Prof. Thomson on Transient Electric Currents. 399 



after which it diminishes gradually, and, as well as the quantity 

 of electricity on the principal conductor, becomes nothing when 



1 k^ 



t=cx) . On the other hand, when pj exceeds ^-p, the expo- 

 nentials and trigonometrical functions in (7) are all real ; and 

 the solution expressed by these equations shows that the prin- 

 cipal conductor loses its charge, becomes charged with a less 

 quantity of the contrary kind of electricity, becomes again dis- 

 charged, and after that charged with a still less quantity of the 

 same kind of electricity as at first, and so on for an infinite ^ 

 number of times before equilibrium is established. The times 

 at which the charge of either kind of electricity on the principal 

 conductor is a maximum, being those at which 7 vanishes, are 

 the roots of the equation sin (a'^)=0, and therefore follow suc- 



cessively from the commencement at equal intervals — . The 

 quantities constituting the successive maximum charges are 



_ kTT _ 2k7r _ 3k7r 



Q^ _Qe 2A«', Qe 2au>^ — Qe 2Aa'^ &c. . (14); 



each being less in absolute magnitude than that which precedes 



it in the ratio of 1 : e^^**', and of the opposite kind. The strength 



of current will be a maximum in either direction when -^ = 0, 



or when 



k 

 ^-T- sin (a7) = oJ cos (aJt) ; 



and therefore if Tj, T^, &c. denote the successive times when 

 this is the case, measured from the commencement of the dis- 

 charge, and 7i, 73, &c. the corresponding maximum values of 

 the strength of the current, and if 6 denote the acute angle 



2Aa' 

 satisfying the^equation tan ^=—7—, we have 



rp_ 0__ _ e + ir _ ^ + 27r 



VGA 4AV VGA 4AV VGA 4AV 



^VCA-4A^) 



It is probable that many remarkable phsenomena which have 

 been observed in connexion with electrical discharges are due to 

 the oscillatory character which we have thus found to be pos* 



