1]6 Professor Airy on the 



Vibration parallel to 0,0,,= 



- 4* (1 - 4 2 ) . sin a + <p . sin f + 4 (1 - A 8 ) . cos a + <£ . cos £ 



2x9 >- 2x9 



+ 44\ sin a + <p . sin f + — 24(1 - **) cos a + <£ . cos£ + -^— 



. v 4x9 , ,, ,ov — r— I r , 4x9 



+ (I -k°-) .sina + <p .sm % + ~y~ +*(!-*) • cos a + <£. cos£ + -y- . 



To avoid unnecessary generalities we will suppose the plates 

 crossed, or a = 90°: which gives 



Vibrations parallel to Oo 1 = 



- (1 - 4 2 ) . sin <p . sin £ + A (1 - 4 2 ) . cos • cos £ 



2x9 1 r 2x9 



- 44 2 sin<£.sin£ + — 24(1 -4') cos . cosf + -j- 



A CJ 4 7T © 



+ 4 2 (1 - **) sin <p . sin ? + ~- + * (1 - *') cos <j> . cos £ + -y- . 



Vibrations parallel to o, 0., = 



-4 2 (1 -4 s )c°stf>.sin£-4(l - 4') . sin <£ . cos £ 



+ 44*cos<£.sin£+^^ + 2 4(1 - 4 5 ) sin . cos f + ~- 



+ (1 - 4 2 ) cos <£ . sin £ + -^ *(1 - 4*) sin <£. cos £ + — y. 



The efficient vibration, or that perpendicular to AP„ will be 

 found by multiplying the former of these by cos </>, the latter 

 by sin tf>, and taking their sum. Thus we have 



- * ~ A< sin 2rf>. sing + 4(1 - 4 5 ) cos 2<p. cos £ 

 2 



