32 Prof. E. Taylor Jones on Electrical 



Hence 



= ^ + T^| 1 +^T--T0 2 } [ ^T + (T-T> 2 } cos J -T(T-T') rinj] 



and 



B 3 ^8 = B 4 e^ 



= 2(T + Totffi^^ cos i - T, ( T " T/ ) sin r] 



In the particular cases dealt with below 4/3 2 /(T — T') 2 is 

 never greater than '0004, and may be neglected. 

 Noticing that 



2/3T + (T-T> 2 = 2/3T / + (T-T / )\ 1 , 



and writing 7i for each of these quantities, also inserting the 

 value of G 1? we find 



^2 = - ^ • (T+T^T-ry t /l C0S T ~ T ( T ~ T/ ) sin f] 



+ 1 M «>" v r&cos^-TYT-TOsin-l- 



2 CT4-T /N )lT rp/\2 /l ^ wo rp/ -L V x 1 P m riv ) 



where & 2 and & 2 are written for the damping coefficients 

 of the two oscillations, viz. : — 



vV-*) and t^(-V + 4 



Since 7i is small in comparison with T(T - T') and T'(T - T'), 

 we may express V 2 in the more convenient form 



i My-^T . it \ 

 v 2 -+ 2 •( T 2._ 1 v 2)cos g sm ^r r ~- 6 ; 



1 Mt^-VT 7 . /■* 



2(T*-T' 2 )cos5' sm VT' / 



where sin S = 



and sin 8' =7^ 



T(T-T') 



T'(T-T')' 



