PROCEEDINGS OP SECTION A. 



whose greatest value is equal to 



a 



which, after a few reductions, is equal to 



M ' cos i/ * r 



41 



E. 



Js - Js - c 



Let one conditiou under which we find this to be a maximum be 

 that M = constant, then, as 



sin^ i^ 

 cos ^^ 



increases with ;^ within the possible range of the latter, we will determine 

 when 



Js + Js - c 

 c 

 is a maximum for a fixed value of sin -^l, the coupling. 



Now J^ + Js - c L 



c 

 and remembering that 



c- = g- + &2 - 2ah cos 2 yh 

 we find that Js - Js - c is a minimum when 



h — a cos^ 1^, 

 and that its minimum value is 



J a sin il/, 



which gives for the max. max. amp. of Co, when M and the coupling 

 are given, the value 



tan \h \ p 



~Ja 'M' ' 



which increases as the coupling is increased. 



Hence when M is given the max. max. amp. of G^ is obtained when 

 the tuning is done in accordance wth the law 



T2 = ^1 sec ^b 

 after making the coupling sin xp as close as is desirable. 



12. If initial conditions, different to those we have up to the 

 present assumed, be given to the motion, either of the circuits or the 

 pendulums, different results will ensue, and one case is sufficiently 

 interesting to be briefly discussed here. 



