DAVIS. LONGITUDINAL VIBRATIONS OF A RUBBED STRING. 721 



T"0 ) T l ) T 2 5 T 3 ) 



r,x (= t 2j ) , 



2 7" 2T 



— e , + e , £, 1- c, ... 2 2 1 — £ 



? ? 



r F 3T 3T T 



q q q q <7 



In either case 



and furthermore 



V + # 2 3 + of + • • • + tr\ = o, 



because the net gain in the height of the curve through a period is zero. 

 Under these conditions, Krigar-Menzel's formula becomes 



A * } _ T T a i J cos ^ M ffT o i/ii f C0 H W7rT i 

 ( sin ) 2 ( sin ) 1 



- <r-\ \ cos I ^=5 + ri | cos 1 !L^zi"| 



^~ 2 ( sin \ T ' ^- 2 ( sin ) T 



;r -- |_ ( cos ) \ i 1 



+ T \ . fUTTTi — TQ 



sin 



+ # 2 



2 J \ T 2 



3 J Sin | / » 7T T3 + T.A /W7T T 3 - T 2 



\co* iVr—jr J ""VT 2 



+ 6T-; { r - I m •*-* ' •*-« ) sin ' W7ri >- 1 1 V 



^-l j sin | /n7r V -i + Ty-jA 



^" 2 i cos ) V T 2 y 



When p is odd, this becomes 



A„ ) 2T . niref., (sin)/0??7r\ „,(sin)2»7r 



" ■■= =F -r-5 sin -=- \ So 1 ] [( ) + 6 2 3 ] [ + . 



B n ) n 2 ir 2 T { cos ) \ q J ( cos ) q 



, ffj-1 j sin ^ 2(q — 1) mr "| 

 + ^" 2 ( cos j " ? J 



VOL. XLI. — 46 



