String Galvanometer of Einthoven. 219 



Case of return to zero position in a uniform 

 field when n g > -£• 



It is not necessary to multiply examples, and we pass to a 

 consideration of the transient portion of the motion given 

 above in (29), (31), and (35) in the normal coordinates. 



When n 8 >^4, and the magnetic field is uniform, 



_i? , -M 9 



y = Ai<? 2 cos (V*-«i) sin™ + A 2 e 2 cos(w 2 '*-« 2 )sin ~ 



k£ 

 + . . . . +A 8 e 2 cos(n s 't — ««)sin^y- . . (50) 



As a first particular case suppose the string has been 

 deflected by a steady direct current, and then the circuit 

 suddenly opened, so that we may put R = oo, and k 8 — k. 

 If'%>i&> then n s >ik, and the oscillatory case applies to all 

 the harmonics which occur. It is now necessary to find the 



values of the constants A„ A 2 , . . . a l3 « 2 , according to 



the assumption that the initial position of the string is the 

 circular arc given by (9), and that the velocity of projection 

 is zero when * = 0. Putting t=0 in (50), we find 



3/=A 1 cos« 1 sin -j- + A 2 cos a 2 siD-^ + . . . A 8 cos u 3 sin S ~ u 



This is the same curve as (9) and the coefficients of 



. TTX . 2-TTX 



sm ~T' Sm- T"' ma y equated, giving 



a 32 1 



A 1 COSa 1 =^?/ 

 7T 



1 3 9 

 A 3cos« s =^^y y. .(51) 



A 2 COS a 2 = A 4 COS a 4 = A 6 COSa 6 = &C. =0. ^ 



By writing out the velocities from (36), when k s — k we 

 have 



TTX 



!1 I 



V—{ —A! I - cos(V* — «i) + V sin (n/^ — ai) si 



— A 2 ^ - cos (n 2 't — oc 2 ) + n 2 r sin (n 2 't - « 2 ) J sin-^ 



-A 8 £ . . . &c. . . . | e 2 . (52) 



