380. Need of Galvanometer Shunts.—The currents which a reflecting galvanometer may measure are extremely small. Thus, if a pin be connected by a wire to one terminal of the galvanometer and a needle be connected to the other and the pin and needle be held tightly between the fingers, the contact of the two dissimilar metals with the slight moisture of the fingers will drive a sufficient current through the coil to cause the mirror to run entirely off the scale. In order therefore to measure even minute currents we must employ a shunt by which, as explained in Par. 301, only one-tenth, one-hundredth, or one-thousandth of the total current is permitted to flow through the instrument. Even in this case it is usual to insert in the circuit a resistance of 50,000 or 100,000 ohms by which the current is reduced to measurable intensity. 381. The Universal Shunt.—We saw in Par. 301 that the resistance of a galvanometer shunt must bear a fixed relation to the resistance of the galvanometer with which it is used and that shunts are not interchangeable and can be used only with the galvanometer for which they are constructed. The phosphor-bronze suspension of a suspended coil galvanometer is frequently broken and must be replaced by a new one, in doing which the resistance of the galvanometer is usually considerably changed and this change would render useless a shunt designed to accompany the original resistance. Reflection will show, however, that if we simply wish to compare currents relatively it is not necessary to know what fraction of the total current flows through the galvanometer, for if 1/xth of a current /' flowing through a galvanometer produces a certain deflection, and if 1/xth of a different current I" produces a deflection twice as great, then the current /" is twice as great as the current /'. Carrying out the idea farther, Ayrton devised a universal shunt which may be used with any galvanometer and which can be so varied that, irrespective of the resistance of the galvanometer, the deflection produced is proportional to one-tenth, one-hundredth, or one-thousandth, etc., of the total current. This shunt is shown diagrammatically in Fig. 169. Five contacts (sometimes six) are arranged in the arc of a circle and marked, 1, -^j, T45, ^v and 0. Between these contacts are resistance coils A, B, C, D. If R be the total resistance, A is .9 of R, A + B is .99 of R and A + B-fC is .999 of R. A common arrangement of these resistances is to have A = 9000, B = 900, C = 90 and D = 10 ohms, a total of 10,000 ohms. The current enters by K and leaves by H. The arm attached to K can be placed on any desired contact. The galvanometer is connected in shunt with the total resistance as shown. Let the resistance of the galvanometer be x. With the arm on contact 1, let the total current be I, and the current through the galvanometer be Ig. The joint resistance from K to H is „ _* (Par. 293). Xfc I «C .99S + Z+ .0lfl R + x If the total current be now /' and the current through the galvanometer be /'„ From (I) and (II) /': / = 100/', :/, (III) Or if D be the deflection produced by the first current and D' that produced by the second /' : / = 100. D' :D or the ratio of the total current when the arm is on the TJ5 contact, to the total current when the arm is on the 1 contact, is as one hundred times the deflection produced in the first case, is to the deflection produced in the second case. It will be noted that x, the resistance of the galvanometer, does not appear in (III), hence the shunt may be used with any galvanometer. Fig. 170. 382. Weber's Electro-Dynamometer.—This instrument, an example of a galvanometer of the second class (Par. 372), that is, one in which a coil swings in a magnetic field produced by other coils, is shown diagrammatically in Fig. 170. It consists of two large parallel coils A and B mounted so that they have a common axis and their planes are vertical. Midway between these there hangs by a bifilar suspension (Par. 127) a small coil C so arranged that its axis is in the same horizontal plane but at right angles to the common axis of A and B. As generally used the same current traverses all three coils. Entering at E it flows around the coil A and out to F, thence by the wire to G, thence down the slender wire suspension to C, around this coil, up the other suspension to H , down to D, around the coil B and finally out by K. If the currents in the two coils flow as indicated by the small arrows, the field of AB will be from right to left; that of C from rear to front and therefore C, viewed from above, takes up a clockwise motion, or, in accordance with Maxwell's law, tends to turn so that its field coincides in direction with the field of AB. The angle of deflection is read, as in the mirror galvanometer, by means of a small mirror attached to the suspended coil. The controlling force is gravity which tends to pull the inner coil back to its primary position; the moment of this force being directly proportional to the sine of the angle of deflection, or M c = a . sin 5 The deflecting force is dup to the interaction of the fields of the suspended and the fixed coils and since these fields are severally proportional to the currents flowing in the coils (Par. 354), the deflecting force is proportional to the square of the- current. The moment of the deflecting force is proportional to the product of the square of the current and the cosine of the angle of deflection, or Md = b.P.cosS When the coil comes to rest the two moments are equal and opposed, hence 6./2.cos5=a.sin 5 whence or, the square of the cur rent is proportional to the tangent of the angle of deflection. This fact might have been anticipated since reflection will show that the instrument is virtually a tangent galvanometer. In making an actual observation a number of refinements must be observed in determining the constants a and b above, and it may also be necessary to allow for the effects of the earth's field. Should the current through the instrument be reversed in direction, the fields in the coils will also be reversed but from the figure it will be seen that the tendency will still be for the movable coil to turn in a clockwise direction. Since this direction of deflection does not vary with reversal of the current, instruments of this class, that is, two-coil instruments, are employed in the measurement of alternating currents, or those currents which reverse many times per second. 383. Siemen's Electro-Dynamometer.—Siemen's electro-dynamometer, shown diagrammatically in Fig. 171, is in principle the Fig. 171. same as Weber's but differs in that the movable coil is external to the fixed, and that the controlling force is the torsion of a delicate coiled spring. The base and supporting upright are of wood. There are two fixed coils, one of a few turns of heavy wire for use with large currents, the other of many turns of a finer wire for use with smaller currents. The short coil is wrapped upon the long |