114 



Professor Airy on the 



Whence the vibrations, after emerging from the second plate, 

 are (omitting the common multiplier y+J?-> ' n Edition to the 

 former) : 



In O.o'i 1 - h°. cos a + (j> . sin £ + A (1 - k") . sin a + (j> . cos f . 



In o\o', - ¥ (1 - &) . sin a + <p . sin £ + A (1 - A") . cos a + (p . cos £. 



2x0 



2x9 



In -EV, 2A-. cos a + </> . sin £ + -^- + 2#\ sin a + . cos £ + ^- . 



2x0 



2x9 



In «;>',, 2A°. sin a + <£ . sin £ + -^ 2A cos a + <j> . cos £ + x 



Similarly for the vibrations in Ee l and e,^: 



Ee l = w sin £ + -^— + * cos I + -y- 



. „ 2x9 .. , 2^0 



+ y sin £ + -r— + 2 cos £ + — ^~ 



>- 2 "- e ,7 r , 27r0 



C^j = — A# sin 5 + — — + Aw cos t, + — r— 



~ . - 2x9 y ». 2x6 



2x9 r 27r © 



Comparing the coefficients ot sin £ + — — - and cost; + -^— , 



2 *"" — T^ 



W = ^ COS a + 0, 



1+k- 



k" COS a+<p = «> + y, 



— A sin a + <p = .x + z, 



- 2A 



sin a + = — Jcx + , , 



A COS a + <2>= Aw - ^, 



whence < 



-#>(1-A') -— r 



y = — ^m — cos a + ^' 



1+A- 



1-A 

 1 + A 2 



A(l-A 3 ) . — — 

 Vs =— r— »! sina + 0. 



