Electromagnetic Induction. 335 



As the state of the battery was liable to change and the 

 strength of the current to vary, it was important that 

 errors arising from these causes should as far as possible be 

 eliminated. In order to effect this, a double set of observations 

 was taken, first with increasing distances between the coils, 

 and next with decreasing distances. In every position de- 

 flections were taken towards both ends of the scale ; so that the 

 recorded results represent the means of never less than four 

 readings ; and in most cases they are the means of twelve or 

 sixteen. The observations were begun with the coils A and 

 B as close together as possible without touching, and were 

 continued till the distance between them was 70 centim.; but 

 beyond about 50 centim. the galvanometer above mentioned, 

 formed by the juxtaposition of the coils C and D, was not 

 sufficiently sensitive. It was therefore replaced for these 

 distances by a delicate reflecting galvanometer; and the 

 necessary reduction was made after the ratio of the indications 

 of the two instruments had been found. The deflections of 

 the needle were indicated by the movements of a spot of light 

 on a circular scale of one metre radius. The readings were 

 obtained in centimetres and millimetres, and, after having been 

 corrected for the effect of damping, were reduced to degrees. 

 The value of the induced electromotive force, or, in other 

 words, the strength of the induced current, was in each case 

 taken as being proportional to the sine of half the angle 

 through which the needle was deflected — that is, proportional 

 to the sine of one fourth of the corrected scale-reading reduced 

 to degrees. In using the numbers thus obtained for plotting 

 a curve which graphically represents the values of the coeffi- 

 cient of mutual induction M for different distances of the coils 

 A and B, the distances read off along the scale E F for the 

 positions of the coil B were taken as abscissae, and the values 

 obtained for the sines were taken as ordinates. The results of 

 these experiments are given in Table I., where the columns 

 headed x give distances between the coils, and the columns z 

 give the corresponding values of the coefficient of mutual 

 induction. The curve plotted by means of these numbers is 

 given in fig. 1, Plate XL; the centres of the small circles in 

 that and the following curves represent the points found in 

 the experiments. 



This curve is related to the curves of constant induction 

 which form the main subject of this paper as the vertical 

 section of a surface is related to the contour-lines of that 

 surface. Imagine, then, a surface such that the three rect- 

 angular coordinates x, y, and z of any point upon it represent 

 respectively the distance of that point from the centre of the 



