of Coefficients of Mutual Induction. 419 



Feb. 25. P field-magnets, with two bichromates. 



S armature, ballistic galvanometer, and 1000 coil, 

 with and without 1000 B.A. units, so that 



R=1045, K =45. 



By reversal. 



Gralvano- 

 a. (3. 6. meter. Amperes. M. 



179'-5 179' 39° 24' 2 2-54 10 7 x3<685 



By formula M=^ 10'0 10 7 x 4*95 



Addendum. 

 March 5. Supplementary Notes. 



1. Calculation of coefficients by the elliptic integral table 

 in the new edition of Maxwell, combined with the formula 

 for approximation to the effect of the sections of the coils. 



I have now calculated the experiments of Feb. 22 and 

 Feb. 23-24 by this method, which is the most complete that 

 exists, short of calculating all the single combinations of 

 circles in the two coils. The accordance with experiment is 

 somewhat better, but still far from close. 



Observed. Calculated. 



Feb. 22. 10 8 x 1-259 10 8 x 1*176 



„ 23-24. 10 6 x 6-015 10 6 x 5-585 



2. Simple formula for approximate calculation of the 

 coefficient. 



Assume that the field in a due to A is everywhere the same 

 as at the centre of a. Then the total lines of force for unit 



current are 



2ttA ; 



(A 2 + 6 2 )F 



where b is the distance between the planes of the circles, or, 



if t- = tan 6, this becomes 



b 27r 3 a 2 sin B 



A 

 which is simpler to calculate than Maxwell's approximate 

 formula. 



The following is the comparison of this formula with 

 observation. 



Observed. Calculated. 



Feb. 21. 10 7 x 7-690 10 7 x 8-991 



22. 10 8 x 1-259 10 8 x 1-133 



„ 23-24. 10 6 x 6-015 10 6 x 5'036 

 2 F 2 



