474 Lord Rayleigh on the Self-induction and 



of the coils were coincident, or the planes parallel. In this 

 position M is arithmetically a maximum (M ) ; and we con- 

 sider its algebraic sign to be positive. At 90°, when the 

 axes are at right angles, M = 0. At 180° M would be nega- 

 tive, and of the same arithmetic value (M ) as at 0°. 



The coils are wound upon boxwood rings, and in each there 

 are 45 convolutions. The mean diameters are about 3 inches 

 and 1J inch. 



Some of the earlier experiments were interpreted by a 

 theory of the compensator, which I knew at the time to be 

 very rough. If the small coil be treated as infinitely small, 

 then 



M=M o cos0. 



On the same supposition we have, from the roughly measured 

 dimensions, 



M = 60,000 centim. 



The law of the simple cosine was found to lead to consi- 

 derable anomalies; and when at a later date (August 19) I 

 carried out my intended calibrations, some very curious 

 results revealed themselves. 



The best arrangement for calibration and for determination 

 of the constant of the instruments is to institute distinct pri- 

 mary and secondary circuits. The former included a battery, 

 a scraping contact (p. 472), and the two outer (larger) coils 

 of the compensators. The latter included the two inner coils 

 and a telephone. The precise procedure will depend upon 

 whether we can assume the exact equality of the two com- 

 pensators. In that case we may introduce, and retain during 

 the observations, another pair of induction-coils, one of course 

 in the primary and the other in the secondary circuit, and of 

 such power as to produce a displacement of about 30° of the 

 compensator. Thus, while in the absence of the additional 

 coils, balance would be obtained when both compensators stand 

 at 90°, their introduction would lead to such readings as 90°, 

 60°; 100°, 70°; 110°, 80°; &c. By this means various parts 

 of the scale of one compensator can be compared with non- 

 corresponding parts of the other ; and this is sufficient if the 

 two are similar. 



This method was used ; but it is perhaps better to arrange so 

 that each compensator is calibrated independently of the other. 

 In this case alternate readings are taken with and without the 

 cooperation of the additional coils; and the equivalent induc- 

 tion is found for each compensator at various parts of its 

 scale. The following set of readings will give an idea of the 

 modus operandi. 



