the Oscillatory Discharge of a Condenser. 147 



=(v-w[-^;-^-f(-^)+&c] 



all terms in the square brackets, with the exception of thoso 

 written, vanish with p. 



Now put p = 0, kp= —j~, and referring to the complete 



equation (4) we see that the '"'equivalent" R" and L" become 

 respectively 



4L 



r "=r— -^r4>o— $\!, 



, 4L 2 2L 



^o — ^ W^°~li ^°' 



It may be easily verified that these expressions agree with 



those got from equations (15) and (16) of the paper quoted, 



"P 



when the values zero and -rj are put for p and /^respectively. 

 We see now that the use of the condition 



o _4L " 



IV' 2 



is equivalent, mathematically, to writing equation (4) in the 

 form 



putting for a? inside the brackets the value — :, and treating 



2 lv ° 



the equation as a quadratic with constant coefficients. 



As regards the degree of approximation given by this 



R " 2 

 method, if we expand ° „■, we get 



which agrees with the accurate expansion in (9) up to and 

 including terms of the second order in 0. Or expressing the 

 condition in a series of powers of u/jl, as in (10), the two series 

 coincide up to and including terms in a 5 //, . 



March 2nd, 1899. 



L2 



