.Resistance of Compound Conductors. 



475 



Additional coils in. 



Additional coils out. 



Reading of I. 



Reading of II. 



Reading of I. 



Reading of II. 



o 



92 

 102£ 

 113 

 124* 

 135£ 

 148* 



o 

 30 



42£ 



53 



64 



75£ 



86£ 



o 



92 

 102£ 

 113 



im 



135£ 

 1481 



O, 



42| 



53 



II 

 64 



75* 



86* 



98 



It will be seen that the adjustment is made alternately on 

 the two compensators. Thus in the second compensator the 

 steps 30°-42J°, 42i°-53°, 53°- 64°, &c. have all the same 

 value, whatever may be the construction of the first compen- 

 sator, which indeed need not be graduated at all. In like 

 manner, the steps from 92°-102i°, 102i°-113°, &c. on the 

 first compensator have an equal value. 



An examination of these and other results, not here re- 

 corded, leads to the unexpected conclusion that from 40° 

 to 140°, i. e. through a range of 100° about the perpendi- 

 cular position, the scale of induction does not differ appre- 

 ciably from the scale of degrees. From 30° to 40°, or from 

 140° to 150°, the induction is something like a tenth part 

 less than that corresponding to 10° in the neighbourhood of 

 90°. Within the whole mechanical range of the instruments, 

 from 30° to 150°, there could scarcely be an error of 2 per 

 cent, in assuming M proportional to the angle measured from 

 perpendicularity, i. e. (i 77 " - "^)? or > sa y? &* 



The general explanation of this very convenient property 

 is not difficult to understand ; since for high values of 6' the 

 approximation over the whole circumference of coils of not 

 very unequal diameters must lead to a more rapid increase of 

 M than if the smaller coil were very small ; and it is con- 

 ceivable that for some particular ratio of diameters the 

 increase may just so much exceed that represented by sin 0', 

 as to correspond nearly to 6' . I was desirous, however, of 

 explaining this very peculiar relation more completely, and 

 have therefore developed the theory for the case of a ratio of 

 2 : 1 (nearly that of my apparatus) on the basis of formulae 

 given by Maxwell. The details of the calculation are given 

 in the form of an appendix (p. 498). 



