like frequency are said to differ in phase when they do not simultaneously attain their respec- tive maximum positive, maximum negative, and zero values. The difference in phase is usually expressed in terms of the cosine of the angle between the two radii passing through the corresponding zero values, when the circumference of a circle whose perimeter is one wave length is used as the refer- ence line. This expression for phase difference is rigorously correct only when the currents are sinusoidal, and not, as is frequently the case in practice, when they are of different wave forms. FIG. 216. 270 ELECTRIC AND MAGNETIC MEASUREMENTS. Assuming sine waves, we would have in an alternating current circuit in which there is a difference in phase between the potential and current curves, the expression P = E I cos < in which E and / are the effective potential and current as measured by a voltmeter and ammeter of the static, hot wire, or electromagnetic type before- described, and P is the power. Phase meters are instruments for indicating the value of the angle <. Voltmeter, Ammeter, and Wattmeter Method. If the difference in* phase between the current and potential curves in an alternating current circuit is desired, one way to determine it is to use a wattmeter, and in addition to insert a voltmeter and an ammeter in the line. If all three readings are observed simultaneously, the cosine of the angle of lag may be calculated from the formula P = E I cos $ mentioned above, all of the factors with the exception of cos being known from the observation. Oscillograph Method. The double oscillographs described on page 264 may be used to determine the difference in phase between two alternating currents, by passing one through one of the movable elements of this apparatus and the other through the other. If the resultant figures are thrown on a translucent plate or are photo- graphed, two curves will appear together with the zero or reference line made by the fixed mirror, and the difference in phase can be scaled off therefrom. Oscillographs are but seldom available, however, so that this method is in very restricted use. Dobrowolsky Phase Indicator. This is an instrument in which a pointer sweeping over a graduated scale shows directly the difference in phase between two currents. Referring to Fig. 217, the movable element to which the pointer is attached is a disk of soft iron pivoted at its center and having its motion opposed by a volute spring. If the current through the two sets of windings shown as sur- rounding the disk at right angles to one another are in phase, no force will be exerted to rotate the disk. If, however, a MISCELLANEOUS DETERMINATIONS. 271 FIG. 217. phase difference exists, there is set up a rotary magnetic field, which in turn exerts a torque on the disk and tends to turn it. If the changes in strength of one current lag behind those of the other, the torque will be in one direction, and if vice versa the needle will be oppositely rotated. The instrument, after being calibrated with known phase differences, will therefore indicate not only the difference in phase, but which current is leading and which is lagging. If the instrument is being used on a circuit in which both the frequency and the effective potential are constant, the scale graduation may be made to show either the effective amperage or the wattless current that is, the component of the total cur- rent that is not effective in doing work flowing through it. An instrument so graduated is frequently convenient for use in central stations. Hartmann and Braun Phase Indicator. This instrument is somewhat similar to an indicating watt- meter, having a stationary coil through which the whole current to be measured is passed. The movable element, however, instead of consisting of but one fine wire coil, consists of two such mounted with their planes at right angles, and supported above and below by pivots. Current is led into and out of these windings through flexible silver strips so fine that no appreciable force prevents the needle attached to the coil pair from assuming any position within the limit of its travel. One of the instruments is shown in Fig. 218. In series with one of the two movable coils there is placed a non-inductive resistance, and the other coil has in series with it a highly inductive resistance, as is indicated by the two spools mounted on the transformer-like core. The non-inductive resis- tance and its spool are connected in parallel with the inductive resistance and its spool, a non-inductive resistance being placed 272 ELECTRIC AND MAGNETIC MEASUREMENTS. in series with the pair to cut down the applied potential. Owing to the presence of an inductance in one coil circuit and the fact that there is none in the other, the currents in the two differ in phase by ninety degrees. These displaced currents set up a rotary field, which in turn is located within the influence of the field due to the current through the stationary winding. When, therefore, the current through the series coil differs in phase from that flowing through the potential coils by a given .amount, the potential coils will assume one fixed position where the rotative effort is zero. When the phase difference between two currents changes, however, the angle of the double FIG. 218. coil movable element relative to the fixed one must change also. The scale over which the needle of this instrument swings may therefore be graduated empirically to indicate phase difference. It should be noted that while this form of device is inde- pendent of the amount of current flowing and of the E.M.F. applied, it is dependent on the frequency and must be specially calibrated for each frequency, if correct results are to be had. SYNCHRONISM INDICATORS. In order that two sources of alternating current may be con- nected in parallel so as to jointly supply current to any given MISCELLANEO US DETERMINA TIONS. 273 circuit, it is not only desirable but in. many instances absolutely necessary, that some device be employed which will indicate when the current furnished by the source about to be added is in synchronism with the one already delivering current, in order that it may be connected at that time. If it were coupled in when the currents are out of phase, an interchange of current between the sources would ensue, which current may be so large as to cause disastrous results. Lamp Synchronizers. The simplest form of apparatus for indicating synchronism between two sources of alternating current is shown in Fig. 219. Here 6r and Gr r are the sources, T and T f transformers energized by them, and L and L f incandescent lamps. It will FIG. 219. be seen that the secondary windings of the transformers are connected in series. If, now, the currents from 6r and 6r' are in phase, the current impulses of the transformer secondaries evidently increase in value simultaneously, and if they are oppo- site in direction, no current will flow through the lamps and these will remain dark. Should there be a difference of phase, some current will flow in the lamp circuit, and this will be a maximum when the phases are 180 degrees apart; that is to say, when the currents of the two secondaries are assisting each other. Hence, if 6r is a machine already running and G* is one to be thrown in, the lamps will be illuminated and extinguished in rapid succession when Gr f is first started, and these successive periods of light and darkness will succeed each other with decreasing frequency as the speed of rotation of & rises until its 274 ELECTRIC AND MAGNETIC MEASUREMENTS. speed is exactly that of 6r and the current delivered thereby in phase therewith, at which time the lamps will remain dark. The operation of connections in parallel may then be accom- plished by closing an appropriate switch. By reversing the connections of the secondary of either one of the two trans- formers, the lamps will be burning at full brilliancy when syn- chronism is attained, instead of being extinguished' at that time. The first method is, however, preferable, as after watching lamps during the time at which 6r''s speed is being raised to its desired value the eye becomes fatigued, and it is more difficult to determine the instant of maximum brilliancy than that of complete darkness. Voltmeter Method. If in the above plan an alternating current voltmeter is sub- stituted for the two lamps its indications can be used to show the attainment of synchronism with greater accuracy than is possible with the lamps. As alternating-current voltmeters are of less sensibility near zero than in the working range of the scale, or in other words, as the deflection per unit of potential difference is less near zero than up the scale, it is advisable to use the second scheme of connections mentioned ; that is, the one in which the transformer secondaries are connected, so that their E.M.F.'s assist each other when synchronism is attained. In using a voltmeter its indications are merely observed until the needle is practically at rest at a maximum indication, whereupon the incoming machine is coupled in as before. The Mutter Synchronism Indicator. For commercial purposes it is desirable that the synchronizing apparatus shall show not only when synchronism between the incoming generator and the one or ones already supplying cur- rent is reached, but that it should show whether the incoming machine has too high or too low a frequency, that is, whether it is running too fast or too slow, as this enables the attendant to regulate the speed accordingly. An instrument fulfilling these requirements is shown in Fig. 220. As illustrated, it is arranged for use on a three-phase cir- cuit. An outer ring of laminated iron is wound about with wire MISCELLANEOUS DETERMINATIONS. 275 and has leads tapped into its convolutions at three equidistant points. These three terminals are attached to the bus-bars. Within this ring there is a similar one provided with a shaft on which it rotates and having three collector rings so that electri- cal contact may be made through brushes to three leads tapped into its winding at equidistant points, as in the case of the stationary ring. The brush terminals are connected to those of the incoming machine. The rotating element carries a target or pointer, so that its movement may readily be discerned. The electrical connections are made such that the rotary magnetic fields set up by each of the rings rotate in the same direction. When, therefore, the frequency of the potentials supplied to the FIG. 220. two windings is the same, the fields rotate in the same direction with the same velocity and no turning effort is exerted on the inner member. When the two are not in phase, however, turn- ing effort exists, and this will rotate the target in one direction if the frequency in the inner ring is greater than that in the outer, and vice versa if it is less. A stationary target secured to the outer ring is used as a reference mark, the two currents being of the same frequency and also in phase when the r^ tating disk masks it. It should be noted that the movable disk will always remain stationary when the frequencies are the same, but that its vertical position is assumed only when the currents are also in phase. At other times the angle between the fixed 276 ELECTRIC AND MAGNETIC MEASUREMENTS. and rotary targets is a measure of the phase angle between the currents. Lincoln Synchronizer. In this instrument, illustrated in Fig. 221, the position of a pointer relative to a fixed mark on the dial over which it rotates shows the phase relations and difference in frequency between two alternating currents just as does the Muller instrument just described. The principle of operation is, however, somewhat different. Referring to Fig. 222, if within the fixed coil F there is mounted on the freely movable shaft C a coil A, and an alter- FlG. 221. nating current is passed through A and .Fin series, A will rotate until it takes up the position shown parallel to the plane of F. If the connections between A and F are reversed, or, which amounts to the same thing, the two are fed by currents of like frequencies differing in phase by 180 degrees, A will rotate 180 degrees. The force tending to carry the coil A into position is, under the conditions laid down, a maximum when A and F are parallel and it is zero when they are at right angles. An instrument with a single coil would thus have a " dead center " position, which would not be admissible. MISCELLANEOUS DETERMINATIONS. 277 If, however, a second coil B be added, rigidly secured at right angles to the coil A and, by suitable means, the current in B is made to differ in phase from that in A by the same angle of 90 degrees, B will be in a position where it exerts a maximum torque when A is at its zero torque position. Hence, if there existed a difference in phase of 90 degrees between the currents in A and F, A would always come to rest at right angles to F, and if the currents in the two were in phase, A would turn until it was parallel to F. For intermediate phase differences, A would assume intermediate angles, and hence a pointer attached to A would show these differences on a dial. In the actual instrument the coil F and the coils A and B are wound on laminated iron cores, forming a structure like a small motor. The difference of 90 degrees in phase between the currents in A and B is produced by putting a highly inductive resist- ance in series with one and a non-inductive re- sistance in series with the other. The currents whose phase and fre- quency relati ons are sought are, of course, led, the one through the windings of F and the other through the coils A and B with their respective resistances. As in the case of the Miiller instrument, the Lincoln synchro- nizer exerts a considerable torque, so that it is possible to use a robust construction with heavy bearings without introducing frictional errors. SPEED INDICATORS. Using a Magneto and a Voltmeter. From the law of dynamo-electric machines the potential de- livered by a given armature rotating in a magnetic field of con- stant strength is directly proportional to the speed of rotation' of the armature. In other words, if we take a small dynamo whose field is supplied by permanent magnets, the voltage at its brushes varies directly with the speed and can be used as a measure of that speed. Fig. 223 shows such a magneto adapted 278 ELECTRIC AND MAGNETIC MEASUREMENTS. to be belt driven by 'the shaft whose speed is to be measured. The revolution indicator used with it is simply a voltmeter, usually of one of the commercial types described on page 193 et seq, whose scale has been arbitrarily calibrated to show revo- lutions, by noting the position of the needle when the magneto is driven at various known speeds. This method of speed indication has the advantage that the indicating element may be placed at any reasonable distance from the shaft whose speed is being observed, and that* the rate of rotation is .shown at each instant on a scale which may be.- of considerable length so that close readings can be had. It is also possible to have two or more indicating stations with the FIG. 223. one magneto, as this involves only the addition of another volt- meter. Direction of rotation can be shown also by using a per- manent magnet type voltmeter having the zero in the center of the scale, in which event the needle will deflect in one direction for a given direction of rotation of the magneto, and in the other for the other. Eddy Current Revolution Indicator. In Fig. 224 d is a copper cylinder mounted on a shaft run- ning through its axis and driven by a belt from the shaft whose speed is to be measured. Pivoted co-axially within the cylinder MISCELLANEO US DE TERM IN A TIONS. 279 is a soft iron needle, n, s, carrying an index I, that sweeps over a graduated scale. The cylinder is embraced by the polar ex- tremities of a permanent magnet $, N. When the cylinder d is set in rotation, eddy currents are generated therein as it cuts the lines of force of the permanent magnet, and these currents react on the soft iron needle and tend to carry it along. The tendency of n, *, to rotate is opposed by the directive force ex- erted on it by the permanent magnet, the latter acting in this respect like the magnet in the Ayrton and Perry instrument mentioned on page 152. The scale is graduated empirically as in the case of the magneto and voltmeter combination above named. Changes in strength of the field supplied by the permanent magnet affect the accuracy of the indications but slightly, be- cause as this changes, the eddy currents in d changing likewise, the restraining force on the needle, n, s, changes also. Experi- ments show that the strength of the permanent magnet; may decrease as much as twenty per cent without causing an error in indications greater than one per cent. Several modifications of this form of speed indicator have been proposed. 280 ELECTRIC AND MAGNETIC MEASUREMENTS. Scholkmann Speed Indicator. In this device a small inductor alternator is driven by the shaft whose speed of rotation is to be measured. The moving part is a simple structure of laminated iron and the stationary portion has two sets of windings wound on alternate poles. One of the sets is energized by any convenient source of direct current, such as a storage battery, and alternating currents are induced in the other by the rotating core. The current thus set up is carried through wires to the indicating instrument, which consists of a small two-phase motor. In series with one of the windings of this motor there is placed an inductance so as to cause a phase displacement and give rise to a rotary field which in turn exerts a torque on the armature, the latter being an aluminum cylinder which is rotated against the tension of a volute spring. A pointer carried by the cylinder moves over * a prop- erly divided scale which shows the speed in revolutions directly. As the indications of the indicator are dependent on the fre- quency and not on the potential of the current supplied to it by the generator, it is not necessary to have the direct current source for energizing the latter of constant E.M.F. Stroboscopic Methods. If an alternating current is used to energize a source of light, such as an arc lamp or an incandescent lamp with a thin fila- ment, the intensity of the illumination is constantly varying as the strength of the current varies. This phenomenon is not ordinarily detected by the eye, because on commercial circuits the frequency with which the alternations succeed each other is greater than the eye can detect, whence, because of the persist- ence of vision, the resulting illumination appears uniform. These successive variations in illumination may, however, be used in measuring speed of rotation if the number of alternations of the supply circuit is known. A conspicuous mark, such as a streak of white paint, is made on the periphery of a pulley on the shaft whose speed is to be taken, and this mark will appear to remain stationary when illuminated by an arc lamp fed by the current named if the number of alternations and revolutions are alike, as the illumination from the arc will be a maximum at the same angular position of the mark at each revolution. MISCELLANEOUS DETERMINATIONS. 281 Should the apparatus whose speed is being measured be driven from a source that is not rotating in synchronism with the alter- nations, the times of equal illumination will occur at varying angular positions of the mark, and the latter will therefore seem to the eye to rotate at a rate that increases as the difference in speed between the two sources increases. The source of illumination in stroboscopic methods of meas- uring speeds is often a spark from the secondary winding of an induction coil whose primary is excited at known intervals, usually through a contact made by a tuning-fork whose period has been determined. TRANSFORMER TESTING. Efficiency. Transformers waste in themselves a certain amount of en- ergy, so that the ratio of the electrical input to the output is not unity. The losses are the sum of the following factors : in the primary winding, the PR loss, this being the energy re- quired to overcome the resistance of the primary winding ; in the secondary winding, a corresponding PR loss ; the loss due to the hysteresis of the iron forming the magnetic circuit ; and finally, the eddy current losses. The PR losses in both primary and secondary windings are easy of measurement. Direct current of the normal full ampere capacity of each winding may, for instance, be passed and the drop across the winding terminals simultaneously observed by using a low-reading voltmeter. The product of these values is, of course, PR in each case. Another way is to measure the re- sistance of each winding by any of the suitable methods outlined in the chapter on resistance measurements, and to multiply these values by the squares of the strengths of the currents which they are to carry. The sum of the hysteresis and eddy current losses can be measured indirectly by measuring the input and output of the transformer by indicating wattmeters, when the difference be- tween the indications, less the sum of the PR losses in the primary and secondary windings, gives the result. Another way is to pass full normal current through either the 282 ELECTRIC AND MAGNETIC MEASUREMENTS. primary or secondary winding, the secondary (or primary as the case may be) circuit remaining open at the same time, and in- serting a wattmeter in the energized circuit. The wattmeter reading gives the hysteresis and eddy current losses plus the primary (or secondary) PR loss. The latter is measured sep- arately, as already explained, and then deducted from the result. To have this test an accurate one, it is necessary to employ a wattmeter which will give a large scale deflection on a very low power factor, preferably one in which full scale is given with not over ten per cent of the maximum volt-ampere capacity. The instrument must also give accurate readings on these low- power factors, a requirement which excludes all types in which the angle between the fixed and movable coils is a variable, and practically limits the choice to true dynamometers in which a Wattmeter Transformer* r torsion head must be rotated manually to get a reading. The connections for the above test are given in Fig. 227. The method of testing above described is objectionable for very large transformers, as it calls for an amount of current suf- ficient to fully load the apparatus during the time that the test is in progress. Where it is not possible or advisable to make this heavy draught on the supply lines, Sumpner's method may be brought into play. To make this test, two identical transformers of the size to be tested are required, and there is needed also a third trans- former with a capacity sufficient to supply enough current to make up the sum of the losses of the two others, but whose efficiency is immaterial and need not be measured. Wattmeters and an ammeter all connected in circuit as shown in Fig. 228 are the instruments needed. The ammeter A 1 is not essential, and the same is the case with the voltmeter V, but these give MISCELLANEOUS DETERMINATIONS. 283 data of interest. From the connections it will be noted that the transformers are so connected that each supplies the other with current, the small transformer receiving enough current from the mains to add to the large transformer circuit, current sufficient to overcome the losses in the transformers A and B. When the test is made, the regulating resistance R is varied until the ammeter A shows that full current is flowing through the secondary windings. The ammeter and voltmeter in the pri- mary circuits should simultaneously show that the volume and potential of the current flowing in these is the normal maximum. The wattmeters IF and W will then give the desired information, the indications of W giving the sum of the iron losses in the two transformers, and W the copper losses of the two plus those in the leads and in the wattmeter W and ammeter A. Transformer Insulation Test. One of the important tests to which every transformer should be subjected before it is placed in circuit is that to determine Wattmeter W FlG. 228, the insulation resistance of its windings. To have the results of any value, it is necessary that they be made with high ap- plied potentials, as it is found that the behavior of the insulating material is entirely different under high electrical stresses than under low ones. The best test is the rough and ready one of using a source having a potential at least double that of the highest voltage to which the device will be connected in use, and then with this potential testing to see whether a breakdown can be made through the primary insulation to the core, through the secondary insulation to the core, or from the primary to the 284 ELECTRIC AND MAGNETIC MEASUREMENTS. secondary winding. In an electric-lighting plant where but one potential is in use, the testing potential is easily obtained by connecting in series the fine wire windings of two or three transformers whose coarse wire windings are connected in par- allel to the low-tension mains. For general testing work a regular step-up transformer with a spark gauge is preferable. Transformer Polarity. If two or more transformers are to be used, connected to- gether in series or parallel, it is necessary to know the relative instantaneous directions of the current flow in each, in order that they may not oppose each other in the first case or short circuit through each other in the second. For making this polarity test the most elementary and in the majority of cases the most satisfactory method is, in the case where the \levices are connected in series, to make this series connection at ran- dom, and then attach a voltmeter to the free terminals. If then the connections are arranged so that the potentials assist each other, the voltmeter will show double the voltage indicated by the secondary of a single similar transformer, while if they are connected in opposition the voltage reading will be zero. Where the secondaries are to be connected in parallel this may also be done at random, fuses being inserted between them. If when the primary circuits are closed the fuses blow, the con- nections are such that the transformers are short circuited on each other. If they remain intact the coils are properly con- nected in parallel. In the latter test the capacity of the fuses should be from two to five per cent of the full load capacity of the transformer windings. It is necessary to allow a margin as transformers are never exactly alike, and there is always a small interchange of current even with windings properly paralleled. G-eneral. In all transformer tests it is advisable to place in series with the circuit through which the exciting current is passed, a fuse rated to blow at about 50 per cent greater current than the maximum full load current desired. This precaution is neces- sary, because when current was last passed through the trans- former it has, except in 'the very rare instance in which it was MISCELLANEOUS DETERMINATIONS. 285 interrupted as the current curve passed through the zero value, been cut off when the iron core was magnetized in one or the other direction. If, when current is again thrown on, the direction of the initial impulse is such that the residual magnet- ism of the core tends to assist instead of oppose the initial rise in current strength in the transformer winding, the current value may rise to an amount so greatly in excess of the capacity of the measuring instruments that the needles of the latter will be bent or the movements otherwise damaged. The fuse protec- tion will generally save the instruments from this harm. TESTING INTEGRATING METERS. Integrating, or as they are erroneously but more commonly termed, " recording " instruments, used to measure the amount of power supplied to a consumer, form a class of electrical measuring apparatus that for various reasons requires frequent checking to determine whether or not the accuracy is still within permissible limits. Test with Indicating Instruments. A common method of testing an integrating meter consists in connecting in circuit with it an instrument of the indicating pattern and then putting on a steady load for a length of time measured accurately by a stop-watch. The integrating instru- ment is supposed to show on its dials the ampere hours (or watt hours, as the case may be), and if in calibration its indica- tions should of course correspond with the ampere (or watt) hour rate figured from the readings of the indicating apparatus and the watch. The meter dials are seldom sufficiently sub- divided to allow of an accurate reading of its indication unless the test is extended over a period of hours. As in practically all of them, however, the motion of the moving element is reduced through a train of gears, it is possible to shorten the time of the test by observing the number of revolutions made by the rotating element if the gear reduction ratio is known. A paint mark on the rotating part makes it possible to count the revolutions accurately. Tests made with portable indicating meters have the great advantage that the integrating meter may thus be checked in place on the consumers' premises, the load being adjusted by 286 ELECTRIC AND MAGNETIC MEASUREMENTS. switching on the proper number of lamps. That the meter is erected at the point where it is to be when doing its normal work is of importance for accuracy, as well as convenience, since all such devices are influenced to a considerable extent by mechanical vibrations, and a meter which would show up as correct in a test made in a quiet laboratory might register wrongly when erected on the consumers' premises. Vibration causes the moving element to jump up and down on its pivot, and the friction in this case is well known to be less than the friction existing where no vibration is present. The error is, of course, in favor of the supply company in so far as the readings are apt to be, if anything, high, but on the other hand it is approaching too closely to the comic-paper gas-meter standard if the appara- tus is found to register current when none is being drawn by the consumer. v The test in place with indicating instruments, while allowing for some of the peculiar conditions in each installation, is not always feasible. For instance, in many cases the load on the meter is not steady at a given point for long intervals, but with motor loads, and particularly when these motors are driving elevators, is fluctuating violently at frequent and irregular intervals. To follow the ampere fluctuations with an ammeter or the watt fluctuations with an indicating wattmeter and simul- taneously assign the correct duration period to each by referring to a stop-watch, is practically impossible. In this event if the current is continuous it is advisable to resort to the following scheme. Testing with Electrolytic Meter. The standard in this case becomes a voltammeter, usually of the copper pattern described on page 14. By comparing the am- pere hours as shown by the gain in weight of the cathode after being in circuit for any desired period with the ampere hours shown by the dial of the integrating instrument, the accuracy of the latter can be determined offhand. As an electrolytic meter shows the product of the true average current by the time that it has been in circuit, results of a high degree of accuracy may be obtained with a fair chemical balance and a very ordinary timepiece if the period over which the test extends is made reasonably long. MISCELLANEOUS DETERMINATIONS. 287 If the integrating meter shows watt hours instead of ampere hours a voltmeter is needed in addition to the voltammeter, and from its indications it is necessary to derive some mean volt value which will fairly represent the mean voltage during the test. The volt approximation may be made very closely, as its extreme fluctuations are usually but a few per cent, so that the average can be ascertained to a fraction of a per cent. Still another method involves the use of a regulation motor type integrating meter as the standard, this one being con- nected in circuit with the one under test, so that the attached load is simultaneously measured by both. The readings of the two must obviously agree if the calibration of the tested one is correct. The meter used as the standard is usually specially constructed so as to obtain maximum accuracy. The gear train and dials of the ordinary meter are omitted to reduce the fric- tional errors, and their place is taken by a pointer attached directly to the shaft of the rotating element so that its revolu- tion may be closely observed. The bearings are often made of diamond instead of sapphire, and particular care is observed in constructing the pivots and adjusting the calibration. Such a standard must itself be checked from time to time by comparison with an indicating instrument and a stop-watch, but this may be attended to at the station, where the facilities for such work are better than on the consumers' premises. CHAPTER XII. THE LOCATION OF FAULTS. IN a great many cases electrical measurements may be made to locate electrical faults, which measurements, while involving principles that have been mentioned before in this volume, appear for one reason or another somewhat out of place in the chapter setting forth their said principles. The author therefore resorts to the subterfuge of the present " miscellaneous " chapter to describe and discuss the more com- mon and useful of the methods which can be included itf this convenient category. While it gives a by no means complete list of the numerous expedients employed in various of the more specialized methods of testing, it is thought that the descriptions taken in connec- tion with what has gone before will prove of assistance in figur- ing out ways and means of locating cases of electrical trouble that seem to be somewhat out of the usual run. One of the most common and often at the same time the most difficult electrical tests that has to be made is for the location of a fault in a conductor. Such faults may for our present purposes conveniently be divided into two classes, the first being grounds and short circuits, and the second complete breaks or open circuits. LOCATION OF CROSSES AND GBOUNDSo If the fault in a grounded or crossed conductor were always of practically infinitely low resistance that is to say, if it were a " dead " ground or short circuit its location could easily be detected by measuring the resistance from the point of test and back again through the ground or through the other conductor affected, by any of the Wheatstone bridge methods described in the chapter on resistance measurements. Unfortunately, how- ever, it is seldom the case that this condition exists, and tests giving results that are independent of the resistance of the THE LOCATION OF FAULTS. 289 return circuits and at the point of trouble are therefore necessary. Another very frequent source of inconvenience and error lies in the fact that at the fault there may exist an E.M.F. due in some instances to the contact potential difference between the faulty conductor and that on which it is grounded, or more commonly, with ground return circuits such as telegraph lines, to foreign earth currents. In the majority of cases it is possible to obtain electrical access to both ends of the faulty conductor. If this is a cable coiled up in a tank we have the simplest case, as the two ends will, of course, be close together and may be carried direct to the measuring apparatus. Where the fault is on a line wire or cable it is almost invariably the case that another parallel con- ductor that is not faulty is available, and if this is connected to the faulty one at the distant station a loop is formed whose terminals are adjacent in the testing station. Tests which require that access be had to both terminals of a conductor so formed are called " loop tests," the most prominent ones being the following : The Murray Lop Test. Referring to Fig. 229, _Z?, P, E is the looped conductor, B, P being the outgoing wire having a fault at /, and P, E the return wire joined to the former at the distant station P. This loop is used to form one side of a Wheatetone bridge, the two other arms of the bridge, b and d, being formed by adjustable resistances such as those in an ordinary post-office pattern test- ing set. The galvanometer G- and battery 8 are attached as shown, suitable keys K l and K 2 being inserted in the respective circuits. Then, as is the case in the ordinary Wheatstone bridge, a resistance in the battery circuit introduces no error in the result, requiring only increased battery power to get the same sensibility. This resistance in the Murray test is that offered by the earth between the battery terminals and the fault plus that of the fault itself. In making measurements, the resistances in b and d are first made equal and the galvanometer key K 2 then closed, whereupon, if an earth current is present the galvanometer will deflect a certain amount, which should be noted. The ratio of the resistance b to d is then altered until an adjustment is reached such that the galvanometer shows the 290 ELECTRIC AND MAGNETIC MEASUREMENTS. same deflection, whether K 2 is alone depressed, or both K 1 and K 2 are depressed. If the resistance of the circuit B, P, E, which we will call L, is known, we then have from the law governing the Wheatstone bridge, x=- The resistance of B,P,E o -f- d is measured by a Wheatstone bridge in the ordinaiy way. It is advisable to have the key K 1 of a special reversing type, so that when one of its buttons is depressed, current is sent through the circuit J., !S, earth, .F, in one direction, and when the other is depressed, in the reverse direction. This will Ground, FIG. 229. sometimes give slightly different results for the two connections, in which event it is usually safe to assume that their mean is the correct value. If the results differ widely, the contacts should be examined and cleaned, and the apparatus should be more carefully insulated from the ground. The test should then be repeated until concordant results are obtained. Ohmmeter Test. In the Murray loop, as in all other Wheatstone bridge tests, the position of the galvanometer and battery in the network of conductors may be interchanged without affecting the results. THE LOCATION OF FAULTS. 291 The ohmmeter mentioned on page 107 may be used for this modification of the Murray test by making connections as shown in Fig. 230. As will be seen from this, the standard resistance coil forming one arm of a Wheatstone bridge in the apparatus is cut out of use by withdrawing the connecting plug and allowing it to hang free. The middle post is connected to ground, and the ends of the looped line wire are attached to the two outer posts. -The stylus is tapped along the wires forming the ratio arms of the bridge, as in finding a resistance, until a point of silence is reached, which point is of course an image of the point of trouble on the line. The latter can then be located by reference to the equally divided scales that come with the apparatus, and which show the result in percentage of the total line length in- cluded between the two posts. The result so found is, however, correct only when there is no difference of potential between the grounded wire and the grounded 'post on the ohmmeter, as if such exists, due to earth Ground' FIG. 230. currents or otherwise, the point of silence on the bridge wire is not the image of the fault, but a false one corresponding to the false result that would be obtained if, in the Murray method above, actual galvanometer zero were used instead of the false zero obtained on depressing the key K l alone. The human ear is unable to identify, with even the roughest accuracy, the loud- ness of the click emitted by the telephone receiver, and there- fore if the ohmmeter is to be successfully used for such fault location work, it must be provided with a galvanometer which can be switched in place of the telephone when making such readings, and the work done from a false zero, as in the ordinary Murray method. The Varley Loop Test. In this, as in the Murray test, the two ends of the faulty cable must be made accessible by forming a loop with it and a 292 ELECTRIC AND MAGNETIC MEASUREMENTS. good return conductor. The connections are then to be made as shown in Fig. 231, from which it will be seen that while the bridge arms, the galvanometer, and the battery are arranged as in the Murray test, a resistance, d, has been inserted between A and E. The arms a and 6, of constant value in this test, are usually made equal to one another, and d is adjustable and varied until the galvanometer shows the same deflection whether its key K 2 alone is closed or both it and K l are down at the b L a d same time. Under these circumstances x = b -f a In the ^VCuUjMA^J (rrouunds. FIG. 231. case assumed above, i.e., when b = a, this expression becomes L- d --5 In order to have this test work at all it is necessary that the fault should be on the wire that is connected to the variable resistance d, because if it is not no balance can be obtained. In connection with the Murray and Varley loop tests de- scribed above, the distinction between earth currents and those due to E.M.F.'s set up at the fault should be carefully borne in mind. Earth currents are possible only on lines a part of THE LOCATION OF FAULTS. 293 whose circuit is formed through the earth, as is the case of most telegraph and a few telephone installations. Contact E.M.F.'s at the break are, on the other hand, present both in ground return lines and in metallic circuits. As will be noted by care- ful reference to Figs. 229 and 231, a deflection of the galva- nometer will be given when its key is closed and that of the battery circuit left open only when an earth current exists, and it is therefore correct to use the false zero as a balancing point only with grounded circuits. Where earth currents are absent, false zeros should not be used at all, and if there is a galva- nometer deflection when the galvanometer key is closed and the battery key left open, it shows simply that there is leakage from the instrument and battery itself to ground. If this state of affairs exists, the leakage should be stopped by carefully clean- ing all dirt and moisture from the insulating surfaces, and if necessary, by interposing additional resistances in the shape of porcelain insulators. With all loop tests the accuracy is greatest with a high-resist- ance conductor. While telegraph and telephone lines have enough resistance to enable faults to be located with a sufficient degree of accuracy, such is unfortunately not the case with the heavy wires used in electric light plants. The errors are so large as to make the results perfectly useless, and recourse must therefore be had to other methods. Induction Method. This is one that, generally speaking, is possible with alter- nating-current circuits only. It consists in winding up of many turns of wire a coil that is made as large as possible con- sistent with portability, and is carried along by a couple of assistants over the faulty conductor with one of its flat sides parallel thereto. A telephone receiver is placed in the circuit of this " exploring coil," and as long as alternating current is flowing through the conductor, the current induced in the exploring winding will of course produce a loud humming noise in the receiver. Referring to Fig. 232, if the fault / is at B, the observer listening to the receiver when the exploring coil E is being carried along parallel to A, C, will hear a note until E has passed B . The terminal of the alternator supplying current to the good conductor must of course be grounded at 294 ELECTRIC AND MAGNETIC MEASUREMENTS. the generating station in order that current may flow back through the ground at the fault. This test is beautifully simple, but unfortunately not always applicable, especially under the conditions where buried alter- nating mains are most likely to be used, that is, in densely pop- ulated cities, as here numerous gas and other metallic pipes are usually present and the conductor may itself be inclosed in a lead sheathing, all of which so modifies the tone in the receiver that instead of there being an almost abrupt point of silence when the fault is reached, the noise simply decreases slightly, and it is very difficult to say just where this occurs. Compass Test. This simple and remarkably efficient test described by Mr. Stott in 1901 is available for the location of grounds not only in circuits which can be isolated while the measurement is be- Telephone Receiver B Ground Ground, FIG. 232. ing made, but, in the case of alternating-current systems, where the conductor is in use as well. It consists in sending through the faulty wire, the fault on it and back through the ground to the testing station a direct current of the highest convenient value. The direction of this continuous current is reversed at known and approximately equal intervals of, say, ten seconds, by means of a commutator that is driven either manually or by a small motor. Referring to Fig. 233, if the lower of the two conductors is grounded as shown, and if a periodically reversed direct current is being passed through the conductor, the ground, and back to the test station by the aid of the reversing commu- tator indicated in the figure, the needle of a pocket compass placed parallel to the faulty main, will be deflected to a position nearly at right angles to the wire in one direction THE LOCATION OF FAULTS. 295 until the continuous current is reversed, at which time it will jump and take up a position removed nearly 180 degrees from the first one. If the wire under test is an underground conductor, the compass needle can be laid on its covering at each successive manhole until one is found where these periodical reversals of deflection no longer exist. The ground is then of course be- tween the last point where the deflections were given and this one, and if the cable is tapped at the former, the point of trouble will usually be found there. In any event it has been located between two manholes, which is all that is usually required in practice, as if it exists in the intervening conductor, the cable must be pulled out of the ducts anyway in order to effect its desired repair. The alternating current flowing through the main B does not affect the compass needle appreciably, as the rate at which the alternations take place is so much greater than the period of oscillation of the needle, that the latter either does not move at Ground, Orownoi FIG . 233. all or else simply trembles slightly, and has a motion which is negligible as compared with that due to the passage of the con- tinuous test current. It is evidently impossible to make the same test with direct current in the mains J., B, as this causes a continued deflection of the needle in one direction, irrespective of any attempt to superimpose on it a reversed current. It is however possible in this case to substitute an exploring coil arid telephone receiver for the compass needle and an alternating- current generator for the direct-current source with its reversing commutator R, but the current delivered by the d c machine must be sufficiently smooth to avoid producing a confusing noise in the telephone receiver. The current delivered by a Thomson- Houston arc machine is an example of one that pulsates suf- ficiently to make this exploring coil test out of the question. 296 ELECTRIC AND MAGNETIC MEASUREMENTS. Fall of Potential Methods. An elegant method of locating a ground in a faulty conductor is diagrammatical ly illustrated in Fig. 234. In this the faulty conductor is the line B, D ; A, B being a length of good con- ductor connected in series with and preferably located parallel to B, I). A source of current S, usually a set of storage bat- teries, is used to cause a current to flow through the circuit, J., .B,/, G-, G- as shown, and an ammeter C is inserted in that cir- cuit so that it may be determined that the current strength is kept absolutely constant. If now we know the resistance of A, B, and take the drop in potential measured by a galvanometer or milli voltmeter across J., B, and B, D, respectively, the resistance of the faulty cable from Btof will be to the resist- B !? c "'-===- G Grotmd, Ground FIG. 234. ance of the good cable from A to B, as the deflection due to the potential drop between J5, D, is to the deflection given when the instrument terminals are connected to J., D. In order that the resistance of the galvanometer leads may not introduce an error, it is necessary to use either a galvanometer whose resist- ance is extremely high as compared with that of R and X in the figure, or else, which amounts to the same thing, to have it of such high sensibility that a large resistance may be inserted in its circuit. If a section of conductor running parallel to B, D, cannot be used as R, a low resistance can of course be used in its place, but this plan is not as good, as the temperature of the stretch X is unknown, and if it differs greatly from the assumed 70 Fahr., on which its resistance measurement is based, an error equal to that of the temperature coefficient of copper, that is, two tenths of a per cent per degree Fahr., will be introduced. As the resistance at the fault /is often variable, it is most con- THE LOCATION OF FAULTS. 297 venient to use two galvanometers connected to the points A, B, and B, D, respectively, both graduated in known fractions of a volt, and then observe their de- A B flections simulta- neously. If this ^^^^^^^^^^^^^^^^^^^^^g cannot be done, a single instru- FlG - 235 - ment and a switch for shifting the connections rapidly should be used, a careful watch being kept on the ammeter to be sure that the current has not changed, as on its having the same value during both readings depends the accuracy of the result. Location of Crosses. Crosses are simply the grounding of one conductor on another, and may be located in exactly the same way that grounds are located, as described above, if the wire with which the cross has been made is substituted for the earth circuit in the ground tests. The localization of crosses is usually a more simple test than with grounded circuits, as the question of earth currents is entirely eliminated, and E.M.F.'s at the point of contact are of less common occurrence. Location of Breaks. Where a conductor is actually broken, and the return circuit from the break is therefore of a resistance that is practically in- finitely high, we are confronted with a new set of conditions. Whether the conductor is an aerial one or whether it is a cable buried in the earth or submerged in water, it may be considered as one coating of a condenser, the dielectric being the insulation from the point of test to the break, and the other coating being the earth or the surrounding water, as the case may be. The capacity of the condenser so formed may be measured by any of the methods of capacity measurement mentioned in Chapter VIII, and if this capacity is compared with that of a neighboring good conductor whose length to the distant station B, Fig. 235, is known, the location of the fault /is given directly by the ratio of the capacities. Where no apparatus capable of measuring capacity in microfarads is available the fault may still be lo- cated by simple comparison of the capacity of A, f with that of 298 ELECTRIC AND MAGNETIC MEASUREMENTS. the good conductor A, B. The already much described ohmmeter can be used for this test to advantage, the connections being as in Fig. 236. In this test it is necessary that the potential ap- plied to the bridge wire terminals be an alternating one which may conveniently be obtained from the secondary of an induc- FlG. 236. tion coil. The point of silence on the bridge wire is then one which divides up the total bridge wire length into two sections which are to each other as the capacities of the broken and good conductors. This ohmmeter test can be used only under favorable condi- Telephone r^ r if i 1 I JS^ - 4 f gji ' 1 R - J fe ] 1 *=> <=> d> FIG. 237. tions, as the resistance of the slide wire is but small, and while it is without capacity has a small self-induction due to the fact that the wire forms a loop. A device for the location of breaks that THE LOCATION OF FAULTS. 299 depends on a somewhat different principle and which is appli- cable to a greater variety of cases is the Meyers break finder illustrated diagrammatically in Fig. 237 and in perspective in Fig. 238. In this the secondary of an induction coil wound as a long spool has its terminals attached to the ends of the faulty and good wires respectively, and a narrow primary coil winding is arranged to slide up and down along the secondary. Simple inspection of the figure will show that the primary may M FIG. 238. be moved to a position such that a telephone receiver connected across the secondary terminals will cease to emit a hum, and that if an index attached to the primary moves over a scale, the scale may be divided so that the ratio of the capacity of the good to the broken conductor and hence the ratio of the length of the good conductor to that of the faulty one up to the break will be shown directly. AKMATURE TESTING. One of the most common tests that has to be made under commercial conditions is the location of a fault in the armature of a generator or motor. The extent and nature of the discol- 300 ELECTRIC AND MAGNETIC MEASUREMENTS. oration of the commutator bars will sometimes give an indica- tion of the nature of the difficulty if the machine has been in operation, but the trouble may be more surely located by calling in the aid of measuring apparatus. Electrical faults in the windings of an armature consist either of a ground between the winding and the iron core, or of a wholly or partially short-circuited section, or of a section that is of high resistance or all-together opened. Testing for Grounds. The fact that a ground exists in an armature is easily deter- mined in a dozen different ways, one of the simplest being to FIG. 239. pass current from an outside source through an incandescent lamp in series with which there is placed the suspected arma- ture, one wire being attached to the shaft and the other to the commutator bars. If the lamp lights, there is of course elec- trical contact between the windings and the shaft. If this or any other method shows that a ground exists, it may be located as follows : Referring to Fig. 239, current is passed from the THE LOCATION OF FAULTS. 301 shaft through the ground and back to the commutator by means of conductors attached to one brush and to the shaft respec- tively. The current may be taken from a convenient electric- light main, an incandescent lamp being interposed to prevent an excessive flow. A galvanometer, which in central stations may conveniently be a switchboard ammeter of the shunt type with its shunt disconnected, is then attached so that one terminal is on the shaft and the other free to be moved around the commu- tator. If the ground is at that point of the winding designated by the cross in the figure, the deflection of the galvanometer will be a minimum when its terminals rest on the commutator bar to which that lead is attached. If the ground were midway be- tween the terminals attached to two adjacent commutator bars, the deflection at these two bars would be alike and both would be less than that given at any other point on the commutator. All that is usually desired is to know which coil the ground is in, but this feature enables one to tell approximately at what point on the length of the coil the ground is located as well by observing the magnitude of the deflection given when the gal- vanometer terminal is on the two adjoining commutator bars. Location of Crosses. Current is passed through the armature under test through two of its sets of brushes, these two being usually selected so as to be diametrically opposite. The current is taken from another main, as in the preceding test. Terminals from a galvanometer, which may likewise be a shunt type ammeter without its shunt, are then placed on adjacent commutator bars, as shown in Fig. 240, and the deflection noted. This operation is repeated around the whole circumference of the commutator, bar by bar, and the deflections will all be alike (if the strength of the current flow- ing through the armature is kept constant), until the bars to which the ends of the defective coil are attached are reached, whereupon the deflection will naturally be less as the current, instead of being obliged to flow through the full length of the coil, then shunts part of it through the short circuit. This is usually called the " bar to bar test." In making the above test, it must be borne in mind that any decrease in the strength of the current through the armature means a decrease in drop between adjacent bars. When testing 302 ELECTRIC AND MAGNETIC MEASUREMENTS. on a fairly steady circuit, it is usually sufficient to place an am- meter in the supply line and see that the current does not change too greatly. When the current is taken from a source like a street railway line, however, where the E.M.F. is constantly varying over a wide range, it is better to use either two separate millivoltme- ters or a combination one like that mentioned on page 129. By using a separate armature coil known to be perfect, or even a length of the wire leads to the armature of equivalent resist- ance, as a shunt to one instrument, the other instrument will give the same reading when its terminals are touched to the adjacent segments of a good coil and a lesser one for a short- FIG. 240. circuited coiL The deflections may vary at different times, but as long as they are alike the coil under test is known to be good, Location of Open Circuits. For locating open-circuited coils connections are made ex- actly as shown in Fig. 240, but the strength of the current passed through the armature is decreased or the galvanometer sensibil- ity made less by inserting a resistance in series with it or a shunt across its terminals. No deflection will be given as the galva- nometer terminals are carried from each adjacent commutator bar pair to the next until those two are reached between which the open circuit exists. At this point there will be an electromotive force equal to the total drop between the two brushes, and the galvanometer needle will be violently deflected. THE LOCATION OF FAULTS. SOS Location of Reversed Coils. A coil whose connection to the commutator bars is the reverse of the proper one is a rare occurrence, but it sometimes happens that in winding an armature this mistake is made. If the arma- ture is tested by the bar to bar method above described, a re- versed coil is detected at once when the galvanometer terminals are applied, as the needle will swing in a direction opposite to that which it took with all the other and properly connected coils. Coil Resistances. If the strength of the current that is being passed through an armature is known by inserting an ammeter in that circuit, and if the galvanometer is calibrated in millivolts, the bar to bar test will give the actual coil resistance in ohms by simple cal- culation, using Ohm's law. In making such calculations the armature connections must be borne in mind, as the current through a good armature flows always through two and often through more branches of equal resistance connected in parallel, so that the current shown by the ammeter must be accordingly reckoned per coil. PART II. CHAPTER I. RECORDING INSTRUMENTS. THE phrase " recording instruments" is often used to designate an integrating instrument whose indications show the product of the average current or wattage by time, but the term is incorrect in this sense, as it actually has reference to an instrument in which some marking device inscribes on a record chart a line showing the instantaneous values of voltage, potential, current, or power, at all times. Such recording instruments are also called registering instruments. The principle on which such devices are based permits of dividing them into three general classes : the first is that in which an ordinary indicating instrument of any of the types heretofore described has attached to its needle a marking pen or pencil which moves over a chart that is being continuously pulled forward by clockwork ; the second class takes in those recorders in which there is likewise used an indicating instrument mechanism, but whose needle is free to move and take up any desired position, a device being attached through whose aid the needle positions are marked on a clockwork-driven chart at regu- lar intervals ; the third class of recorders might be termed " relay recorders," in which the mechanism of an indicating instrument actuates a marking device, not directly, but through relays which control some source of mechanical power of relatively great strength. RECORDERS OF THE FIRST CLASS. Bristol Recorders. The simplest of the recorders of the first class made in this country is the Bristol instrument illustrated in Fig. 241. In it the chart takes the form of a paper disk, which is rotated by clock- 304 RECORDING INSTRUMENTS. 305 work at an appropriate rate. The instrument mechanism consists of a solenoid voltmeter or ammeter whose main winding is a coil whose axis is placed horizontally, and whose core actuates the upper end of the needle shown, the force opposing the motion of the needle being the elasticity of its lower flat spring end. The upper end of the needle carries a V-shaped trough in which there is placed a drop or two of slow-drying glycerine aniline ink which is drawn to the end of the trough by capillary attraction and so makes a fine line on the paper. Aside from the fact that the charts on such instruments are unsatisfactory because the ab- scissa and ordinates are not straight lines crossing at right angles, but circle arcs, so that the records are difficult to in- terpret and practically impos- sible to integrate with a plani- meter, the friction between the pen and the paper is so great as compared with the power exerted by the instrument mech- anism that a considerable change in load must take place before the pen will move, and even then it may take up a position which does not accu- rately indicate the new value. The error due to this friction may easily be in excess of 5 per cent. FIG. 241. Chauvin and Arnoux Recorders. An ingenious device for partially eliminating the above- mentioned friction errors is used on the recording instru- ment made by Chauvin and Arnoux, of Paris. This consists of an ink roller which is attached to the end of a needle actuated by an enlarged specimen of an ordinary indicating instrument movement, the roller being shown in Fig. 242. It consists of two halves, A and B, the former of which is open above and below and the latter above only. A 306 ELECTRIC AND MAGNETIC MEASUREMENTS. lenticular piece of porous porcelain or a disk of blotting paper is placed between A and B and the two then screwed together by an appropriate thread, so that only a very fine gap is left between them. Both the upper end of A and the lower end of B are provided with small jew- eled bearings which in turn rest on pivots, both of the pivots being secured to the pen frame, f F. This leaves the roller free to rotate about its axis. A drop of alcohol is first allowed to fall into the open end of A, and this moistens the porous washer and tends to flow outward through the crevice between A and B. FIG. 242. Aniline ink is put into A imme- \ diately after, and this follows the course of the alcohol, so that the ink is drawn to the edge and will of course make a mark on the paper chart rotated at right angles to and in contact with it. A complete Chauvin and Arnoux recorder having an actuating mechanism of the hot wire indicating instrument pattern is shown in Fig. 243, which cut will make the method of attaching the pen more clear. This rolling pen reduces the friction between the marking device and the chart very materially, but it makes rather a broad line, so that it is difficult to detect minute changes by inspection of the record curve. Creneral ^Electric Co. Recorder. Strictly speaking, this also is a recorder in which the records are obtained by attaching to the extremity of the needle of an indicating pattern instrument a pen, which by its travels over the surface of a paper chart carried beneath it by means of clockwork, traces a curve showing the variations in current strength. The problem of eliminating the frictional errors due to the friction of the pen on the record sheet has in this device been attacked by an endeavor to make the torque of the moving system so high that the frictional retarding forces form but an RECORDING INSTRUMENTS. 307 inappreciable percentage thereof. One of the expedients involved is the reduction of the angular motion of the needle to about 20 in place of the conventional 80 or 90. This of itself brings about a quadrupling of the effort exerted for a given percentage change in load, although it involves, too, chart ordinates which are very short. A still further increase in the power for actuating the recording pen is obtained as follows: The measuring instrument portion of the apparatus is that of the conventional d'Arsonval meter kinematically inverted, that is to say, the moving coil carries a steady current of the maximum strength permitted by the design and swings in a mag- netic field whose intensity varies with the load to be measured, in place of having the coil current the variable and the field strength fixed at the maximum that the design allows. There is thus a moving coil whose windings carry a constant, uniform current from some separate source and stationary coils furnish- ing the field in which the movable one swings. The plan necessitates the compli- cation of a set of storage batteries to supply the mov- ing coil current and an in- dicating instrument in that battery line to show that the cur- rent strength remains unchanged, but has the advantage that the current from the source to be measured may be of almost any value as it flows through stationary windings, and 'here are hence no difficulties because of the limited current capacity of springs or the like. Excellent damping qualities result also, owing to the intensity of the field in which the coil swings. A General Electric recording ammeter is shown in Fig. 244, FIG. 243. 308 ELECTRIC AND MAGNETIC MEASUREMENTS. where the indicating instrument relied upon to show that the strength of the current through the movable coil windings remains unchanged, is likewise visible. The same clockwork that draws the. band of paper along under the marking pen makes marks on the chart at regular time intervals, from which marks the elapsed time may thus be read off. While heavy, cumbersome, and costly, the apparatus forms probably the best means available to-day for obtaining con- tinuous records of rapidly fluctuating loads within its capacity, FIG. 244. being specially valuable for such work as the plotting of the current input curves of elevator and street railway motors. RECORDERS OF THE SECOND CLASS. Grans and Croldschmidt Instrument. In this device the clockwork and paper drum arrangement is much the same as in the Chauvin and Arnoux recorders, but the pen carried by the indicating instrument is not kept in constant contact with the paper. As can be seen from Fig. 245, a curved arm extends across the scale and above the RECORDING INSTRUMENTS. 309 needle. This arm is sharply knocked down toward the paper at regular intervals, controlled by a clock, and as this happens, the marker attached to the indicating needle is likewise ham- mered against the paper, so that registry of a number of individual indications is made and conveys practically the same information as if the record of the meter were a continuous one. This type of instrument is attractive on account of the fact that the mechanism actuated by the current may be of the con- ventional indicating instrument power and design, for, being entirely unhampered in its motion, except at the instants when it is struck by the striker bar, the needle swings as freely as that of an indicating device. The periodic arresting of needle motion is, if anything, rather an advantage in so far as these FIG. 245. checks serve to prevent the needle of otherwise poorly damped apparatus from swinging about too violently. The apparatus is not satisfactory on a rapidly fluctuating load, as the striker bar does not work with a rapidity sufficient to cause the suc- cessive dots on the chart to follow one another closely enough to give an approximation to a continuous line under the circumstances. No meters of the type are made in this country, but they are in limited use abroad, particularly for recording the deflection of instruments with low torques like galvanometers. 310 ELECTRIC AND MAGNETIC MEASUREMENTS. RECORDERS OF THE THIRD CLASS. The Callendar Recorder. One of the earliest relay recorders is the Callendar instrument, which is primarily a recording slide-wire bridge. Fig. 246 shows its method of operation. In that figure MN is the straight stretched wire of an ordinary slide-wire bridge, the standard and unknown resistances being inserted in the usual way, as likewise are the battery and galvanometer circuits. The sliding contact on S slides along a bar, and is pulled toward MOT JV, as the case may be, by the endless cord shown passing over the idle pulleys, Z>Z>, and making a turn around the drum, P. The galvanometer is special, in that when it deflects because the bridge circuits are unbalanced its needle comes against one of the other of the Goto. FIG. 246. stops E and F. When it is against E, a circuit which can be traced out from the figure is closed, and this energizes an electromagnet, I. This magnet pulls down one end of a lever, and in so doing raises the other end, which is a brake that prevents the gear wheel, R, from turning. As R then rotates, it in turn actuates the pinion, B, which latter rotates the drum, P, and pulls the sliding contact in the direction that it must be moved in order to restore the balance. If the galvano- meter needle touched P instead, the pinion, J., would be actuated, and the drum, P, would pull the sliding contact in the opposite direction. The manner in which the drum, P, is caused to rotate in one direction or the other, according as B or A is turn- ing, is best seen from Fig. 247, which shows an enlarged view of this mechanical appliance. Q is a stationary shaft on which RECORDING INSTRUMENTS. 311 a gear wheel, K, may rotate freely. This wheel and its mate, L, are provided with both spur and bevel teeth. L is free to rotate on the outer surface of the shaft, T, carrying the drum, P. Fastened at right angles to T is an arm, 7, on which there rotates the bevel pinion, V. If A and therefore K are stationary, and B rotates, L will evidently be revolved about I 7 and in so doing will not only rotate V about its axis, C7, but will carry U around the shaft, Q. In like manner, if B and hence L are stationary, and A rotates, K will rotate U about Q in the opposite direc- FIG. 247. tion. If both A and B were released from the control of their brakes simultaneously, as would practically be the case if the galvanometer were subjected to heavy mechanical vibration so that it tapped E and F in rapid succession, V would rotate about /", but U would not rotate T around Q. This device is like the balance gear used on automobiles. The power for driving A and B is obtained from a pair of independent clockworks. A pen carried by the arm that sup- ports the sliding contact, on S, is drawn backward and forward on the record paper by it, and so makes the desired chart. 312 ELECTRIC AND MAGNETIC MEASUREMENTS. While the instrument as described is e, recording bridge giving a record of any changes in the value of resistance, Jf, it can, as is evident from the chapter on slide-wire bridges, easily be modified to become a recording potentiometer, in which case it will give records of potentials, currents, temperatures, etc. The Arconi Recorder. In this device the needle of an indicating instrument actuates, as is shown in Fig. 248, a contact which comes against one or FIG. 248. the other of the stops A and B when the value of the current flowing through the instrument changes. A motor, M, is set in rotation when the needle is in contact with either stop by com- pleting the circuit through the motor armature, and revolves in RECORDING INSTRUMENTS. 313 one direction with the contact on ^4, and in the reverse direction when it is on B. The torque exerted by the instrument needle is opposed by that of the coiled spring, S, and the free end of that spring is attached to a carriage that is driven by the motor. FIG. 249. The connections are such that when the current strength increases the needle makes the contact for that circuit wLich will revolve the motor armature, and hence move the spring terminal in such a way as to increase the spring tension. The motor will of course be kept on rotating until this increased tension is sufficient to pull the needle away from its stop, 314 ELECTRIC AND MAGNETIC MEASUREMENTS. whereupon the circuit is broken and the motor comes to rest. A pen, JP, is attached to the rack that is moved by the motor and traces on the chart the varying positions that the rack has assumed and which show the measures of the current strength. The indicating instrument mechanism may obviously be either a voltmeter, ammeter, or a wattmeter, according to the quantity that it is desired to observe. A complete instrument of this kind is illustrated in Fig. 249. The Weston Recorder. This device is similar to the Arconi recorder, in that an indicating instrument mechanism causes the direction of rotation FIG. 250. of an electric motor to reverse according as the needle deflects against one or the other of a pair of stops, and in that the pen that makes the record on the chart is moved back and forth by the motor. Instead, however, of varying the magnitude of the torque resisting the swing of the needle by the position of the recorder carriage, the torque actuating the needle is varied by varying a resistance placed in series with the indicating mechan- ism. A diagrammatic illustration of this device is shown in Fig. 250, and will be understood without further explanation. Another form of Weston recorder is that illustrated in Fig. 251. In this neither the torque of the indicating needle nor that of the spring opposing its motion is varied, but the position RE-CORDING INSTRUMENTS. 315 of the stop contacts is changed instead. As is shown by the figure, the stops are carried on a frame mounted co-axially with the indicating mechanism, and are caused to rotate by a motor which drives their frame through gears. The direction of the rotation of the motor is determined by the pair of stops with which the needle is in contact, and it carries the frame with the contacts along, until the circuit is broken and the needle left free. The recording pen is driven back and forth on its chart by the motor. Boyle's Recorder. This piece of apparatus is diagrammatically illustrated in Fig. 252. It employs an ordinary indicating instrument mech- anism, J, on which there is a needle with a contact point at its end, as in the apparatus above. The stops against which this contact plays are, however, not stationary, but composed of two plates, 8 and jP, insulated from one another but mechani- cally secured to a com- mon framework and in rigid connection with a piston, P, mov- ing in a cylinder. When the needle makes contact with one of the plates, say $, a circuit is closed through a local battery and S, and through two electrically controlled valves, E 1 , E\ When current flows through the valve windings both are opened. As will be seen from the figure, this with the piping arrangement shown will admit water that is supplied under pressure from ordinary service mains to the lower sido of the piston, through the valve, JE 2 , while at the same time the opening of the valve, E l , offers a free passage for the escape of the water from the upper and opposite side of the piston, P, to the atmosphere. The result of this unbalanced pressure on the FIG. 251. 316 ELECTRIC AND MAGNETIC MEASUREMENTS. piston is to raise it, together with the contact plates, $ and T, attached to the piston rod, so that the pointer of I is free to deflect further toward the left. As long as the torque of J, exerted by the current flowing through the mechanism, is less than the restraining force offered by the springs, I will remain in contact with S, but as S moves up a position will FIG. 252. finally be attained where the forces acting on the needle are in equilibrium, and its extremity will therefore rest between the plates S and T, but not in contact with either. If an increasing load were applied to /, the pair of valves, F 1 and _F 2 , would be opened, and T and S would rise instead of fall. A pointer, R, is attached to the piston rod and moves over a scale which is divided so that the values of the current strengths may be read off directly. The same rod carries also RECORDING INSTRUMENTS. 317 an inking pen that rests in contact with the clockwork-driven record sheet. A detail view of one of the electrically operated valves is shown in Fig. 253, which is practically self-explanatory. The upper part of this apparatus is held to the lower one by means of a clamp, so that if it is desired to have access to the valve at any time this can be done by the simple removal of a screw. A copper diaphragm is interposed between the windings of the electro- magnet and the iron core on which it acts, in order that moisture may not enter and spoil the windings. The possibility of varying the outline of the gap left between the plates S and T of the recorder forms an interesting feature of this apparatus. If the instrument whose fluc- tuations are to be re- \ corded is of the equally { divided scale type in which equal current increments give equal increase of angular displacement of the needle, the straight slot illustrated is em- ployed, and the result- ant record chart is one for which ordinary cross-section paper may be employed, like numbers of divisions of the ordinates indicating like amounts of current at all points between the horizontal reference line and the boundary full capacity line. This enables the mean height of the record curve to be determined by simple integra- tion of its inclosed area with a planimeter and dividing this by the length of the chart, as in the case of steam engine indicator cards. If the excursions of the pointer of the indicating instrument do not vary in direct proportion to the changes in current strength and the straight gap is used, the chart divisions would FIG. 253. 318 ELECTRIC AND MAGNETIC MEASUREMENTS. be like the scale divisions, i.e. 9 if the latter are crowded together at any part of the scale the chart abscissae will be close together at the same part. By suitably curving the slot, however, it is pos- sible to make an indicating instrument movement whose scale divisions are not of equal width give a chart with equal divi- sions by causing the excursions of the piston to vary in direct proportion to the current strength. With an alternating-cur- rent voltmeter having a scale of the character shown in Fig. 149 the slot required to enable the use of ordinary section paper as a chart would be shaped somewhat like that shown in Fig. 254. It will be seen that when the contact on the needle is at the point A a very slight swing of the needle is sufficient to close the circuit in one direction or another, that if the needle is near the point B it will make a larger angular swing before coming in contact with a plate, and that when it is at the original status of affairs recurs, except that here the contact may move a little further, as the scale of the indicating instrument is more open at the highest point of its range than at its lowest. CONTACT TROUBLES. In all of the relay recorders so far de- scribed, the mechanism of an ordinary indicating voltmeter, ammeter, watt- meter, or galvanometer is obliged to ex- ert a sufficient torque to cause a metallic button carried by its needle to make an electrical contact with a stop. Even with fresh, smooth surfaces the pressure that must be exerted to force them together firmly enough to obtain good electrical contact is appreciable, and as the contacts become somewhat roughened, due to the slight but constant sparking when the motor or clutch circuit is made and broken thereat, the pressure required becomes still higher. The requirement of high contact pressure means low sensibil- ity of the instrument as a whole, and its failure to record small fluctuations, as large current changes must take place before the contact carried by the movable element is pressed against its mate with the requisite force. Obviously a very small particle FlG. 254. RECORDING INSTRUMENTS. 319 of dust lodging between the contacts will have the same effect. This difficulty, while seemingly trivial, has proven to be the greatest drawback to relay instruments, and in fact is the principal reason why none of them are yet in extensive use although their inception dates back many years. Various devices have been employed to minimize the trouble, the more prominent being the following : Rubbing Contacts. Fig. 255 shows the expedient devised by Professor Callendar for use in his recorder. As will be seen from this, the needle, S, Threcul&ett FIG. 255. of the galvanometer plays between two contacts which are made in the form of wheels that are being slowly rotated by a light thread belt driven by a clockwork mechanism. Each wheel is of brass, and into its periphery there is let a circle of platinum wire which projects above the wheel face. The tip of the galvanometer needle is of platinum also, so that when it defects against either wheel edge, a contact is made between platinum and platinum, and one of the faces is kept rotating at right angles to the other, thereby not only continuously presenting a fresh surface, so that the heat developed at the point of contact 320 ELECTRIC AND MAGNETIC MEASUREMENTS. is less apt to prevent incipient fusing, but the rubbing polishes the surfaces and thus tends to keep them in good condition. In the figure the contacts between the wheels and the brake circuits are shown as being made through springs pressing on the wheel hubs. This is often modified by supporting the axles on which the wheels turn in plain metallic bearings, the amount of current to be transmitted being sufficiently small to admit of this practice. Relays. Another method of overcoming the difficulty due to handling comparatively large currents through the contact made between the instrument needle and its stop is to use ordinary electric relays similar to those employed in telegraph practice, so that this circuit need carry only enough current to energize the relay, leaving the relay contacts to carry the heavy current that is necessary to work the clutches or the motor. By this expe- dient the current controlled by the instruments may be limited to one in which the sparking between the needle contact and its stops is inappreciable, or at all events not enough to roughen them with a consequent decrease in sensibility. Such relays are, however, open to the objection that they involve the use of an additional battery circuit, and so add con- siderably to the complexity of the device and to the fact that they are expensive. Without them, on the other hand, it is exceedingly difficult, if not impossible, to make a recorder of the third class that will be free from contact troubles when used for extended periods. WADDELL AND LEGRAND RECORDER. These interesting instruments are based on a novel prin- ciple. Referring to Fig. 256 herewith, air under a pressure of approximately three pounds to the square inch is supplied through a pipe, A, to the instrument. This air is first obliged to pass through a long fine-bore passage, B, and then into a chamber, (7, of relatively large volume. This chamber is supplied with an escape valve, 7), which is similar to a safety valve, the load on whose disk, E, is determined by the strength of the current to be measured. As in the case of any vessel provided with a safety valve of comparatively very large capacity, the pressure RECORDING INSTRUMENTS. 321 in the vessel is determined solely by the blowing-off pressure to which the valve is loaded. Small variations in the pressure of the air supplied through A do not vitiate this result, as the effec- tive area of the passage, B, is so much less than that through the valve, D, that the latter can take care of any of the fluctuations in the rate of supply to the chamber, O. The manner in which the valve disk, E, is loaded by varying currents is also shown in the figure. A coil, F, of insulated wire is arranged in the annu- lar field supplied by the magnet, SN, with its extension pole piece, s.s. This coil is supported on one end of a lever, 6r, that is free to oscillate about the fulcrum, H, and is partially counter- balanced by the adjustable weight, /. When current flows through the spool the reaction between the magnetic field that Pen, FIG. 256. it furnishes and that of the permanent magnet exerts a pressure on the valve that is in direct proportion to the current strength. The valve is therefore loaded in proportion to the current strength, and the pressure in the chamber, (7, hence varies with the current. The recording device is formed by a float, <7, that is carried up and down in the manometer, K, *by the variation in pressure on its surface. A pen is carried on a rod that is rig- idly secured to the float, and as it is moved up and down by the latter traces a line on the chart that is revolved before it by clockwork and shows the variations in current strength. A complete instrument of this class is illustrated in Fig. 257. As described, the apparatus is suitable only for the measure- ment of continuous currents, as only these will give the neces- 322 ELECTRIC AND MAGNETIC MEASUREMENTS. sary reaction between the permanent magnet and the coil through which the current flows. Alternating currents are measured by substituting for the magnet and coil mechanism, any of the indicating instrument mechanisms that have been described on preceding pages and arranging them so that there is no restraining force, the needle instead pressing on the valve. A modification of this kind is the recorder for measuring FIG. 257. the total output of a multiphase circuit, this being shown in Fig. 258. Here the lever which loads the valve is double ended and carries at each extremity a spool through which there flows current of a strength proportional to the volt- age. Each spool works in the field furnished by a solenoid through which passes the total current to be measured, and each end of the lever is hence a wattmeter. By making the electrical connections such that the right-hand end, A, of the spool is RECORDING INSTRUMENTS. 323 depressed and the left-hand end, B, raised when current flows through its windings, the load on the valve evidently is the sum of the efforts. As was pointed out on page 230 the output of a three-phase circuit is obtained by adding together the indications of two wattmeters having their series coils connected in two of the three legs and the potential coils attached respectively between each of these legs and the third one. In the instrument in question, the addition instead of being made arithmetically is made mechanically, in that it is the sum of the efforts of the coils which causes the downward pressure on the valve. The same instrument or simple modification thereof can of course be used for recording the output of two-phase or any other multiphase lines. In the actual apparatus the contracted passage, B, Fig. 256, is formed, not of a long small diameter tube, but of a series of disks of filter paper which are the equivalent of the capillary tube pneumatically, and which have the incidental advantage of removing particles of dust from the air supplied through A in the same figure, and so preventing clogging the valve, D. The air for working these recorders is supplied either by a small air compressor driven by any suitable means, or through a reducing valve from any high-pressure air supply that may be available. CHAPTER II. INTEGRATING METERS. As has already been stated, integrating meters are devices for registering the product of the mean value of current or power supplied through a given circuit during any given period, by that period. In the great majority of cases they are used to measure the amount of current or energy supplied to the cus- tomer of electricity in order to form a just and definite basis for the bills. The name, " recording meters," by which they have long been known, is rapidly falling into disfavor, and the* terms " integrating meter " and " electricity meter," both of which describe them more correctly, are coming into use. Because of the fact that these devices form the basis on which the charges are made by central stations to their custom- ers, the number in use is exceedingly large, and while already many times as great as the number of indicating or true record- ing instruments employed, is increasing at a rate that is daily becoming larger. As they are subject to conditions under which few of the instruments heretofore described are employed, and as they are inherently of such construction that the wear is greater and the length of time that they will remain in calibration and also their life is shorter, they come under a somewhat differ- ent category, and their peculiarities and ills are more appropri- ately treated in a volume devoted to them exclusively. A brief description of the principles on which the more prominent types are based is, however, thought properly to form a part of a treat- ise on the general subject of electric measurements and measur- ing apparatus. Integrating meters may conveniently be divided into the following general classes : Chemical meters, these being ones in which the desired current data is obtained through electro deposition; motor meters, in which the device showing the current or energy integral is actuated by an electric motor mechanism ; and mechanical meters in which a mechanical 324 INTEGRATING METERS. 325 integrating device like a planimeter is actuated by an indicating instrument and its indications used to show the result. In all of these it is desired to obtain a record of the total amount of energy passed through the meter, and where the apparatus is an integrating wattmeter, this result is attained directly. Some of the instruments give, however, not watt hours, but ampere hours, and the resultant charge made to the customer is based 011 the assumption that current has been delivered at a constant potential. This state of affairs, while never actually existing, as the potential at the customer's prem- ises may easily vary 5 per cent, is generally sufficiently close as an average to form a basis of charge that is as equitable as is the watt-hour basis. CHEMICAL METERS. Edison Chemical Meters. The most prominent and practically the only representative of the chemical meters is the Edison meter. It consists of a voltameter in which the plates are of zinc and the solution of zinc-sulphate, instead of copper and copper sulphate, respec- tively, as in the case of the voltameters, mentioned on page 14. A shunt is inserted in the supply circuit and combined with the meter itself, so that only a known fraction of the total current passes through the voltameter. Two voltameter cells con- nected in series with each other are usually employed in order to afford a double check, and a thermostat is also added which consists of a compound metallic strip that closes a circuit through an incandescent lamp when the temperature falls too low, so that the heat from the latter may serve to keep the cells from freezing or becoming sufficiently cold to introduce errors. An Edison chemical meter is shown in Pig. 259. Instruments of this type possess the very great advantage of containing no moving parts and hence not being subject to de- terioration. Their accuracy is also of the highest, as the fVt that there is no friction means that the smallest loads are regis- tered with the same accuracy as the greatest ones within their capacity. Further, there is no inertia, so that if the current passed through them is fluctuating in strength, the meter 326 ELECTRIC AND MAGNETIC MEASUREMENTS. takes account of it all without having that inertia introduce errors because of its refusal to allow the apparatus to get up to speed before the current has again fallen. Its drawbacks are that in order to obtain readings the jars containing the plates must be removed from the meter and carried to some point where the delicate operations of cleaning and drying the plates and weighing the change in weight can be attended to. Where the instrument is in constant use, this means that two sets of voltameters must be supplied, the one being in the recorder while the other is at the station. An incidental, but impor- tant, further drawback is that the customer to whom current FlG. 259. is being sold and whose bills are figured from the indications of the recorder, is left without even the crudest means for ascertaining what the meter readings are, and is therefore obliged to rely entirely on the accuracy of the station reports as rendered in the form of bills. The comic-paper man with his gas-meter jokes has rendered sucli apparatus out of the question. Even an instrument which a customer can read himself is viewed with suspicion, and when no means of this kind are afforded it is generally a waste of time and breath to attempt to persuade him that bills are not made up simply by guesswork and with an idea of having them as large as he will stand without protest. It is for the latter INTEGRATING METERS. 327 reason in many cases, as much as any other, that the Edison meters are going out of use and being replaced by integrating instruments of the motor type. MOTOR METERS. Thomson Integrating Meters. One of the oldest and certainly the most widely used motor meter is the Thomson integrating watt-hour instrument shown with its protective casing removed in Fig. 260. It consists of FIG. 260. an electric motor with a vertical shaft, the armature being of the drum-wound type and both it and the field windings being with- out iron cores. The armature wires are of small diameter and carry a current varying in proportion to the potential between 328 ELECTRIC AND MAGNETIC MEASUREMENTS. the service mains, acting like the potential windings of an indi- cating wattmeter. The field windings are of heavy wire, and through them is passed the total current. The torque exerted under these conditions is evidently proportional to the product of the simultaneous instantaneous values of the current and potential, that is to say, to the watts, whether the current is direct or alternating. The load for the motor is supplied by a copper disk secured on the lower part of the shaft and rotating between the pole faces of a pair of permanent magnets, the eddy currents generated in the disk by its rotation in this magnetic field forming a drag that increases in strength in direct propor- tion to the speed. As the torque of the motor increases in direct proportion to the watts, it is clear that each wattage calls forth a corresponding opposing load and that the speed there- fore increases in direct proportion to the watts. It is hence possible simply to attach a train of gears to be driver! by the rotating shaft and to affix pointers to appropriate members of this train which will thereupon show on appropriately divided dials over which they sweep, the watt hours that have been consumed. If the apparatus were frictionless, it would operate correctly when made along the simple lines described. This is, however, not the case, as the friction between the bearing on which the foot of the shaft rests, and between the commutator and the brushes, is not an inappreciable quantity. It is, however, a quan- tity that may safely be assumed to be nearly constant irrespec- tive of the speed of rotation of the shaft, and provision is hence made to supply a constant torque which will just balance this frictional resistance. The means is a coil wound like the station- ary field coils, and of a size that will just slip inside of one of them, the coil being of fine wire and connected in series with the armature and the non-inductive calibrating resistance. As the circuit so formed is always connected across the mains, current is continuously flowing through it, and by properly adjusting the distance between the fixed coil and the armature, the field that the coil supplies may be made of a strength that is just sufficient to make the torque of the armature in it one that balances the frictional drag. In practice it is necessary to adjust the position of this so-called " starting coil " after the meter has been erected in place. This is because a meter INTEGRATING METERS. 329 subject to mechanical vibration has less friction of the lower bearing than if the same instrument were installed at a perfectly quiet point. The adjustment is made empirically, the starting coil being pushed inward toward the armature until the latter just begins to rotate with no current flowing through the series winding, whereupon the coil is slightly retracted and then made fast. As there are two series field coils the instrument is easily arranged for measuring the input on a three-wire circuit, one of the coils being placed in series with each of the outer mains and the potential coil between one of the outer mains and the neutral, as is shown in Fig. 261. For very heavy currents such as in central stations, the current windings take the form of a flat copper bar as shown in Fig. 262, and two armatures, each of which is placed within the influence of the field surrounding the bar, are used connected to FIG. 261. a common shaft. In all of the instruments the calibration may be adjusted by varying the radial distance between the shaft turned by the armature and the center of the pole faces embrac- ing the copper disk and so changing the opposing torque. 330 ELECTRIC AND MAGNETIC MEASUREMENTS. Sangamo Integrating Meters. In this apparatus, as in the Thomson described above, a motor exerting a torque proportional to the watt consumption of the circuit in which it is connected, rotates a disk of conduct- ing material between the jaws of stationary permanent magnets, and the number of its revolutions as shown by pointers sweeping over appropriately divided dials is a measure of the watt hours. FIG. 262. The motor element and many of the details of the apparatus differ markedly from the Thomson device. The former will be understood by reference to accompanying Fig. 263. Here a disk, A, of copper provided with a float chamber,'^, is sub- merged in a bath of mercury, (7, inclosed in a chamber of insulating material, D. Bedded into the walls of the chamber are a block of iron, 6r6r', and the extremities, EE', of a laminated core electromagnet EFE f . Copper lugs, HH', are INTEGRATING METERS. 331 also bedded into the chamber at diametrically opposite points. When such a structure is connected in circuit as the figure shows, the disk, J., is evidently located within the field of force of the electromagnet, the flux direction being from E to 6r and from 6r' to Jtf * The disk at the same time is being traversed by a current flowing in the direction shown by the arrows, coming in through the lug, H, through the short gap between A and H that is filled with mercury, and similarly out from A to H f . We thus have an Arago disk motor whose torque is in proportion to the watt consumption of the load under measurement, as the disk current is that required by the FIG. % J(. load, while the magnetic field against which it reacts is of a strength proportional to the applied potential, the windings of the electromagnet being connected across the supply line. In this meter the device for obtaining a small and adjustable initial torque to compensate for the retardational effect of the friction of the moving parts consists of a small spiral of bare resistance wire wound on a hard rubber rod and electrically connected at J and K in shunt to the disk circuit. Current for the potential circuit of the meter is tapped off from this spiral at any desired point of its length by shifting along the movable contact, L. The resistance of the spiral is high as 332 ELECTRIC AND MAGNETIC MEASUREMENTS. compared with that of the circuit through the disk. With L near J, the major portion of the current drawn by the windings, JV, of the potential circuit, evidently flows direct from J through LN to M-, a small portion only flowing through the by-path, JHAH'KL, owing to the much higher resistance of that path. There is then but a feeble current through the disk, A. When L is moved over to K, the high resistance of the spiral means that the major portion of the potential circuit current flows through the disk circuit instead of through JK as before, and similarly for intermediate positions of L. The proportions are such that this small current which constantly flows through the disk, independent of the load, may, by shifting X, be brought to a value setting up a torque which just balances friction. The meters are claimed to be superior to the Thomson form. For one thing the commutator, which is always a more or less troublesome element and a source of variable friction errors, is eliminated. For another thing, the buoyant effect of the mercury is utilized to entirely relieve the lower shaft bearing of the weight of the moving system ; in fact, the design gives a very slight upward thrust of about two per cent of down- ward pressure in a non-floated meter. This reduced press- ure means greatly decreased friction and wear and a much lessened liability to injury of the jewel or staff end if the apparatus is jarred or run sub- ject to vibration. Another feature is the ability to use shunts similar to those util- ized with indicating ammeters of the direct-current type, to increase the ampere capacity. This point is of a decided ad- vantage from the standpoint FIG. 264. of cost, as a shunt can be built for a fraction of the expense involved in constructing the stationary conductors in a commutator type meter of material INTEGRATING METERS. 333 heavy enough to carry currents of high value. Shunts are not feasible with commutator apparatus. Fig. 264 shows the parts of the motor member of a Sangarno meter disassembled and arranged one above the other in the order in which they go together. The downwardly pro- jecting tube on the top cover plate contains a pierced jewel through which the shaft, P, Fig. 263, passes and which acts as a guide bearing for that shaft. The fact that the minute clear- ance between the shaft and its bearing is the only point where mercury could escape, and that the mercury can never get at that point owing to the " patent ink well " type of construction, makes it pos- sible to ship such apparatus from place to place with the mercury in position and without danger of spilling any of it. A Sangamo meter with the cover removed is shown in Fig. 265. Aaron Meter. The Aaron integrating in- strument can be considered as belonging to the class of motor meters only in that the indices which show the current or energy consumption are driven over the dials by spring motors. The apparatus is not in use in this country, and it is doubtful whether it ever will be employed to any extent here, as it is both bulky and costly and rather too complex to suit the fancy of our engineers. Its ingenious prin- ciple, however, entitles it to at least brief mention in this volume. The apparatus takes on many different forms, according to the kind of circuit on which it is to be used, but all rest on the following principle : Two separate clockworks having escapements of the pendulum pattern are mounted together FlG. 265. 334 ELECTRIC AND MAGNETIC MEASUREMENTS. on a common framework, and these are adjusted so that their rate is exactly the same. The two trains of clockwork mesh into two gears, P and P' respectively (Fig. 266), which gears, together with the pinion, J, form a device like the gear in the Callendar recorder illustrated in Fig. 247. As long as the trains are moving at the same rate, P and P' will rotate without causing the shaft that carries I to rotate about its axis, X. If, however, one of the trains should be caused to run more slowly than the other, X will be rotated, and the pinion on it will set the indicating hands attached to the gears in mesh with the pinion which it carries in rotation over their respective dials. A difference in speed of the gear trains of the two clocks is brought about and made to vary in proportion to the strength of the measured current in the following way: Referring to Fig. 267, which shows an Aaron meter with the case open, it can be seen that the lefkhand one of the clocks is provided with an ordinary pendulum, this being made of brass or any other non-magnetic material. The bob of the right-hand pendulum is a U-shaped permanent magnet, which swings over the end of a solenoid through which the current to be measured is passed. When no current is flowing the solenoid of course exerts no influence on the magnet, and the clocks are free to run at the like speed to which they are primarily adjusted. When, how- ever, current flows, the swings of the magnet are retarded, and the amount of retardation increases in direct proportion to the current strength. For alternating-current work, a laminated iron core swinging within a horizontally placed solenoid is substituted for the other arrangement, and for the measurement of watt hours instead of ampere hours the pendulum bob is formed of a coil of fine wire that is connected across the line through FIG. 266. INTEGRATING METERS. 335 the interposition of a suitable auxiliary resistance. As the planes of the fixed and swinging coils are parallel, the attraction between them varies with the watts, as in the case of an indicate ing wattmeter. Other possible modifications rendering the apparatus suitable for use on three-wire and multiphase circuits will suggest themselves. ALTERNATING-CURRENT METERS. The Thomson commutator meter above described and others of its class may be used 011 alternating as well as direct current, just as a dyna- mometer type wattmeter is available for either kind of circuit, but they are but seldom so employed in practice, principally be- cause the commutator with its attendant ills and the heavy duty on the jewel bearing because of the great weight of the moving system, are con- sidered evils to be tol- erated only where their presence is essential. The Sangamo meter in which, as explained, the commu- tator is absent and the jewel pressure extremely small, forms an acceptable alternating-current device when a condenser is in- serted in the potential circuit to compensate for the self-induction of that winding and cause the changes in magnetization of the iron core to vary in phase with the line potential. This pattern is relatively new, but seems growing in favor. The class of meter for alternating-current service in most extensive use is, however, the induction type, which, while FIG. 267. 336 ELECTRIC AND MAGNETIC MEASUREMENTS. operative only on alternating circuits, is attractive because of its simplicity and durability. The earliest form of induction meter that came into general service is the Shallenberger Meter. The Shallenberger meter records ampere hours and, as is seen from Fig. 268, contains a stationary flattened coil of heavy wire through which the current to be measured is passed. Within this coil there is a second one similarly shaped, and placed with its longitudinal axis at an angle to the above series coil and having its windings short-circuited on itself. Located in the plane of both coils is an aluminum disk. The alternating cur- rent flowing through the outer coil produces another current in the short-circuited one, and the resultant of the magnetic fields set up by the two is evidently shifting around the axis >f the inclosed disk. This rotating field carries the disk along with it, the torque being di- rectly proportional to the current in the series coil. The torque opposing the ro- tation of the aluminum disk is furnished by four light vanes of aluminum secured to radial arms, forming a fan whose opposing torque varies as the speed and the work necessary to rotate it, as the square of the speed. The revolu- tions of the rotating element are registered by a train of gears driven by the rotating shaft as in other motor meters. Induction Wattmeters. The Shallenberger meter above mentioned is evidently an ampere-hour meter. Induction instruments may be built to register watt hours instead by causing a rotatably mounted disk or drum of good conducting material, usually aluminum, to be acted upon by two sets of coils, one carrying the line current and the other a current varying in proportion to the applied potential and hence connected across the line. In order that these two currents may set up a rotating magnetic field so as to INTEGRATING METERS. 337 cany the aluminum disk along and thus drive the train of gears actuating the indices which show the watt hours consumption, one must be displaced in phase from the other. This is accom- plished in commercial meters by placing in series with the potential winding, which is connected across the line, a highly inductive resistance which of course causes the phase of the current flowing therethrough to be displaced nearly ninety degrees. The torque exerted on the rotatable member is pro- portional to the product of the simultaneous instantaneous strengths of the currents in the two windings, that is to say, to the watts being expended in the circuit beyond. The mechanical disposition of the elements of such meters evidently admits of considerable variation. MECHANICALLY INTEGRATING METERS. A type of integrating meter possessing many attractive fea- tures and which is periodically re-invented, consists in transfer- ring the indications of an indicating ammeter or wattmeter to a clockwork or motor-driven counting train. The needle of the indicating instrument swings over a scale as usual and carries a stop or else some transmitting device. A clockwork operated mechanism is set in motion at successive intervals of time, and either rotates through a distance determined by the position of the stop as determined by tho load passing through the instru- ment, or works the counting train through a transfer gear car- ried by the needle for a length of time that is likewise determined by the needle's position. The number of such devices in actual use is so exceedingly small that the devotion of any extended space to them and their peculiarities and drawbacks is not warranted. Mention is made as the principle at least is of interest. BOYLE INTEGRATOR. Another form of integrating meter in which the mechanism of an indicating device is utilized is the recorder mentioned on page 314. To the rod which carries the record pen and the index that sweeps over the graduated scale, there is secured, as is seen from Fig. 269, an arm with a fork-shaped end which in rising carries with it a small wheel, A. A is free to slide along the ?haft, B, which has at its end a worm that drives the count- 338 ELECTRIC AND MAGNETIC MEASUREMENTS. ing train. A drives B in that the latter is provided with a key-way running for its whole length, A being supplied with a feather that runs in it. A is in contact with the face of a large disk, D, that is driven by clockwork at a constant speed, and the plane of whose face is at right angles to that of A. When A is at the center of D the latter will rotate without causing A FIG. 269. to turn ; when, however, A is carried above the center by the fork J 7 , D will drive it and hence the counting train, and the rate of rotation will be in direct proportion to the distance of .F from the center. The latter distance is proportional to the current through the meter which controls the position of the needle, U, on the scale, S, and the counting train hence gives am- pere or watt hours according as that meter is an ampere or a wattmeter. CHAPTER III. MAXIMUM DEMAND METERS. IN order to be able to charge the purchaser of electrical energy an equitable amount, it is desirable to know not only the product of the mean value of the energy by time it was supplied, but also to know the maximum amount that has been called for during any appreciable period, in order that the purchaser may be properly taxed for that proper- tion of the total supply equip- ment that must be held in reserve for him, so that he may make that demand at any time. Instruments for measuring this largest call are known as maximum demand, or simply demand, meters. Wright Maximum Meters. This instrument, which is illus- trated in Fig. 270, consists of a U-shaped glass tube, having en- larged chambers at both extremi- ties and a side tube opening out of one of them. The chamber that has not the side outlet is sur- rounded with a couple of turns of high-resistance alloy that is made in the form of a thin ribbon wound tightly about the chamber, in order that the heat generated therein by the passage of the current may waism the air in the chamber. The tube is filled with liquid to about the height shown. When current flows through the resistance strip the expansion of the air in the chamber, A, due to the heat, forces the surface of the liquid in the left-hand leg of the tube down- ward, and that in the right-hand one correspondingly up FIG. 270. 340 ELECTRIC AND MAGNETIC MEASUREMENTS. ward. Should the current strength be sufficiently high, the surface of R will rise until the liquid will overflow into the central tube, 8. If the current is then reduced or cut off, and afterward put on again, R cannot rise sufficiently to overflow into S unless the current strength is greater than the preceding one. The greater the current, however, the greater is the amount of liquid that will flow into the center tube, and the scale placed alongside of the tube may, therefore, be graduated to show the maximum amperage that has passed through the heater strip. The air in the chamber, A, does not heat up in- stantaneously, and the surface of R, therefore, does not vary at once with change in current strength, but lags considerably behind it, the time ele- ment being such that if a given cur- rent flows through the winding for five minutes, only about 80 per cent of the amount of liquid will flow into 8 that would get there if the cur- rent were left on indefinitely : about 95 per cent of the total amount will be measured in ten minutes, and all of it in half an hour. This feature is of importance, as it means that the customer is not penalized because of the existence of a momentary short circuit on his line, which does not injure the supply station in any way, and account is not taken of a heavy current momentarily drawn, as when starting- a motor, which also FIG. 271. , ' does not inconvenience the station. The meter can be reset, that is, the liquid drained out of the tube, S, by inverting the U-shaped portion so that it all flows into the chamber, B, as after it is lowered to its original position again that liquid will flow into R instead of 8. Variations in the temperature of the atmosphere do not affect the device, as MAXIMUM DEMAND METERS. 341 it is in reality simply a maximum indicating differential ther- mometer actuated by the difference in temperature between its two bulbs. The apparatus is put in a locked case, so that this resetting cannot be done Iby unauthorized parties. A complete instrument is shown in Fig. 271. Schattner Maximum Mater. In this device, illustrated in Fig. 272, a glass tube bent as shown is partially filled with steel balls which fit its bore quite closely, and then entirely filled with an oil of greater or less FIG. 272. viscosity, according to the lag in indications desired, after which it is sealed. This tube is then secured by clips to the sector- shaped plate carried by a suitably journaled shaft, which shaft is rotated over an angle proportionate to the strength of the cur- rent flowing through the curved solenoid in the lower left-hand corner of the containing case because of the attraction c f that solenoid on its iron core. As the sector and hence the tube are so tilted, the steel balls, which are initially all contained in the tube's curved arm, tend to run out of this arm and down into the straight one. The curvature is such that for a small inclination 342 ELECTRIC AND MAGNETIC MEASUREMENTS. only one ball is on a downward grade and that the number so situated increases with the angular deflection of the sector. The oil in the tube gives a dashpot effect to the movement of the steel balls such that a momentary overload or short circuit would not be registered, that is to say it introduces the same time lag that exists in the indications of the Wright meter. Different lags are obtained by using oils of different viscosities. On the face of the sector is printed a table as shown, giving the ampere flows through the solenoid required to cause varying numbers of balls to run down into the straight tube. The sector also has marked on it just above the curved tube, a scale graduated in amperes, the position of said scale relative to a stationary pointer carried by the containing case, thus giving a means of reading the instantaneous values of the current strength. This meter is reset, that is, the balls returned to their initial positions in the curved arm after taking a reading by removing the tube from its clips and hanging it upside down. As this operation is rather a slow one, a spare tube is often supplied fastened in an inverted position inside of the case, and this is exchanged for the first one as readings are made. PART III. CHAPTER I. MAGNETIC UNITS. THE elementary magnet is a straight thin rod or bar whose manifestations of maximum magnetic energy are exerted at or, near its ends at points known as the magnet poles. All magnets have two poles, which are termed by convention positive and negative, the former being that which points toward the north if the magnet is freely suspended in the earth's magnetic field. Magnetic poles of like sign mutually repel one another and poles of unlike sign attract one another with forces that in both cases are directly proportional to the product of the strengths of the two poles and inversely proportional to the square of the distance between them. UNIT MAGNETIC POLE. The unit magnetic pole is taken as one which will act on a pole of like strength with a unit of force (1 dyne) when placed at a unit distance (1 cm.) therefrom. POLE STRENGTH. The paths in the space surrounding a magnet, throughout which magnetic actions of equal force exist, form closed curves starting from one pole and extending through the surrounding medium back to the other. They are the lines seen when iron filings are sprinkled on a piece of glass or paper under which a magnet is placed, as in the familiar illustrations found in every textbook of physics. When it is desired to ascertain their direction it is done by this sprinkling method, or, when that is not feasible, by suspending a very short and very thin magnetized needle so that it is free to assume any position and plotting its successive directions when moved about in the field to be explored. Such a needle is shown in Fig. 273. Although the number of paths is infinite for every magnet, 343 344 ELECTRIC AND MAGNETIC MEASUREMENTS. by convention lines of force are utilized to designate the strength of the magnetic field as well as to show its direction, one line of force per unit of area (1 square crn.) at right angles to its direction being taken as representing the unit force. This unit force is that exerted by a unit pole at a distance of 1 cm. As the surface surrounding the ideal unit pole is a sphere and has an area of 4?rr, and as r is unity at the unit distance, the number of lines of magnetic force that proceed from a unit pole is 4?r, which is thus the unit pole strength ; its symbol is usually written m. STRENGTH OF FIELD. The strength or intensity of a magnetic field at any point is measured by the force that it would exert on a unit magnetic pole placed at that point, and therefore under the above con- vention is the number of lines of force per square cm. there. Field strength is designated by the symbol If. MAGNETIZING FORCE. Usually the force causing a magnetic flux through a given circuit is supplied by a coil or solenoid of wire through which an electric current is being passed. If that solenoid has a length which is great as compared with its diameter, the direc- tions of the lines of force within it will be parallel except at the ends. If the coil has JV turns, its length is L, and the cur- rent through it is expressed in absolute units (1 absolute unit equals 10 amperes) the magnetizing force of the solenoid exerted on the medium within it is 5 for if a unit pole were moved 10Z/ along one of the lines of force within the solenoid for a distance of 1 cm. its 4?r lines would cut JV-s- L turns of wire, generating an E.M.F. of - and the work done would be - -=- -L \\j_L This is the strength of the field within the coil, and is, there- fore, also the H above. The number of turns per unit of length N of the solenoid is often written ^, that is, -=- = n ; in this case Ju the above formula becomes - MAGNETIC UNITS. 345 MAGNETIC INDUCTION. If the core of the above solenoid were of a magnetic material, say iron, instead of air, while the magnetizing force H would remain the same, the flux of magnetic force through the core would become very much greater. The value of this induced flux is dependent not only on the nature of the material forming the core, that is to say, whether it is of iron, steel, cobalt, etc., but on the magnitude of the magnetizing force, i.e., on the value of H. Flux density is designated by the symbol B, and its unit, the Gauss, is one line of force per square cm. of cross- section. PERMEABILITY. The ratio of the magnetizing force to the magnetic induction, that is, of B to H, is the magnetic permeability, and is usually written /A. If the core within the solenoid is made a vacuum, H equals B and /JL equals 1. The permeability of all gases, liquids, and solids, with the exception of nickel, cobalt, and iron and its compounds, is at ordinary temperatures practically that of the vacuum that is used as the unit. No known substance has a permeability of zero ; that is, there is no known substance that will prevent the flow of a magnetic flux, and none has a sufficiently low value of fji to be considered as a magnetic insulator in the sense that glass, rubber, etc., are electrical insulators. MAGNETOMOTIVE FORCE. The magnetizing force that drives a flux through a reluctance is called a magnetomotive force. As the magnetizing force If is simply the magnetomotive force per unit of length of the magnetizing coil, the value of the magnetomotive force of a 1 - TT T TT 47TJV7 4:7TNI ,, given coil is H, L, or as H = is ^ Magnetomo- tive force is expressed in gilberts, and, as is seen from the formula, a gilbert is .7958 ampere turns. Its symbol is F. MAGNETIC MOMENT. If a straight-bar magnet is freely suspended in a uniform magnetic field it will take up a position such that its axis is parallel to the lines of force. The turning moment tending to 346 ELECTRIC AND MAGNETIC MEASUREMENTS. bring it into parallelism is a maximum when the bar is at right angles to the field and is dependent on the distance between the magnet poles, the strength of the poles, and the strength of the field. If H, the field strength, is unity, the moment, M, of the magnet is the product of the strength of either pole by the distance between them, that is to say, it is ml. INTENSITY OF MAGNETIZATION. The intensity of magnetization, J, of a magnet having its poles at its ends is the pole strength, m, divided by the polar area & It is also the magnetic moment, M y of the magnet divided by its Y volume, V, for if I is the length, V = IS, or S = . The M moment is M Im, or m = Substituting these values in ' A the formula for pole strength, we have = 8 V The relations in a magnetic circuit are governed by the law : flux equals magnetomotive force divided by reluctance, a form- ula that is easily recognized as being analogous to Ohm's law for electric circuits. CHAPTER II. MEASUREMENT OF FIELD STRENGTH. BY CALCULATION. THE strength of the magnetic field within a solenoid having a non-magnetic core may be calculated directly from the form- ula H = - = given on page 344. The number of turns, -ZV, 3 /> is counted, the length of the solenoid, X, is measured, and the current, J, read with the aid of any appropriate currenkmeasur- ing instrument. Where the field to be measured is that of a permanent mag- net, or where for other reasons the method of calculation can- not be employed, means of direct measurement must be resorted to. The first of these is the METHOD OF OSCILLATION OF A MAGNET. This is due to Gauss and is suitable only for the measure- ment of very weak fields, as, for instance, that of the earth. Two sets of observations must be made, the first being the time of oscillation of a suspended magnet, and the second the deflec- tions of that magnet when acted on by the field of another. The first gives the value of the product, MH, from the formula Tf 2 = MR. In this formula K is the moment of inertia of the magnet, t the time of a single oscillation of the magnet, and 6 the ratio of torsion of the supporting thread. If the magnet is a simple geometrical body and known to be homogeneous, its moment of inertia can be calculated from its weight and dimensions in the ordinary way. If it is irregular the following expedient may be adopted. The time of a single oscillation, with the magnet in its original condition, is first observed and re- corded. It is then loaded with a ring whose mass and dimen- sions are known, and whose own time of inertia can therefore be calculated. The magnet loaded with this ring is then set 347 348 ELECTRIC AND MAGNETIC MEASUREMENTS. swinging and the time of an oscillation noted as before. If this time be called ^ the value of MJT= -- ^ - 2 - -^ . The (l + 0) (r -- t x ) ratio of torsion in the formula is the ratio between the restoring forces due to the elasticity of the suspension and to the action of the magnetic fields respectively when the magnet is only slightly deflected from the magnetic meridian. To find its value, the torsion head attached to the suspension carrying the magnet should be twisted through an angle of about 360 degrees and the resulting deflection noted. If the angle of twist of the torsion head is called a and that of the deflection 5, 6= -- The time of oscillation, , is best observed with a o the aid of a stop-watch and a telescope and scale or lamp and scale arrangement, such as that used with reflecting gal^anom- eters (see page 42). The second observation in the oscillation method of measure- ment of weak fields is that of the ratio of M to H. To obtain it, it is necessary to use a magnetometer, a device for comparing the magnetic moments of different magnets. The magnetometer consists of a light silvered mirror, to the back of which are cemented two or three short strips of magnetized watch spring which serve as a small magnetic needle. This will of course hang with its plane in the magnetic meridian. The magnet, whose time of oscillation has been determined, is now placed with its axis at right angles to the axis of the magnetometer needle and will thereupon cause the magnetometer reading to change. The angular deflection of the magnetometer is noted, as is also the distance between the center of the test bar and the instrument. Call the distance between the center of the magnetometer needle and the magnet r. The operation is then to be repeated, using a different value for the distance between the magnetometer needle and the bar. Call this distance ^ and let the corresponding angular deflections be and (p l . The value _ ., is then M _ r 5 tan r f tan <* In testing any weak field extreme care must be taken to see that there are no bodies of magnetic material in the immediate MEASUREMENT OF FIELD STRENGTH. 349 vicinity of the apparatus, and that there are no movable mag- netic masses, even if they are nothing but a bunch of keys car- ried in the pocket, as either will seriously modify the field and introduce large errors in the results. The conditions are par- ticularly difficult when measuring the intensity of the earth's field, as this is always varying slightly in itself and is much influenced by the fields due to current-carrying conductors,, INDUCTION METHODS. (SNAP AND ROTATING COILS.) If a conductor consisting of N turns of wire and inclosing an area, S, is placed in a magnetic field of uniform intensity, J?, it is traversed by a total flux, SH, if its plane is at right angles to the direction of the lines of force. If this coil is sharply rotated through 180 degrees about a diametral axis, an E.M.F. will be induced therein having a value of 2 N/SIL This E.M.F. lasts but momentarily, and a ballistic galvanometer must be utilized if it is to be observed. Suppose such a galvanometer to be attached to the terminals of such a coil, and that galva- nometer resistance is g. Let the resistance of the coil be r and that of the leads plus any auxiliary resistances that may be placed in the circuit in order to bring the galvanometer deflec- tion down to a reasonable point be R. The E.M.F. generated by the rotation of the coil would then cause the quantity of electric- 2NSH ity q = p to flow through the galvanometer circuit. The value of _/Z~can be calculated directly from this formula if the galvanometer constant is known. The latter can be found for any particular instrument by discharging a condenser through it, in the usual manner. If the gap in which the field to be measured exists is so narrow that it is impossible to rotate the coil of wire, it can be sharply moved by hand at right angles to the lines of force or the same thing accomplished with a trigger-released, spring- actuated device. In this modification the formula becomes JTa 7 7VT , in which I is the distance through which th coil has been moved. This latter method must be used in the narrow clearance space existing between the armature and the pole pieces of a dynamo or motor, and the coil is usually moved, not between two fixed 350 ELECTRIC AND MAGNETIC MEASUREMENTS. limits, but between a position in the gap and one outside of it where the field does not exist, as this is easier than attempting to arrest a coil suddenly and accurately. The rotation method is more convenient when there is sufficient space to allow of revolving the coils, and is specially useful in measuring the intensity of the stray field of generators. If the angle of rotation is made exactly 180 degrees, the results obtained are very reliable. The rotating coil method may also be used for the determina- tion of weak fields such as that of the earth if the coil area S is made very large. BISMUTH SPIRAL. The metal bismuth has the peculiar property of offering an increased electrical resistance when placed in a magnetic field. The intensity of the field can be measured from this increase in FIG. 274. resistance, being proportional to the difference between the re- sistance when in the field and when out of it divided by the re- sistance when out of it. The actual apparatus for measuring field strength in this way takes the form of a flat spiral of bismuth wire doubled back on itself, so as to avoid induction errors, and attached to a handle as shown in Fig. 274. The windings are held in place by being cemented between two plates of mica and form a coil so thin that it can easily be intro- duced into the clearance space between an armature and its field magnets. The resistance of the coil when not within the MEASUREMENT OF FIELD STRENGTH. 351 influence of a field is usually made about 10 ohms. The relation between the field strength and resistance is determined separately for each spiral and remains sensibly constant under all commer- cial circumstances. The varying resistance is easily determined with the aid of a bridge, and the field strength found by consult- ing a table or curve which comes with the coil, or in some instances, by having the bridge specially calibrated, so that when used with a given spiral the values of H are indicated directly. Fig. 275 shows the calibration curve of an average specimen. ELECTROMAGNETIC METHOD. In the commercial ammeters and voltmeters of the permanent magnet pattern described in Chapter VI, current strength is measured by the reaction between a constant field and the 0.7 0.6 ?Q5 0.4 0.3 0.2 O.I QO ^ x^ x*"^ ^ x* ^x ^ \ x^ "5? x^ x x^ ,- - ^ 2000 4000 6000 8000 10000 GOOD <4000 BOO F Lines of Force per Sq Cm FIG. 275. unknown current, as indicated by an index attached to a moving coil working against a spring which offers an opposing force like the spring in a spring balance. It is evident that the reverse of this method can be used to measure the strength of the field if the strength of the current flowing through the movable con- ductor is known. An apparatus based on this principle is shown in Fig. 276. Here a conductor, , is rigidly attached to an arm, (7, a known current measured by an ammeter being passed through I by means of the flexible strips//'. If I is introduced into the gap in a magnetic circuit so that the current through it flows at right angles to the lines of force, it will be -acted upon by a force IHl in which I is the current, H the field inten- sity, and I the length of the conductor. The force is measured by varying the tension of the spring R by turning the screw V. 352 ELECTRIC AND MAGNETIC MEASUREMENTS. The screw is calibrated so that the force exerted is known and a micrometer index attached to it can therefore be made to indi- .p FIG. 276. cate field strengths directly with the current J adjusted to a given value. The shortness of the length, 7, and the small current that may be passed through it because of the neces- sity of making the conducting strips, //, so thin that they offer no appreciable resist- ance to Z's movement, makes the forces involved small, so that such apparatus can be used only for the measurement of power- ful fields. Various modifications of this apparatus dependent on the reaction between the field and a current-carrying conductor will sug- gest themselves. MIOT INDUCTIOMETER. An interesting piece of apparatus for measuring field strength is the Miot In- ductiometer illustrated in Fig. 277. It consists of a three-legged glass tube filled with mercury to the level shown by the heavily shaded areas. A similarly shaped but shorter three-legged tube is attached to its lower end by means of rubber tubing, so that it can be placed at any desired angle to the upper one. The lower member of the short tube is placed in the field whose strength is to be measured and current passed FIG. 277. MEASUREMENT OF FIELD STRENGTH. 353 through the mercury contained therein in the direction indicated by the arrows. The position of the lower tube is made such that the flow of current traverses the fields perpendicular to the lines of force, and therefore the reaction between that field and the current through the mercury causes the latter to rise in the central tube. The elevation of the mercury there, as indicated by the rise in the surface of the column of liquid that is poured over its surface, is proportional to the field strength and to the current through the mercury, in other words, ITequals KhL K is a constant which is separately determined for every inductio- meter, n is the head of liquid as measured by the scale placed alongside of the central tube, and Jis read from an ammeter placed in the current circuit. For any given current the scale can evidently be divided so as to show If directly. CHAPTER III. MEASUREMENT OF PERMEABILITY. THE determination of the permeability, /-t, of various speci- mens of magnetic material is of the utmost importance in the calculation of electrical machinery, as on this quality depends the magnetizing force that must be supplied to obtain a mag- netic field of sufficient strength to obtain the desired reactions. It is more difficult to make this determination than that of electrical conductivity, chiefly because of the fact that a joint in a magnetic circuit such as must be used in the majority of permeability measuring devices has, unless made with extreme care, a magnetic resistance that is so high as compared with that of the iron that errors amounting to over 100 per cent are only too readily introduced. Take, for instance, a case in which the air gap between two of the magnetic conductors forming the circuit is as small as .01 mm. ; if /JL is 2000 this is the resistance of a four millimeter length of the iron and means that a corresponding error will be present in the result. It is there- fore clear that with short specimens great pains must be taken to obtain a perfect magnetic contact, machining the surfaces as true as possible and then tightly clamping them together by appro- priate devices such as screws, etc Another difficulty in per- meability measurements is that, as already stated, there is no magnetic insulator, and hence no way of confining the flux to a given path, so that leakage factors of unknown magnitude must be allowed for. As the value of ft varies with different values of the magnet- izing force, it is necessary, in order to obtain a complete record of the behavior of a given specimen, to subject it to fields of varying intensities. A specimen should first of all be entirely demagnetized ; to accomplish this, it is surrounded by a magne- tizing coil through which an alternating current is passed of a value such that the bar will be magnetized more strongly than it has been since subject to the last magnetization. The current should then be gradually decreased in strength by 354 MEASUREMENT OF PERMEABILITY. 355 inserting an external resistance until it is reduced to the lowest possible value, whereupon it should be cut off. The minimum value of the demagnetizing current should be made very low indeed, this being conveniently accomplished by utilizing a liquid resistance, in which the distance between two plates immersed in an electrolyte may be constantly increased until one plate is finally withdrawn. The bar is now magnetized by passing a small current through the surrounding solenoid and observing by one of the methods to be described later on the flux induced therein. The exciting current is then increased by successive steps and the various values of B corresponding to different ones of H plotted in the form of a curve. A set of such curves from soft steel, wrought iron, and cast iron specimens is shown in Fig. 278. It will be noted that in each case the value of B increases with an increase in the value of H, at first quite slowly, then more rapidly to a maximum rate, and finally more slowly again. If the curve were prolonged at the upper end it would be found that a value of H would soon be reached at which the curve became a straight line, B increasing in direct proportion to H only and the iron thus acting like an air core. At this point the iron is said to be " saturated." For reasons that will be made apparent in the chapter on hysteresis, it is necessary in all permeability tests to see that the strength of the magnetizing current is increased from each step to the next and not allowed to first fall and then rise to the new value. MAGNETOMETRIC METHOD. The permeability of a given specimen may be determined with the aid of a magnetometer as follows : The specimen should be a rod having a length at least four hundred and preferably as much as five hundred times its diam- eter, and be enclosed in a magnetizing coil which is slightly longer than itself. The rod should be placed vertically at a known distance from a magnetometer. The solenoid that energizes the bar in itself affects the magnetometer, and this action must be compensated for by the addition of coreless solenoid placed with its axis horizontal in a position found by experiment where the current passed through it, and the bar solenoid in series no longer produces any effect. 356 ELECTRIC AND MAGNETIC MEASUREMENTS. It is generally found that the vertical component of the earth's magnetism acts on the test specimen also, and this must then be compensated for by an auxiliary winding through which a current of appropriate strength is kept flowing. A rheostat FIG. 278. is inserted in the circuit energizing the vertical compensating winding, and another in that of the bar energizing solenoid, so that the value of H may be adjusted at will, the whole appa- ratus being connected as shown in Fig. 279. MEASUREMENT OF PERMEABILITY. 357 After being set up, the compensation for the effect of the main solenoid on the magnetometer is accomplished by shifting the coil as already indicated. The adjustment of the current through the solenoid that compensates for the vertical compo- nent of the earth's field is affected by first causing the maximum current to be employed to flow through the main winding and then gradually decreasing it to zero by increasing the resistance in the rheostat R, the current being rapidly reversed at the same time by means of a suitable commutator. If the magnetometer shows no traces of magnetism of the bar when R has reduced the current value to zero, the strength of the current through a b is correct; if action does exist, the strength of the current through ah must be adjusted until this disappears. We now have the equip- ment so arranged that the strength of the magnet N iS can be measured by the mag- netometer, this being ob- tained in terms of the strength H e of the earth's field at the point of obser- vation. The test bar is so long that its poles maysafely be assumed as being at the extreme ends, and the dis- i ,, , FIG. 279. tance between the poles is so great that the magnetometer may be considered as being in- fluenced by the upper one only. To obtain the curve showing the value of //. the magnetizing current is increased in the desired number of steps and the corresponding values of the induction plotted. The value of H, the magnetizing force, is obtained from the formula JQ- which has already been given. Owing to the fact that it is necessary to know the value of the earth's field where the permeability test is being made by ^*-i^W^eA^4^-*^xAe^c^^ 858 ELECTRIC AND MAGNETIC MEASUREMENTS. magnetometric method as well as to the complication of the apparatus involved, and the fact that the test bar must be of dimensions such that it can rarely be a piece selected from material that is to enter into the construction of electrical appli- ances, this method is but seldom used outside of a laboratory. Its chief value is in the determination of the permeability at very low magnetizing forces, as these act sluggishly and the magnetometer will record the final effect, whereas in most of the other methods to be described further on such is not the case. BALLISTIC METHODS. In the snap coil method of measuring field .strength the E.M.F. induced in the coil by its movement through the field as indicated by a ballistic galvanometer is used to determine the strength of the field. As relative motion between the coil and the magnetic flux is all that is necessary, the same results may be had by keeping the coil stationary and causing the flux cir- cuit to collapse, so that the lines of force cut the coil. Straight Bar Ballistic Test. If the specimen to be measured can be supplied in the form of a long thin rod of the dimensions mentioned in the preceding paragraph, its permeability can be determined with a ballistic galvanometer as follows : The bar- is placed within a magnetizing solenoid as before, but wound around the center of the solenoid there is placed an auxiliary winding of several turns of wire whose terminals are connected to the ballistic galvanometer. If current is suddenly sent through the solenoid, or if a current already flowing through it is abruptly interrupted, an E.M.P. will be induced in the test coil, which will be shown by the deflection of the ballis- tic instrument. If if is the galvanometer constant, /the current strength, and N the turns per centimeter length of solenoid the 4 TrNI S value of B can be found from the equation B = K ^ X -~ in which s is the galvanometer throw with the test bar in place, arid S the same before the bar was inserted. Successive values of fju are obtained by making as many successive readings. Rowland Method. In this the specimen to be tested must be circular in shape having a small radial breadth. This ring is covered by hand MEASUREMENT OF PERMEABILITY. 359 with a known number of turns of wire, and the strength of the current flowing therethrough may be regulated as desired by means of a rheostat, and measured by an ammeter, as shown in Fig. 280. Over a section of the magnetizing winding there is wound a test coil of several turns of fine wire having its termi- nals connected to a ballistic galvanometer. In making the test the ring must first of all be thoroughly demagnetized by the method outlined above. Current is then caused to flow through the energizing winding, and when this is suddenly made or broken the change in flux will produce cur- rents in the exploring coil, and these, as indicated by the galva- nometer, form a means of obtaining the data sought. The value , 4*rwJ -rllO 10* . , . , _. . of IT is ., . _ as above, and of J5, K= in which JTis the 10 I 2 an galvanometer constant, R the resistance of the test coil circuit, 6 FIG. 2 the throw of the galvanometer, a the cross-sectional area of the ring, and n the number of turns in the test coil From the two we have the value of /z. While it is easier to make the test specimen in the form of a ring than to obtain the long straight bar, the inconvenience of placing the winding on it by hand is so great that this test is seldom resorted to. A modification which overcomes this dis- advantage is the Hopkinson Divided Bar Method. Here the test specimen takes the form of a rod again, but one of convenient dimensions, usually about one half inch diam- eter by 14 to 18 inches length, cut into two parts. This rod is inserted into holes drilled in a very heavy wrought-iron yoke, as illustrated in Fig. 281. The right-hand half of the bar is solidly secured in place by means of a clamp screw, but the left-hand 360 ELECTRIC AND MAGNETIC MEASUREMENTS. one may be pulled out by means of the handle shown. The exciting coil supplying the magnetomotive force to drive the flux through the specimen is in two parts, wound on appropriate bobbins, and separated by a space sufficient to admit of the insertion of another and so-called test coil wound concentrically with the exciting coil. The exciting current is taken from a set of batteries, measured by an ammeter and sent in one or the other direction through the coils with the aid of a reversing switch. The test coil has its terminals attached to a ballistic galvanometer, as is shown in the figure. This test coil fits loosely in its place and an elastic cord keeps it pulled against the test bar, so that if the movable section is pulled out the test coil will be snapped out sidewise clear of the whole apparatus. FIG. 281. In making the test the exciting current is adjusted by the rheostat to the desired value in the regular way, the test bar handle pulled so that the test coil snaps out and the resultant galvanometer deflection is noted. As the test coil cuts the whole flux present when the handle was pulled the galvanometer deflection is a measure of the flux. The formula connecting T>A the two is B = K~ 10 8 , the significance of the symbols being as before. The magnetizing force, #, is calculated from the number of turns in the exciting coil and the strength of the current flowing through it as usual ( H = 57^7- ) \ 1U I / MEASUREMENT OF PERMEABILITY. 361 In this divided bar method, correction must be made for the fact that, as the test specimen does not fit closely within the exciting coils, many lines of force pass through the test coil that do not flow through the specimen. The value of this correction is easily determined by making a preliminary measurement, using a non-magnetic test bar in place of the regular specimen. The Hopkinson method assumes that the magnetic resistance of the yoke is so small that the length of the magnetic circuit is the length of the bar between the yoke faces. It also assumes that the magnetic resistance between the test bar and the yoke is negligible. Neither assumption is rigorously correct and the method can hence be used only when approximate determinations are all that are required. The Drysdale Permeameter. A great objection to most of the devices for the measurement of permeability is that it is necessary to prepare special test specimens. Where these are made from lots of sheet metal such as is used in the construction of transformers and armatures, the specimen can as a rule be safely taken as a fair representative of the character of the lot. When, however, the test is to be made on cast metal, either iron or steel, such as enters into the construction of dynamos and motors, a test bar cast from the same pouring as the frame itself cools so much more quickly than the rest that the physical character of the metal is changed, and this affects the magnetic qualities very seriously. To cut a piece out of the casting is both expensive and unreliable, as if a fin-like projection is left to be machined rapidly as off it will cool much more would a separate test bar. A device to overcome these objections has recently (see " Proceedings of the American Institute of Electrical Engi- neers," November, 1901) been devised by Drysdale. A special drill is used with which a hole is drilled in the mass of the material to be tested, leaving a cylindrical central core, as shown by the cross-sectional illustration given in Fig. 282. A tapered iron plug carrying at its lower extremity a pair of coils FIG. 282. 362 ELECTRIC AND MAGNETIC MEASUREMENTS. of insulated wire is arranged to fit in this hole and when pushed in place, as shown by Fig. 283, forms a magnetic circuit in which the central core left is energized by one of the coils, the other coil being for connection to a ballistic galvanometer, as in the case of all tests of this kind. The return mag- netic circuit is through the surrounding body of the mass of metal under test, and through the testing plug. Connections are made, as in Fig. 284, and the various galvanometer throws corre- sponding to the reversals in the exciting current with different values of that cur- rent are plotted in the regu- lar way. In order to have a com- plete self-contained commercial apparatus, the batteries, the rheostat for varying the strength of the exciting current, the reversing switch, the ammeter for measuring current strength, and the ballistic galvanometer are all built into one case, as shown in Fig. 285, a compartment being added to receive the test plug and the cords making connection with same. The FIG. 283. FlG. 284. ammeter, JL, is calibrated in amperes, and the ballistic galvano- meter, B, is made with a needle swinging over a scale instead of a light spot and is calibrated directly in gausses. It is advisable to make the test at three or four different points MEASUREMENT OF PERMEABILITY. 363 in the mass ol metal under examination, to be sure that no error has been introduced because of drilling into an unexpected flaw. When necessary to restore the original condition of the mag- netic circuit as fully as possible, a soft iron plug can be machined which will fit in the opening left by the drill after the test is completed, and if this is solidly driven home but little difference need be expected. The length of the test bar is short, but the character of the contact made by the testing plug is exeptionally good and of large area, so that for high densities such as are used in practice, the results obtained can probably be relied upon with confi- dence. The Quantometer. Where ballistic test methods are used in determining the permeability of large masses of iron, some difficulty arises JPlO. 285. in employing an ordinary ballistic galvanometer, as the mag- netic flux does not instantaneously attain its proper value when the current strength is changed to a new amount. As has been explained in the chapter on ballistic galvanometers, these give correct indications only when the duration of the applied current is so small as compared with the period of swing of the instrument that the former has all passed before the galva- nometer needle has a chance to make a sensible deflection. The time required for the attainment of the maximum flux value in a large mass of metal may be as high as thirty or even sixty seconds, which is far too great as compared with the eight to twenty seconds period of the ordinary ballistic instrument. 364 ELECTRIC AND MAGNETIC MEASUREMENTS To overcome this difficulty, the " quantometer " has been suggested. The quantometer is a galvanometer whose deflections are pro- portional to the quantity of electricity passed through it in spite of this long-time lag. It consists of a d'Arsonval galvanometer with a pivoted coil, like the instruments described on pages 156 to 161, but in place of the volute springs which oppose the coil motion it is equipped with fine filaments of silver or strips of phosphor bronze such as are used for galvanometer suspensions and which are disposed so as to offer no appreciable resistance to the coil motion. The windings are on a short- circuited metallic frame like that which serves to dampen the indications of the d'Arsonval instruments mentioned. Without going into the theory of the instrument, it may be stated that with an apparatus of this nature the deflections are proportional to the quantity of electricity that flows on the assumption that the pivot friction is negligible, the restraining force of the conducting strips nil, and the duration of the cur- rent practically zero. A correction can, however, be applied to allow for the fact that none of these conditions is rigidly correct, and this feature admits of the use of the apparatus for the pur- pose named. (See London Electrician, Dec. 26, 1902.) TBACTIONAL METHODS. A magnet with its one pole in contact with a block of mag- netic material attracts the block with a force expressed by the formula p = 27rJ 2 $, in which S is the cross-sectional area of the pole face. From this the permeability of a given specimen can be determined if the magnetizing force, If, is known, and the latter can be calculated from the strength of the current flowing and the number of turns of the magnetizing coil by the formula H = 4-77 n i (for a long coil) already given. The formula expressing the value of the permeability then is J**p V H*s 1. Thompson Permeameter. One of the earliest permeability measuring instruments depending in principle on this tractive force between a magne- MEASUREMENT OF PERMEABILITY. 365 tized bar and a mass of magnetized material is the Thompson permeameter. As is shown in Fig. 286, it consists of a heavy rectangular yoke of iron, having a hole bored through one side, through which the test rod passes. The point on the inner surface of the oppos- ing yoke against which the test bar rests is carefully machined off to have a perfectly smooth surface, and the test bar end is like- wise treated. It is advisable to have the made slightly ce//& H w-yya-gVgN *' Ybffe Surfaced here FIG. 286. latter conical. The magne- tizing coil wound on a brass tube surrounds the specimen and is itself so inclosed by the yoke that practically all of the lines of force flow through the iron circuit. There is no pull on the test rod where it passes through the upper member of the yoke, as the direction of the lines of force there is at right angles to it. By means of a spring balance whose upper ring is attached to some hook that can be gradually lifted, the pull re- quired to separate the test specimen from the lower leg of the yoke is read off and the value of the magnetizing current simul- taneously read by means of an ammeter. Thompson gives the following formula for the permeability : (1) B = 131T + H H. (2) B = In this, P is the pull in pounds in the first formula o: in grams in the second, and A the area of contact of the test bar in square inches for the first formula and in square centi- meters for the second. If the above are compared with the first equation giving the portative power of a magnet as above, they will be found to be substantially alike. 366 ELECTRIC AND MAGNETIC MEASUREMENTS. Several sources of error exist in this apparatus which are of such magnitude that it is not suitable for work of laboratory accuracy. It can, however, be used for demonstration purposes, and serves fairly well as a comparison instrument for comparing the permeabilities of a standard bar and an approximately similar unknown one at high flux densities. The sources of error in the tractional permeameter are : The variable air gap where the bar passes through the hole in the yoke ; the uncertainty of the contact between the lower end of the bar and the portion of the yoke on which it rests ; the increasing leakage at the lower end of the bar with increasing magnetization, which leakage lines are not effective in increas- ing the force resisting separation ; and the fact that the square FIG. 287. root of the pull is involved in the formula which makes a small error in observation of the spring balance or in the calibration of the same, be a larger and larger per cent as the pull and therefore the magnetizing force decreases. The last objection has so much weight that in practice the instrument cannot be used at all for the determination of per- meability at low values of magnetizing current. Comparative values of specimens of metal for commercial use can, however, be quickly measured by tractional permeameters, more particularly as these are generally worked at high mag- netic densities. A commercial permeameter is shown in Fig. 287, where a spring put in tension by turning the hand crank shown MEASUREMENT OF PERMEABILITY. 367 measures the force required to separate the specimen from the yoke. Another tractional permeameter is shown in Fig. 288. Here sand is allowed to flow through the pipe, T, into a bucket, P, until the test speci- men is torn away, whereupon the flow of sand is at once cut off and the weight subsequently ascer- tained. Ewing Balance. In this instrument for measuring per- meability by t r a c- tional force, an effort is made to eliminate the error due to the variable contact be- tween the test speci- men and the mass of metal closing the magnetic circuit by the expedient shown in Fig. 289. The test bar, E, is made circular in section as usual, and one of its ends rests in a V-shaped notch cut in one end of the iron spool about which the magnetizing coil, B, is wound, the other end resting on a rounded surface at the other end of the spool, as shown at a. The contact between E and FIG. 288. a is necessarily a point, being the contact between two cylin- drical surfaces at right angles to each other. The V-shaped depression in which the end of the specimen E rests forms a kind of a hinge, so that when a lifting force is applied by the steel yard arrangement, F, a alone is raised. The 368 ELECTRIC AND MAGNETIC MEASUREMENTS. force tending to tear the test specimen away from the magnet- izing block is, of course, obtained by sliding the weight, P, out along the graduated arm of the steel yard. In the commercial use of this device the current strength is not fixed by means of an ammeter, but a standard bar is first inserted, and the current varied until it just lets go for a pre- determined position of P. The test bar is then substituted for the standard and the position of P which causes this to be pulled away, is noted. The steel yard is graduated directly in gausses and forms a convenient although somewhat crude arrangement for some workshop tests. ATTBACTIONAL METHODS. Du Bois Magnetic Balance. In this instrument the test specimen, D, Fig. 290, is usually made a rod about 15 centimeters long. By means of clamps its y/////////////////////////////. FIG. 290. ends are brought into close contact with heavy iron pole pieces, P and P, and the magnetic circuit is completed through these, the air gaps, J^and E, and the heavy yoke, F. The magnetizing sole- noid, J5, surrounds the specimen. F is provided with a pair of knife edges located opposite to one another at the point, A, the peculiar distribution of metal shown by the figure being such that the yoke is balanced around A by the weights of the two ends. When current is passed through B the force of magnetic attraction at each of the faces, E and E, is evidently the same, but as the pull through the left-hand gap acts on a longer lever arm, the yoke, P, will tend to descend at that end. This force is balanced by moving the small sliding weight MEASUREMENT OF PERMEABILITY. 369 shown in Fig. 291 along the top of the yoke. Limiting stops are placed at each end of the yoke, one of them, as is shown to the left in Fig. 290, being usually provided with a pair of plat- inum contacts connected in circuit with a battery, and a galva- nometer or bell, so that if that yoke end descends appreciably be- low the normal position, a warning is instantly given. The attraction of the pole pieces on the yoke varies as the square of the flux through the magnetic circuit, and for a given magnetizing current the graduated scale alongside of which the movable weight slides may therefore be calibrated directly in FIG. 291. gausses, the proper allowance for the reluctance of the pole pieces, the air gaps, and the yoke having first been experiment- ally determined and allowed for. The reluctance of the air gaps in this instrument is so great as compared with that of the resistance of the rest of the circuit that small variations in the resistance of the joints between the test specimen and the pole pieces introduces no material error. DEFLECTIOXAL METHODS. If a known current is passed through the movable coil of any of the d'Arsonval types of instruments previously described, the deflection of the needle attached thereto will be in propor- tion to the strength of the magnetic field in which the coil 370 ELECTRIC AND MAGNETIC MEASUREMENTS. works. The flux that forms this field is, for a given strength of current through a solenoid surrounding an iron core to whose ends are attached the pole pieces between which the coil swings, proportionate to the permeability of the core. Instruments for the measurement of permeability based on this principle may conveniently be termed of the deflectional type. Koepsel Permeameter. This prominent instrument based on the above deflectional method is shown in section in Fig. 292. The test bar, E, is placed within the magnetizing coil, B, and firmly clamped in place by means of thumb screws to eliminate as far as possible errors due to the i ints - The heav y iron p le pieces, JJ, embrace the mov- able coil, 5, and to the latter is attached a pointer which swings over a scale graduated directly in gausses. In mak- ing a test current of a known value is, sent through b and the deflection corresponding to different strengths of current through B noted. The complete apparatus is illustrated in Fig. 293, the batteries being shown behind the instrument and the rheo- FIG. 292. FIG. 293. stats for regulating the strength of the current through the magnetizing coil and the moving coil respectively to the right MEASUREMENT OF PERMEABILITY. 371 and left of it. The batteries supply the current for b only, that necessary for B being drawn from a separate source, usually storage, batteries, and measured by a separate ammeter. Carpentier Permeameter. This instrument shown diagrammatically with its accompany- ing connections in Fig. 294, and in perspective in Fig. 295, is somewhat similar to the Koepsel device, but the flux through the heavy iron yoke pieces that complete the magnetic circuit is measured in another way. As is shown in Fig. 294, a small rectangular gap is left at the points of junction of the two yokes, in the upper one of which there is freely suspended a short mag- netic needle. When a flux passes through the yoke the needle of course tends to place itself parallel to the lines, and the FIG. 294. needle attached thereto which can be seen inside of the little rectangular box on top of the apparatus in Fig. 295 is deflected. By turning the knurled head shown in the same figure a spring is wound up, which as in the electro dynamometer (see page 165) introduces a measureable opposing force and brings the needle back to its original position again. The angle of twist of the knurled head required to bring the index to the zero mark is for ach value of the magnetizing current, a measurement of the flux through the yokes, and the permeability of the test speci- men can therefore be determined by reference to a calibration curve which accompanies the apparatus. BRIDGE METHODS. Various magnetic analogues of the Wheatstone Bridge have been proposed and constructed from time to time. The origi- 372 ELECTRIC AND MAGNETIC MEASUREMENTS. nator of the plan seems to have been Ewing, whose bridge is shown in Fig. 296. Two bars of identical dimensions are em- ployed, one of them, A, being a standard, and the other the one whose permeability is to be measured. The ends of these bars are clamped into heavy iron yokes, (7(7, and a pivoted magnet- ized needle, #, placed between their extremities serves to indi- cate whether these yokes are magnetized. The bar, 5, shown is a short permanent magnet which is used to give directive force to the pivoted needle. A and B are surrounded, each with its own magnetizing coil, the two being connected in series, but opposed so that the direc- FiG. 295. tion of flux through the one is opposite to that in the other. The number of turns around the standard specimen is fixed, but that around B is variable by means of a contact arm whose end can be moved over a row of contacts connected to different turns of the winding. This contact arm device is equipped with auxiliary resistances, so that each time a coil is cut out of the magnetizing circuit an equivalent resistance is added to the circuit, so that the strength of the current flowing remains uniform. MEASUREMENT OF PERMEABILITY. 373 When the flux through each specimen is the same, the path of the lines of force is evidently along one and back through the other, none being com- pelled to flow through the yokes and across the gap. No deflection of the nee- dle, a, thus means that the fluxes are the same. In practice the number of turns surrounding the test bar is varied until the needle, a, no longer shows a permanent deflection with the current flowing in one direction or the other, whereupon it is known that the fluxes furnished by the two speci- mens are alike since they neutralize each other. Their permeabilities are hence in the ratio of the turns. To obtain the complete permeability curve the strength of the current being used must be measured by means of an ammeter and successive readings made for different values. MISCELLANEOUS METHODS. The large errors introduced by the variable value of the con- tact between a test specimen and the heavy iron yokes used in most permeameters has led to many attempts to devise some satisfactory method that will give results which are independent of this element. One of the early ones is due to Ewing and operates as follows : Referring to Fig. 297, A is a standard bar and B the one to be measured. Holes are drilled in the iron yokes, and D, into which these bars fit snugly, the contact being made as solid as possible by means of the clamp screws. Solenoids through which are passed the magnetizing current surround both test specimens and are made of a length that just fits between FlG. 296. 374 ELECTRIC AND MAGNETIC MEASUREMENTS. and D with these in the position shown in the figure. An ex- ploring coil surrounds one of the solenoids and the value of the flux through B is found in terms of that through A by a method similar to that used in the Rowland test before described. The magnetic circuit in this case evidently includes the reluctances of the bars A and B plus that of the yokes, O and D, plus that of the four joints between the bar ends and the yokes. After making a determination with the yoke, D, located as illustrated, the clamp screws holding it to the bars are loosened and the yoke slides along to a new position. The test is repeated there, and from this and the preceding one the induction in the test specimen is calculated. As the contacts between the } 7 oke, C, and the two bars are undisturbed their reluctance and that of the yoke is eliminated. The same thing holds good of the re- luctance of the yoke, D, so that the result is correct if the \nag- 'A U c D 1 B i 1 : i i FlG. 297. netic resistance of the joints between A and D and B and D is the same in the first position of D as in the second. It is unfortunate that this last assumption is not entirely valid and that the arrangement therefore gives permeability values which while amply close for practical purposes at high magnetic densities are not sufficiently exact for accurate work or at low densities. Picou Permeameter. In this instrument devised by Picou and modified by Armag- nat, the method of eliminating the errors due to the variable resistance of the magnetic joints is entirely different Referring to Fig. 298, the test specimen, 6, is made rectangu- lar and may take the form of a prism of solid metal or of several layers of sheet iron such as is used for transformer and arma- ture work. There are two yokes, B, B 2 respectively, which are MEASUREMENT OF PERMEABILITY. 375 /M, 111 M U shaped and between the ends of whose legs the test specimen is inserted. Magnetizing coils surround all three as shown and suitable resistances, R^ R^ are inserted in the yoke and test specimen circuits, so that the strength of the current flowing through them may be varied at will. The measurement of the permeability of b involves two steps. First of all, current is sent through the sole- noids surrounding the yokes in such a direc- tion that the resultant magnetic fluxes form a closed path through the yokes only, as is shown by the dotted lines in Fig. 299. Under these circum- stances it is clear that there is no flux through the bar, 5, itself, and that the reluctance of the magnetic circuit is that of the material composing the yokes plus that of the four joints between the test specimen faces and the yoke ends, plus the reluctance of those portions of the length of the test bar, lettered e and a respectively, in Fig. 299. Suppose that under these conditions the flux through the circuit is ascertained by making a ballistic test or in any other convenient manner. The permeability of the circuit can then be calculated from the magnetizing force due to the meas- ured current through the exciting solenoids in the ordinary way. The electrical connections are then changed so that uie direc- tion of the current in one or the other of the exciting solenoids is reversed, with the result that the flux directions through BI B 2 are opposite, as shown in Fig. 300. The magnetic circuit FIG. 298. 376 ELECTRIC AND MAGNETIC MEASUREMENTS. X- I 1 EHxji \ c b a l A 1 i \ lEjEBE- FIG. 299. for each yoke is then completed through the test specimen, and as the reluctance of this circuit is greater than the first by that of the specimen ^ ^ X-K/ for its length, e, the flux through both B l and B 2 is lessened. By passing current through the sole- noid surrounding the test specimen in the proper di- rection a magneto- motive force is set up, which can be adjusted by ma- _ stipulating the rheostat, R^ Fig. 298, until the flux through B l and B 2 becomes again what it was under the conditions in Fig. 299. The reluctance of the test specimen may then be calculated directly from the strength of the current that must be passed through its surrounding solenoid to bring about the above state of affairs, for the magneto- motive force that the coil must sup- ply is just that required to force the known flux through the speci- men, that required to overcome the reluctance at the joints having been accounted for in the first measurement. Knowing the strength of the current around b and the number of turns in its solenoid, the magnetizing force, and therefore finally the permeability, may be determined direct. ""*\ ~ ~ ~r 1 ~^~Y~\~\~ ^ \ \ \ < > 1 1 1 1 b~ "Yiife-fiz -' \ j u L v, ^ \ \ \ 1 \ EEEQE 1 *s ^^ FIG. 300. MEASUREMENT OF PERMEABILITY. 377 Owing to the great superiority of zero methods of measure- ment over methods involving values of deflection, considerable thought has been devoted to modifying this Picou apparatus to bring it into this category. As a result it is now generally FIG. sou supplied arranged as follows : As shown in Fig. 301, a fine wire winding acting as an exploring coil surrounds each yoke and the test specimen. An auxiliary transformer, T, is also employed which is energized by being placed in series with the magnetiz- FIG. 302. ing windings surrounding the yokes and whose transformation ratio may be manually adjusted at will. The secondary circuit of the auxiliary transformer is completed through the two 378 ELECTRIC AND MAGNETIC MEASUREMENTS. exploring coils on the yokes, connections being made so that the E.M.F.'s induced therein are opposite to that induced in the coils. It can readily be seen that by suitably adjusting the trans- formation ratio of T the effect on a galvanometer, 6r, inserted in the coil circuit may be made zero ; the fact that equilibrium has been thus attained must be carefully established by several reversals of the direct magnetizing current. To determine the flux in the bar, , after the electrical con- nections are changed so that the magnetic circuit is completed through it, a special commutator is employed, which cuts the solenoids of B\ and B? out of circuit at the same time that 5's . 303. solenoid is inserted. The discharge through 6's test coil circuit is passed through a ballistic galvanometer, whose scale may be calibrated directly in gausses. The portion of the instrument containing the two yokes with their soils plus the commutator and reversing switch is shown in Fig. 302, that of the portion of the apparatus including the rheostat and galvanometer being illustrated by Fig. 303. It is claimed that the results obtained with this device are of the highest accuracy and that the elimination of the resistance at the joints is so far successful that a practically identical set of readings is obtained for a given stack of sheet iron strips for the order in which they are first placed in the apparatus and that MEASUREMENT OP PERMEABILITY. 379 which they show when subsequently removed, mixed up at ran- dom, and then replaced. Burger Permeameter. This device, while probably not capable of giving as accurate results as the preceding, is in quite extended use and has the advantage of giving the results very rapidly. In it the test bar is cut in half and mounted on a heavy iron yoke in a manner somewhat similar to that employed in the Hopkinson divided bar apparatus. The magnetizing coil surrounds the specimen in the same way also, but instead of having a snap coil in the gap between the bar ends, a bismuth spiral is inserted, as is shown in Fig. 304. The variations in electrical resistance of this spiral form a measure of the strength of the field in which it is placed (see page 350) and hence of the permeability of the rod undar test. As made by Hartmann and Braun, the Burger permeameter is made one self-contained piece of apparatus, as is illustrated in Fig. 305, and includes the yoke with its clamps, magnetizing FIG. 305. coil, and bismuth spiral; two slide-wire bridges, one to make temperature corrections and the other for measuring the resis- tance of the spiral ; a galvanometer for use with the bridge ; an ammeter for measuring the exciting current; a combination galvanometer and battery key for the bridge, and a reversing switch for the energizing circuit. CHAPTER IV. HYSTERESIS. IF we start with a completely demagnetized iron specimen and draw its permeability curve by any of the methods just given the curve will, as has been explained, take the form shown by the solid line in Fig. 306. If after the maximum desired value of H has been been attained the exciting current is (B 16000 15000 14000 19000 12000 11000 10000 9000 7000 000 eooo 400C sooc JOOO 14 16 41 _*0 *3 21 26 28 80 FIG. 306. decreased step by step, the values of B corresponding to those of If will no longer coincide with those found in the initial test, but will give a set of readings which when plotted will form the dotted curve in the same figure. If the direction of H is now reversed, the value of B will continue decreasing until it comes to zero and will then itself reverse in direction until 380 HYSTERESIS. 381 a maximum negative value is attained which will be found equal to the positive value corresponding to the same maximum posi- tive value of H. If H is then brought back to zero, reversed, and then increased, again a similar curve will be given which will join the first when H has reached its first positive maximum value. The curves form a closed figure shown in Fig. 307, which is known as the hysteretic loop. It will be retraced as often as the magnetizing force is made to go through the same cycle of changes in strength. The shape of the loop depends not only on the metal under test, but its physical condition, being, for instance, much more elongated and of larger area for a hard tempered piece of steel than for one cut from the same specimen that was subsequently carefully annealed. It can be shown that if the value of B in Fig. 307 is expressed in lines of force, and that of H in tens of amperes, the area of the hysteresis loop is the energy in ergs required to force the metal to overcome the cycle of changes. Also it has been found that for a given specimen and form of wave of the exciting current, the area of the loop is the same whether the successive reversals in flux succeed one another with the lowest frequency found in commercial apparatus or the highest frequency. The predetermination of the amount of energy consumed by hysteresis is a most important requirement in the design of much electrical machinery. MEASUREMENT OF HYSTERETIC LOSSES. Method of Plotting Curves. A very obvious method of determining the hysteretic loss is to draw the complete loop from successive observations made with differing magnetizing forces by any of the permeability measuring plans spoken of, and then to obtain the area of the resultant loop with the aid of a planirneter. Just as obviously, however, this method is exceedingly tedious because of the large number of observations required, and it is therefore seldom used in the workshop. Wattmeter Method. The energy consumed in the hysteretic cycle may be measured very simply by using a sensitive indicating wattmeter. For this 382 ELECTRIC AND MAGNETIC MEASUREMENTS. test the specimen is surrounded with a magnetizing coil and the energy expended therein measured, first with the specimen removed, and afterward with it in position. The first reading gives the energy required to overcome the resistance of the magnetizing coil itself, and the second that energy plus that expended by hysteresis and eddy currents. As it is difficult to determine the latter separately this meter test is usually used -06 >R (B- * 47 +8000 t6000 44000 JC FIG. 307. only when it is possible to obtain the specimen in the form of thin sheets, which may be electrically insulated from one another by varnishing or otherwise, thus practically eliminating the eddy current loss. Instead of connecting the wattmeter in the usual way, it is advisable to have two windings over the specimen, one of wire through which the magnetizing current flows, and the other of HYSTERESIS. 383 fine wire insulated from the first, and in which there is generated by the alternating flux an E.M.F. that is applied to the poten- tial circuit of the wattmeter. This eliminates the error due to the energy loss in the coil. Connections of this kind are shown in Fig. 308, where there is added also an ammeter and a volt- meter. The two latter instruments are useful for determining the magnetomotive force and the flux respectively. Ewing Hysteresis Meter. The hysteretic loss in a given specimen is the same whether the alternations in the field strength are caused by rotating it through a field or holding it stationary and reversing the direction of the current through the exciting coil. It is also FIG. 308. the same whether the specimen is held stationary and the field rotated or vice versa. One of the best known hysteretic loss meters is the Ewing, which is based on the latter principle and constructed as shown in Fig. 309. In it a C-shaped permanent magnet is supported by knife edges on agate bearings, and between its polar extremi- ties there is placed a clamp to hold the test specimen. This whole clamp may be rapidly rotated by means of the hand wheel, and when this is done the reaction between the field of the specimen and that of the magnet tends to carry the latter along in the same direction, this motion being opposed by suit- able counterweights and indicated by a needle sweeping over a stationary scale. To the lower part of the magnet is fixed a 384 ELECTRIC AND MAGNETIC MEASUREMENTS. flat vane dipping into an oil bath which dampens the indi- cations. Two standard specimens are supplied with each instrument and the deflections that these give are noted before any test is started. These two values are used to establish a curve show- ing the relation between the deflection and the hysteretic losses, so that when the unknown specimen is inserted the hysteresis loss can be found from the deflection by referring to the curve. FIG. 309. The sample must be laminated in order to avoid eddy cur- rents, but it is claimed that the thickness to which they are piled up has such a small affect that within the limit allowed by the clamps no correction need be applied. Professor Ewing has recently determined that the hysteretic loss in the standard test specimens does not remain constant indefinitely, and it is hence advisable to primarily determine the value of that of the standard by some other method if the appa- HYSTERESIS. 385 ratus is to be used for exact determinations. This refinement is however not necessary in workshop practice, because compari- tive results are as a rule all that is desired. Blondell Hysteresis Meter. In this instrument, which is shown in section in Fig. 310, the test specimen is made in the form of a ring which is secured to FIG. 310. a support that can be rotated about the central axis of the device. The tendency to rotate is balanced by means of the spring shown, and a needle attached to the frame carrying it is brought back to a zero mark by turning a knurled head as in a dynamo- meter. The rotating magnetic field is supplied by the U-shaped magnet, and its torque as indicated by the position of the torsion head is a measure of the hysteretic loss. Holden Instrument. Another hysteresis meter, used by the General Electric Com- pany and employing a cylindrical test specimen in a rotary field, is shown in Fig. 311. The magnet is here an electromagnet, 386 ELECTRIC AND MAGNETIC MEASUREMENTS. current being passed through its winding with the aid of two collector rings like those of an alternating current generator. The arrangement for measuring the torque of the sample is the same dynamometer spring affair, the values of the torque being read off from the position of a movable index relative to a fixed scale. In this instrument provision is made also for the measurement of the flux, this being done as follows : A coil surrounds but does not touch the test ring and rotates with it. It has its ter- minals connected to a two-part commutator, so that it delivers direct current to a pair of binding posts that are connected to the brushes. A voltmeter attached to the binding posts then shows the magnetic induction as the number of turns in the exploring coil, the cross-section of the test specimen, the speed of rotation of the magnet, and the resistance of the circuit com- prising the voltmeter, test coil, and con- nections are all known. The test coil feature is a most convenient one, as by its aid the induction in the specimen can be read in each instance and of course readily adjusted to any desired value by varying the strength of the exciting cur- rent. It is claimed that the most impor- tant reason for not adopting the Ewing FIG sii. P^ an ^ employing a rotating permanent magnet in place of the electromagnet is that with the former results obtained on specimens of iron of widely different character were not correct. Searle Method. A very elegant method for measuring the hysteretic loss for a single magnetizing cycle has been proposed by Searle, and involves the use of an instrument that is practically a ballistic wattmeter. As is shown by the diagrammatic sketch in Fig. 312, the test specimen, E, is placed inside of a solenoid, the series coil, of the wattmeter being connected in series with this winding. Another coil surrounds the first, and to its terminals is connnected the potential coil of the wattmeter. To the terminals, A and B, of the magnetizing coil there is connected a reversing commutator, so that the current sent HYSTERESIS. 387 through it and whose value is measured by an ammeter can be suddenly reversed in direction. The electro-motive force induced in the secondary winding is proportional to the rate of change FIG. 312. in flux through the core, that is, to (JLL The current through the primary winding at this instant is Hdt, so that the couple deflecting the wattmeter is Hdt -=- This integrated shows that the deflection of the instrument is proportional to HB, that is to say, to the hysteretic loss. It is, of course, assumed that the reversal is made so quickly that the whole cycle has been completed before the galvanometer has a chance to make a sensible deflection. APPENDIX. THE following list is intended to serve as a general guide to those who desire to ascertain where they may procure instru- ments and devices of the types described in this volume, or to obtain from the makers thereof more detailed information as to construction or operation than has found place in a treatise of the necessarily general nature of this one. It is not contended that the list is complete, in fact it would hardly be feasible in many instances to ascertain and record each maker of each form of device, but it is thought that it will be found accurate as far as it goes and should certainly serve a useful purpose. In those cases where the manufacturer is located abroad, the endeavor has been made to give the name of the United States represen- tative of the line as well as his own so as to enable those inter- ested to promptly communicate with the nearest authoritative source. The schedule is arranged in the order of the serial numbers of the illustrations to facilitate reference thereto. Where an illustration is not mentioned by a number in the list and is not simply diagrammatic or illustrative of a principle, it may usually be taken for granted that the apparatus is of a special or labor- atory character, built to order only, and about which a specialist in fine instrument building should hence be consulted if it is desired to procure the actual apparatus. LIST OF ABBREVIATIONS EMPLOYED. A. E. G. Allgemeine Elektricitats Ges., Berlin, Germany. B. Co. Bristol Company, Waterbury, Conn. C. & A. Chauvin and Arnoux, Paris, France. C. & Co. Crompton and Company, London, England. C. O. C. Ollivetti, Milan, Italy. C. S. I. Co. Cambridge Scientific Inst. Co., Cambridge, England. D. E. M. Co. Duncan Electric Mfg. Co., Lafayette, Ind. D. M. Co. Diamond Meter Co., Peoria, 111. E. B. Elliott Bros., London, England. E. D. Co. Electro Dynamic Co., Bayonne, N. J. E. E. M. Co. Edison Electric Mfg. Co., Orange, N. J. E. V. B. E. V. Baillard, New York, N. Y. 389 390 APPENDIX. F. P. Co. Foote, Pierson & Co., New York, N. Y. F. W. E. Co. Fort Wayne Elect. Co., Fort Wayne, Ind. G. E. Co. General Electric Co., Schenectady, N. Y. G. I. Co. General Inc. Arc. Light Co., Pittsfield, Mass. H. & B. Hartinann and Braun, Frankfort, A. M. J. C. Jules Carpentier, Paris, France. J. G. B. Jas. G. Biddle, Philadelphia, Pa. K. & W. Jas. White, Glasgow, Scotland. L. M. P. L. M. Pignolet, New York, N. Y. L. &N. Leeds and Northrup Co., Philadelphia, Pa. M. E. Mayer and Englund, Philadelphia, Pa. M. & R. Machado and Roller, New York, N. Y. M. B. F. Co. Meyers Break Finder Co., Syracuse, N. Y. N. E. I. Co. Norton Electrical Inst. Co., Manchester, Conn. 0. W. Otto Wollff, Berlin, Germany. Q. Co. Queen and Co., Philadelphia, Pa. R. W. P. R. W. Paul, London, England. S. & H. Siemens and Halske, Berlin, Germany. S. E. Co. Sangaino Electric Co., Springfield, 111. S. E. I. Co. Syracuse Electrical Inst. Co., Syracuse, N. Y. S. E. M. Co. Stanley Electric Mfg. Co., Pittsfield, Mass. W. & G. Willy oung and Gibson Co., New York, N. Y. W. E. Co. Western Electric Co., Chicago, 111. W. E. M. Co. Westinghouse Elect. & Mfg. Co., Pittsburg, Pa. Wag. E. M. Co. Wagner Elec. Mfg. Co., St. Louis, Mo. West. E. I. Co. Weston Elec'l Inst. Co., Waverly Park, N. J. Whit. E. I. Co. Whitney Elec'l Inst. Co., Penacook, N. H. MAKERS OR AGENTS. FIG. No. 1 J. C. 3 L. & N., F. P. Co., W, & G., Q. Co., S. & H., O. 4 E. B. 5 W. & G., Q. Co., L. & N., F. P. Co. 6 " " 7 n < 10 Q. Co., J. G. B., K. & W. 11 J. C. 14 Q. Co., W. & G., L. & N., F. P. Co. 15 West. E. I. Co. 16 Q. Co., W. & G., L. & N., F. P. Co. 20 Q. Co., J. G. B., K. & W., H. & B. 21 22 " " 24 L. & N., Q. Co., W. & G., J. C. 29 L. & N., Q. Co., W. & G., F. P. Co. 31 i 32 M. &R., C. & A. 36 Q. Co., W. &G., L. &N. APPENDIX. 391 FIG. No. 37 L. &N., Q. Co., W. & G., W. E. Co., F. P. Co. 40 << < 40A. C. S. I. Co. 44 L. &N., Q. Co., W. & G., W. E. Co., F. P. Co. 45 E. V. B., 47 < i tt 48 H. &B. 49 H. &B. 51 L. & N., M. &R., C. &Co. 52 Q. & Co. , L. &N., W. &G.,F. P. Co. 53 M. &R., C. & Co. 54 J. G. B., C. S. I. Co. 55 1 1, < < 56 M. & R., C. & Co. 57 L. &N. 58 0. W., L . &N., Q. Co., W. &G. 59 L. &N. 61 Q, Co., L. &N., W. &G. 67 < " F. P. Co., Whit. E. I. Co. 68 * < 69 Whit. E. I. Co. 71 O. W. 73 E. V. B., L. &N. f Q. Co., W. &G. 75 L. &N., Q. Co., W. &G. 76 Whit. E. I. Co. 80 E. B. 88 M. &R., C. & A. 91 L. &N., Q. Co., W. & G. 92 < < 93 < < 7. voltmeters, 205. Electrostatic ammeters, 179. voltmeters, 30, 197. 395 396 INDEX. E.M.F. measurement by drop of poten- tial, 23. by potentiometer, 87. Erection and care of galvanometers, 68. Evershed ohmmeter, 136. Ewing balance, 367. hysteresis meter, 383. permeameter, 374. Exploring needle, 343. Fall of potential method for ground loca- tion, 296. Farad, The, 4. Fessenden contact maker, 258. Field strength, determination of, by oscil- lation of a magnet, 347. measurement of, by ballistic methods, 358. measurement of, by electromagnetic method, 351. measurement of, by induction method, 349. by calculation, 347. Fixed coil instruments, 152. Frequency indicators, 265. meter, accoustic, 266. Galvanometers, 38. Galvanometer resistance by half deflection method, 150. sensibility, 39. shunts, 64. suspensions, 41. Cans and Goldschmidt instrument, 308. General Electric Co. recorders, 306. German silver, 10. Ground detectors, 199. Grounds, location of, by induction method, 293. Guard wires, 133. Hartmann and Brown frequency meters, 265. hot wire instruments, 176. multicellular voltmeters, 197. phase indicator, 271. Henry, The, 5. Bering's liquid potentiometer, 144. High resistance box, 13. resistances measured with galvanometer and voltmeter, 134. measurement by direct deflection method, 131. by leakage method, 135. by drop of potential method, 136. sensibility galvanometers, 49. Holden instrument for hysteresis measure- ment, 385. Hopkinson divided bar method of measure- ment of permeability, 359. Hotchkiss oscillograph, 264. Hot wire ammeters, 174. galvanometers, 59. voltmeters, 205. wattmeters, 223. Hysteresis, 380. loss by wattmeter, 381. Hysteretic losses, measurement of, 381. Impedance, 248. Inductance, 4. by bridge method, 248. by calculation, 253. by comparison with adjustable standard, 253. measurement of, 247. method of measurement with secohm- meter, 252. Induction ammeters, 181. wattmeters, 222, 336. method of locating grounds, 293. method of measurement of field strength 349. Integrating meters, 324. Intensity of magnetic field, 344. of magnetization, 346. Internal resistance of batteries, 146. of storage batteries, 149. Inverted Clark cell, 26. Kelvin ampere balance, 165. ampere gauges, 170. astatic galvanometer, 57. balances, 22. galvanometer, 56. multicellular electrostatic voltmeter, 31. Kennelly ammeter, 158. Kirchhoff bridge, 115. Koepsel permeameter, 370. Kohlrausch bridge, 139. instruments, 167. Lambert capacity key, 244. Lamp synchronizers, 273. Law of divided circuits, 93. Leeds and Northrup potentiometer, 81, 84. Legal ohm, 2. Lincoln synchronizer, 276. Location of breaks, 297. of crosses and grounds, 288. of faults, 288. of open circuits, 302. Lorenz apparatus, 6. Low resistance, measurement of, 114. measurement with an ammeter, 117. measurement by Carey Foster method, 122. Luminous beam for reading deflections, 44. Magnetic induction, 345. moment, 345. vane instruments, 172. units, 343. Magnetomotive force, 345. Magnetometric method of measurement of permeability, 355. Magnetizing force, 344. Mance's method of measuring battery resis- tances, 146. Manganin, 10. Manzetti frequency meter, 268. INDEX. 397 Matthiessen and Hockin bridge, 126. Maximum demand metera, 339. Maxwell's method of measuring inductance, 249, 255. Mechanically integrating meters, 337. Metallic alloy standards, 9. Mercury ohm, 6. Meyers break finder, 299. Mica condensers, 35. Micro-ohmmeter, 120. Miot inductiometer, 352. Modified bridge method of measuring capac- ity, 242. Maxwell method for inductance measure- ments, 250. Moving coil galvanometers, 38, 46. instruments, 156. magnet galvanometers, 38, 54. Miiller synchronism indicator, 274. Multiphase ground detectors, 199. Mutual inductance, 254. by Carey Foster method, 255. Murray loop test, 289. Nichols method of measuring inductance, 254. Ohm, The, 1. the mercury standard, 6. the wire standard, 1,1. Ohm's law, 5. Ohmmeters, 107, 136. Ohmmeter test for grounds, 290. Pellat balance, 23. Permanent magnet voltmeters, 193. Permeability, 345. measurement of, 354. measurement by attractional methods, 368. measurement by bridge method, 371. by magnetometric method, 355. measurement by straight bar, ballistic test, 358. Permeameters, 374. Phase indicators, 269. Picou permeameter, 374. Platinum silver, 10. Pole strength, 343. Post-office pattern Wheatstone bridge, 96. Potentials, measurement of, 193. Potential indicators, 208. Potentiometers, 23, 73. Power consumption of multiphase circuits, 229. measurement of, 215. Properties of resistance alloys, 10. Quantometer, 363. Quartz filament, 39. Radial arm pattern bridges, 101. Radiation galvanometers, 60. Recording instruments, 304. Reflecting electro-dynamometers, 53. electrometers, 61, 195. galvanometer scale errors, 45. Relays, 320. Repulsion electrostatic ground detectors, 200. Resistance alloys, 10. standards, 6. measurement of, 93. measurement with voltmeter and am- meter, 112. measurement with a potentiometer, 91. of batteries, 146. of electrolytes, 139. of galvanometers, 149. coil potentiometer, 82. Resistances without capacity and without inductance, 241. Reversed coils, location of, 303. Rheostats, water cooled, 12, 188. wire, 186. Roller hot wire instruments, 178. Rosa curve tracer, 259. Rowland electro-dynamometer, 54. Rubbing contacts, 319. Sangamo integrating meter, 330. Searle method of measuring hysteresis, 386. Secohmmeter, 140, 252. Series transformers, 183. Schattner maximum meter, 341. Schmidt frequency meter, 268. Scholkmann speed indicator, 280. Shallenberger meter, 336. Shunted ammeters, 162. Shunts, 162. galvanometer, 64. Siemens' dynamometer, 165. ohm, 2. "Silver voltameter," 2. Slide-wire bridges, 102. potentiometers, 73. Speed indicators, 277. Speeds, measurement of, by stroboscopic methods, 280. Standards of capacity, 33. Standard cells, 24. Standard condensers, 34. Standards of inductance, 35. Standard low resistances, 89. Starting coil on integrating meters, 328. Station potentiometer, 210. Stott test for grounds, 294. Stroud and Henderson method of measur- ing electrolytic resistances, 141. Sumpner's method for transformer tests, 282. Suppressed scale voltmeters, 207. Synchronism indicators, 272. Synchronizing by lamps, 273. by voltmeters, 274. Tangent galvanometer, 16. Telephone receiver, 62. Telescope, 42. Temperature coefficients, determination of, 123. 398 INDEX. Testing for grounds in an armature, 300. integrating meters, 285. Thermo-compensators, 164. Thompson double bridge, 119. Thompson's method of measuring galvano- meter resistance, 150. Thompson method of mixtures, 243. permeameter, 364. "Varley Slide," 111. Thomson ammeter, 159. inclined coil instruments, 171. integrating meters, 327. Three-ammeter method, 228. voltmeter method, 227. Tractional methods, 364. Transformer insulation tests, 283. polarity, 284. testing, 281. Unit of capacity, 4. of current strength, 2. of electromotive force, 3. of inductance, 4. of resistance, 1. magnetic pole, 343. Varley bridge, 109. loop test, 291. Volt, The, 3. balance, 32, 195. boxes, 87. Voltmeters, 193. Waddell and Legrand recorder, 320. Water-cooled rheostats, 12, 188. Watt balance, 218. Wave forms, measurement of, 257. form determination by contact methods, 257. by oscillograph methods, 263. Weiss galvanometer, 53. Weston electrodynamometer voltmeter, 201. d. c. ammeter, 156. recorder, 314. standard cell, 27. wattmeter, 220. Wheatstone bridge, 94. for voltmeter calibration, 212. Whitney d. c. ammeter, 157. wattmeter, 218, Wire rheostats, 186. * Wright maximum meters, 339. UNIVERSITY OF CALIFORNIA LIBRARY This book is DUE on the last date stamped below. OCT 19 1947 25Jan'5C LD 21-100m-12,'46(A2012sl6)4120 11111 I ill I I ran '.,/,:>