﻿Galvanometer- JSeedle for Transient Currents. 207 

 equation 



w 1 



(Rx + G) Ci 2 dt = q *l(2E), 



here Gr is the resistance of the galvanometer -coil and 

 connecting leads. 



The internal resistance R L of a condenser can be found 

 easily as follows. Let us suppose that when only the galva- 

 nometer coil is in circuit the distance of the dead point on 

 •discharge from the symmetrical point is D^ Let us now 

 suppose that a resistance R is put in series with the galvano- 

 meter and that the new reading for the dead point is D 2 . 

 Then, by (3), we have 



G + R t + R D 2 



Qt + B* IV 

 and thus 



R^RDj/CDa-DO-G. 



The author has found experimentally that this formula 

 gives consistent values for Ri, both when R and the applied 

 pressure are varied between wide limits. 



Equation (3) above gives an accurate method of determining 

 the ratio of yu-Gr to 7. It also shows that the circumstances 

 favourable to the production of dead-points near the sym- 

 metrical position are : 



(1) low resistance, (2) small galvanometer coefficient, 

 (3) small magnetic moment of needle, (4) a high charging 

 voltage, and (5) a large value of the Rayleigh coefficient 7. 



We shall now consider the throws produced when the 

 needle is initially in a position O . Equating the change in 

 the kinetic energy of the needle to the work done in stopping 

 the swing, we get 



(l/2)MF(Il 2 -co 2 )=^H{l-cos(^-^ )}, 



approximately, where co is the angular velocity of the needle 

 when the deflexion is 0. If X be the value of at the 

 extremity of its swing and if ± be small, we have 



m 2 DJ=fi,E.(0 1 -0 o )\ 



and hence 



(9 1 ~6> =(M^H) 1 2r2. 



Therefore by (2) 



1 -0 O = (l/M£VH) 1/2 {^o + Y#o (?o 2 /2KR) }, (4) 



since in most cases W is a negligibly small part of the total 

 energy. 



