1884.] self-induction of the galvanometer. 213 



once, and diminishes the magnitude to which it does attain, it is 

 yet so effective in maintaining the current that the deficiency is 

 exactly neutralised. 



It appears further that in certain cases the self-induction instead 

 of delaying the transient currents actually accelerates their dis- 

 appearance. 



Integrating equation (1) we get 



Lx + (g + R) x — Ry = constant. 

 Now when t = 0, x = 0, y = 0, 



t = oo , x = 0, y = CE. 



Thus when t = cc,x = ^ CE and is independent of Z, 



g + R 



Though L has no effect on the magnitude of the total currents, 

 it has an important effect on their duration. 



Eliminating y between our two equations, we get 

 CRLx+ (L + CRg) x + (g + R)x= CER. 



The solution takes different forms according as the roots of the 

 equation 



CRL? + (L+CBg)g+(g + R)=0 (3) 



are real or imaginary. 



When the roots are real 



where X - L + GR ^ u? - & + CRg)*- WRL{g + R) 

 wnere a,- 2(JRL , f* - ~^ S WL % ' 



When the roots are imaginary 



• E xt • 

 x = — p e f sm vt, 

 vL 



where r *_ 4CRL(g + R) - (L+ CRgY 



wnere v WWU ' 



Thus when L is small x never changes sign. It rises to a 

 certain value and then falls again to zero. 



When L is increased till it is greater than a certain value a , 

 the motion becomes oscillatory, the condenser is discharged and 

 charged again with a less charge of electricity of opposite sign, 

 discharged again and so on. 



