M. A. F. Sundell on Galvanic Induction. 293 



opposite side of it. If we combine that element with ds, we ob- 

 tain the same numerical value of r and cos 6 V but the latter 

 quantity changes its sign. The electromotive force of this com- 

 bination is 



-^ikhH^-cose.dsds, (13) 



By adding (12) and (13) we obtain 



3 a? 

 + 4 *^ "4g2 i 7 ?" 7 !*) cos Q\ ds <kv • (14) 



If we multiply by br and effect the integration along one of 

 the halves into which the secondary circuit is divided by the 

 plane P, we obtain the inducing force of the element ds. By a 

 second integration along the primary circuity the whole amount 

 of induction will be known.- As none of the finite factors in 

 expression (14) changes sign within the limits of integration, 

 the integral has, mathematically speaking, a finite value. How- 

 ever, it is possible that the effect of the induction may be too 

 feeble to be shown by the experiment, because the coefficient of 

 the second term is very small in comparison with that of the first 

 term*. Moreover an attempt to measure this effect directly by 

 placing the coils so as to annul as much as possible the influ- 

 ence of the first term did not afford a decisive result, though a 

 little modification of the experiment was more successful. It is 

 evident that cos 6 and the first term in expression (1) change 

 sign when the primary current is reversed; on the contrary, 

 the sign of the second term, which contains cos 6 in the second 

 degree, is independent of the direction of the current in the ele- 

 ment ds. Accordingly, if the induction produced, for example, 

 by breaking the primary circuit is observed for the opposite di- 

 rections of the inducing current, the coils being in such a posi- 

 tion that only the second term has an influence, the deflections 

 of the magnetometer must be equal and towards the same side 

 from the position of equilibrium. A perfectly accurate adjust- 

 ment of the coils is not possible ; therefore even the first term 

 must be taken into account, as also other causes of magnetic 

 deflection. Let a denote the deflection corresponding to the 

 first term, b that for the second term, a x and b^ the same for the 

 induction between the primary coil and the coil of the multiplier 

 and its wires, # 2 and b% the induction from the wires of the 

 battery. The primary coil and the wires of the battery were 

 not infinitely distant from the magnetometer ; thus a direct in- 

 fluence on the magnetic needle was possible. Let c denote this 

 influence of the coil, and c l that of the battery wires. The wires 



* Edlund, " Sur la Nature de rElectricite." 



