M. A. F. Sundell on Galvanic Induction. 289 



the radius of the greater coils 21*7 centims. is adopted, being 

 the sum of the inner radius of the coil (21*65 centims.) and the 

 thickness (0-05 centim.) of the inner set of spirals. As regards 

 the smaller coils, to their inner radius (6*95 centims.) must be 

 added half the depth of the incision on the peripheries (0*15 cen- 

 tim.); accordingly their radius is estimated at 7*1 centims. As 

 mean values of the distance between a spiral in the one coil and 

 one in the other coil the distances above given under z are 

 adopted. Let the deflection produced by the induced currents 

 in an experiment be J, we have 



f+Ri x/li 2 — ?/ 2 

 J = 47rcmimn) — L_^ dy, . (6) 



J-*! (R 2 + R? + ^ 2 -f 2B# v 



where /, m, n have the same signification as above (§ 2), and c 

 is a constant containing a and b. We substitute a new variable, 



w= I-, and write B»+B? + * 8 



B'i 



2RR l 

 thus the equation (6) changes into 



J = 7rcv / 2Rr! 1 27mft I 



f/« 



(« + 

 or ___ 



J = 7rc\/2RR 1 z7/?mA, (7) 



if we denote by A the integral depending on a. The value of a. 

 is in all actual cases of induction greater than unity. In order 

 to compare the different series, we have calculated the deflections 

 J 2 corresponding to R = Rj = z — 1 or «==-§, % = 1 = tan 45°, 

 I- 1000, and mn— 100. We have 



J 1 = 100000ttc v / 2.A 1 , (8) 



where K x is the value of A corresponding to «=§ . Elimina- 

 ting c, w T e get 



, lS JBg.,kj (9) 



This equation gives the value of J 2 for every observed J. The 

 theory is confirmed if these values agree within the limits of 

 errors of observation. Then the deflections observed with differ- 

 ent distances between the coils may not differ in any remarkable 

 degree from the corresponding values of J calculated by the for- 

 mula 



T _ fejn/RRj A T 



J ~ iooooo 'v Jl> ' ' ' (iUj 



Phil. Mag. S. 4. Vol. 45. No. 300. April 1873. U 



