378 Prof. Ayrton and Mr. Mather on Galvanometers. 



where 



^=p and g 2 =p-p 





 or </ 2 =p 2 — n 2 , where n 2 = T . 



Let 0=a when £ = 0. 



Also ~=0 „ tf=0, 



then 



If we now lessen the control to — its initial value, so that 



mr 



the period, if undamped, would be lengthened m times, the 



sensitiveness will increased m 2 times, and consequently the 



value of a is increased m 2 times. This change of C alters q, 



but jo is not affected thereby. Let the new value of q be q'. 



Under the altered conditions we have 



We may also write in the form 



Iq 

 and expanding 



-(p-g)li-(p+q)t+(p + gyt 2 - &c]} 

 -(^-2 2 )£[(p-?) 2 -(i>+g) a ]+&°-} 



= J{2?+(P 2 -? 2 ) 3 (-2?) -(p*-q*)^(-ipq) + &C.} 



= «{1-(> 2 -j 2 )[4 ~' 2 P,J + terms involving «* &c.p and/j 



= a{l-u 2 ^ -2 ^|"3 + terms &C -J 

 ,-.6»-«=-«n 2 [|^ -2^ + terras &o.j. 



