476 Lord Rayleigh on the Self-induction and 



It may suffice here to say that the experimental result is 

 abundantly confirmed ; and that reason is found for the con- 

 clusion that the proportionality of induction to angle would 

 be even better maintained if the diameter of the smaller coil 

 were increased from *50 to "55 of that of the larger. The 

 non-mathematical reader may be content to accept this pro- 

 portionality over most of the range of the actual instruments 

 upon the experimental evidence. 



The absolute value of the induction-coefficient corresponding 

 to each degree of the compensators was determined at the time 

 of the calibration by comparison with the calculable induction- 

 coefficient between two coils wound in measured grooves cut 

 on the surface of a wooden cylinder. These coils contained 

 respectively 21 and 22 convolutions ; and the induction- 

 coefficient for the mean windings is found to be 277*3 centim. 

 by a calculation of which it is not necessary to record the 

 details. Hence, for the actual coils, 



M = 21 x 22 x 277-3 = 1-281 x 10 5 centim. 



The obvious procedure for the comparison would be to com- 

 bine the compensators without additional coils, so as to obtain 

 a balance at the telephone when both stand at 90°, and then 

 to observe the displacement or displacements necessary when 

 the standard cylinder coils are introduced. In my case, 

 however, the range of induction provided by the compensators 

 was insufficient to balance the standard, if used in this way, even 

 when displacements were made in such (opposite) directions 

 as to cooperate in changing the total induction. An addi- 

 tional pair of coils was therefore introduced, for the purpose, 

 as it were, of shifting the zero, of which nothing required to 

 be known, since they remained connected whether or not the 

 standard coils were in operation. With this modification, 

 balance could be attained in both cases. 



With standard coils in, one pair of readings was 130°, 

 43|°; and with standard coils out, 50°, 127|°. The connections 

 were such that when there was no external change, the cor- 

 responding readings would move in the same direction (p. 475); 

 and thus the number of degrees of one compensator equivalent 

 to the standard is 



130-50 + 1274-421 viz. 165. 



Accordingly, every degree of either compensator, not too far 

 removed from the middle of the range, represents 776*3 centim. 

 of induction-coefficient. 



The maximum coefficient, when 0=0, according to Table 

 II. (Appendix), would be about 56100 centim, 



