260 Prof. Thompson, A Method of Comparing the [Feb. 11, 



*S+^l+«^=» (2> 



Eliminating y we get 



^1 + ^5 + ^1+^^ = (3>> 



where 



A=LN-M\ 



B = L8 + NR, 



If we had eliminated x we should have obtained a precisely 

 similar equation for y. 



Now suppose we have a fixed coil in series with the primary 

 circuit and we insert in this an exhausted bulb, which is the same 

 in all experiments, a bright discharge will pass through the bulb; 

 the brightness of this discharge changes with the resistance of the 

 secondary circuit. 



Since dx/dt is the current flowing through the primary circuit, 

 the number of lines of magnetic force passing through the coil in 

 series with the primary is proportional to dw/dt ; thus the rate of 

 change of the number of lines of magnetic force passing through 

 the bulb, and therefore the electromotive force acting on the bulb, 

 is proportional to d^ocjdf, we may therefore take 



^d^os 



as a measure of the brightness of the discharge in the bulb, 



the integration extending over the whole time of discharge of the 



Leyden jar. 



d^x 

 To find the value of this quantity multiply (3) by -^ and 



integrate with respect to t, remembering that initially dx/dt = 0, 

 and that finally x and all its differential coefficients vanish : per- 

 forming the integration we find 



-*-(S):+^/@)'''--/(s^-« (^)' 



where -j-^ ) denotes the initial value of dxjdf. Now multiply 



