852 Mr. E. C. Snow on Pirani's Method 



From this we see that the discharge of the condenser will 

 be continuous or oscillatory according as « 1? a 2 , and « 3 are 

 all real or one real and two imaginary (these are the only 

 cases which have to be considered for a cubic equation). 

 But from the above value of x, if a u a 2 , and a 3 are all real it is 

 seen that the discharge of the galvanometer is continuous, 

 while if two roots are imaginary it is oscillatory. Hence 

 the discharge of the condenser is of the same nature as that 

 through the galvanometer. 



To consider the case of the oscillatory discharge of the 

 condenser, therefore, we must put 



#2 = ^2 "4" ^3? 



and consequently 



a 3 = Jc 2 — ik B , i being v — 1 . 



The terms A 2 e~ a2t + A 3 -a 3* now become A 4 ^ _A ^cos (k s t — e). 

 A 4 and e being other constants. 

 The complete value of x now is 



x = A ± e- ait -f A±e~ k2i cos (k 3 t — e) . 



The initial conditions will be of the form 



to»= ' (S') =M ' and (S)„ = "' 



u and v being constants. 



Differentiating the expression for x and putting t = 0, we 

 shall have the following equations to determine the constants 



A 1? A 4 , and e. 



Ai + A 4 cos€ = 0, 



A 1 ot 1 -\- AJc 9 cos e— A^k 3 sin e=—u, 

 A^! 2 + A 4 (£ 2 2 — h 2 ) c o s e — 2 A 4 & 2 & 3 sin e = v. 

 These give 



AA 1 = v + 2uJc 2 , 



A A 4 cos e = — v — 2uk 2 , 



AA 4 sin e = — J / ai _£ 2 )(tf + 2wA; 2 ) + At* i. 

 ^3 L J 



where A = (a 1 — a 2 )(a : — a 3 ), a 2 and a 3 having the values used 

 above. 



In the case of a constant E.M.F. a ballistic galvano- 

 meter is used. This measures the total quantity of electricity 



