Vibrations of twitched and stroked Strings. 215 



case, but that the points 



_L ,_ 2L __ m-l T 



X — • x— • • • • #? — Jj. 



m m' m ' 



which just now as node-points remained fixed, themselves 

 execute vibrations in accordance with the law enunciated in 

 (27). Evidently we have then 



if rj signifies the function denoted in (27) by y, and if Atj sig- 

 nifies the function denoted in no. 15 by y\ only we must in 

 the latter substitute for A another constant B, and replace T 



u T 

 by — 



We thus find, if < x < -, 

 = — m 



y= [A(L -*) + B g -*)] < for < i < £, 



t ^ 2Jj—mx 

 2mL~ } 



*-^->y*$-')&-') 



„ 2L — mx < t < 2L + mx 



2mL =T= 2mL > 



»-[A(?-)+»g -')]« 



(35) 



p 2h + mx ^t^, 4Jj—mx „ 



for -^ir=T=^ir' &c - 



We have generally: — 



for 2 ( t '— 1 )^ i "" m ^ < 1 < ^L—m^ 

 2mL =T= 2mL ; 



„ 2iL — mx < t < 2iL + mx 

 2mL =T= 2mL ; 



for 2zL + ^ < L < 2 (^+l)L— W2ff 

 2mL = T = 2^1 ' 



