The experiment described is really one of the original methods by which the absolute resistance of a wire was determined. For suppose we work with a pair of coils of which the coefficient of mutual induction can be found by calculation based on the value of their radii and their relative position, then м is known in centimetres, and we may re-write the equation thus : The various ratios on the right-hand side can be observed, and the value of R found in terms of the units of length and time. It follows from the above equation that the dimensions of R are those of a velocity. It will readily be understood that to obtain high accuracy in a complicated experiment like the above various precautions, which have only been just alluded to, or even passed over in silence, are necessary. It is inserted here chiefly by way of introduction to the system of absolute measurement. Experiment.-Determine in terms of a resistance and a time the coefficient of mutual induction of two coils. Enter the results thus : R = Resistance of secondary = 5840 ohms. K = 90000 + 5600 ohms. B (in scale divisions) 95 (mean of 4 observations). Distance from mirror to scale, in scale divisions = 1000. M 109 = 5840 × 5.62×5°27 × 1022 × 47'5 × 7133. M = 1566 × 10 centimetres. г. Comparison of a Coefficient of Mutual Induction with the Capacity of a Condenser and the Product of Two Resistances. The method of making this measurement has been already indicated in § Y (1), fig. xlvii. In order to carry it out connect up the apparatus as in fig. 1, placing a key, K in the secondary circuit. Connect one set of plates of the condenser to one end of the resistance box x, the other set being connected through a key, K3, to the mirror galvanometer M G. Connect the galvanometer to the other end of the resistance box x. Thus, when K, is made and K3 broken, the galvanometer is in the secondary circuit; when K3 is made and K, broken, it is in the condenser circuit. The tangent galvanometer in the primary circuit is not needed for the present experiment. To perform the experiment, make K, and break K3. On making contact at K, we get an induction throw in the galvanometer, and if 0; be the throw, we have Now break the battery circuit; then break K2 and make K3. On again making the battery the condenser is charged through the galvanometer. The potential difference between the plates of the condenser will be that between the ends of the box X, or xi. Thus the quantity of electricity which flows through the galvanometer is cxi, c being the capacity of the condenser ; and if 0, is the throw, very approximately, if &,, d, be the two observed deflexions. Thus We have seen that in experiments with a condenser a high-resistance galvanometer is required. The quantity of electricity required to charge the condenser is small, and the same quantity will pass round the galvanometer, whatever be its resistance. By having a large number of turns this quantity is made to circulate round the needle a large number of times, and hence to produce a measureable effect. For measuring the induction current the galvanometer resistance need not be very large. In the above experiment we must use a galvanometer which will make the quantities, and d, not very different. Suppose that the condenser has a capacity of about 1 microfarad; a pair of coils such as those described in § Y may have a coefficient of mutual induction comparable with 10 centimetres, and 1 microfarad is equal to 10-15 C.G.S. units of capacity. Thus the ratio M/C is of the order 1023. The values of 8 and 8 should be of about the same order; thus the product of the two resistances X, R is 1023 in C.G.S. units, or, since I ohm = 10° C.G.S. units, the product XR in ohms is of the order 1023/1018, or 105. Thus, if the resistance of the secondary circuit, including the galvanometer, is of the order 1000 ohms, then the resistance x will be comparable with 100 ohms. In order to obtain a sufficient current through this to affect the galvanometer appreciably several cells should be used. Experiments. Compare the coefficient of mutual induction between the given coils with the capacity of the given condenser. Enter results thus: (1) R = 5840 ohms. X = 100 ohms. C = 2 microfarad. 81 = 127, 127, 127; mean 127. § A. Comparison of Two Coefficients of Mutual Induction. If the coefficient of mutual induction of one pair of coils be known, it may be used as a standard, and that of another pair under varying circumstances compared with it. Thus we could examine how the coefficient of a pair of coaxial circular coils changes as the distance between the coils varies. For this comparison various methods are available; we will consider two. (1) Arrange the two pairs of coils so that the current in the primary of one does not produce induction in the secondary of the other, and also so that neither primary affects the galvanometer directly. Connect the two primaries in series with a battery and key (fig. li). Measure the resistance of each of the two secondaries and of the galvanometer; let the secondary resistances be s, and S2, that of the galvanometer R, and let M1, M2 be the coefficients of induction. Connect the secondary s, to the galvanometer, and make contact in the primary circuit; an induction throw 8, will be observed. Measure this; let i be the primary current. Then if 8, is not too large, since the secondary resistance is S1 + R, we have Now break the connection between s, and the galvanometer, and connect s, in the same way. The resistance in the primary circuit is the same, so that if the battery be fairly constant the primary current will be the same, and we have |