314 Pi-of. Stokes's Examination of the possible effeet af 



great or very small compai'ed with n. It follows from (13.) that 

 the decrease of intensity in going one wave's length in the direc- 

 tion of propagation is a maximum when tan-yfr, and therefore 

 ^jr, is a maximum. Now (12.) shows that a/t is a maximum 

 when yu _i -- 



■ ^^^ . 



jti biuow rnnJ£'iaqai3J lo ?«)■";-* an/ .tfiflj gwoUoV Ji Hofilv/ W/rl 



^^we got from (11.) and (i2.)f^"'i^'^^^«'5'f "i^^« '^>^' "^^''^ '"f^^ 

 A oJ 8nr;ytt=«/t"*K~*, g-f = tan ' K*- tan '.KTJ.l.ii-(,7/{17«> 



•"9?fife' Velocity of propagation, which is equal to nyu,-'4fec"^, flt(6s 

 n'ot inuch differ fi'om n/i~', since •^, as will immediately appear, 

 iS' iiot very large. It may be observed, that the expression for 

 n/i~' given by the first of equations (17.), is a geometric mean 

 between the velocities of propagation resultine from the theories 

 of' Newton and Laplace. ' ■- "-■•' :^' ^' -i^!>'i>, .v.ii;;^bm .dT 

 The value of K, deduced from experlmfents iii' whidli the theory 

 df 'feoimd is not assumed, is about 1'36*, whence 2-\|r = 8° 47 . 

 If — / be the index of e in (13.) when x is equal to one wave's 

 length, we have //. sin ^Ir . a: = /, /x cosi/r , x = 27r, whence /= 27r tan yjr, 

 e~' = 0*6172; so that the intensity, supposed to vaiy as the 

 square of the amplitude of vibration, would be diminished in the 

 ratio of 2-625 to 1. Supposing the period of vibration to be 

 the yipdth part of a second, which would correspond to a note 

 of moderate pitch, and taking the velocity of propagation at 1 100 

 feet per second, we should have 44 inches for the length of one 

 wave. Hence in travelling 20 yards, or 16"36 wave-lengths, the 

 intensity would be diminished in the ratio of (2*625) '^'^^ to 1^ dr' 

 about 7 millions to 1 . A decrease of intensity like this is utterly 

 contrary to observation, and therefore we are really compelled to 

 suppose that the ratio of q to n is either vei-y much greater Br 

 very much less than what has just been detemiined. Sinc^'iW 

 the case supposed M = 27rT~' = 60077, we get from (16.) 



^ = 2198, (18.) 



which, it is to be remembered, is referred to a second as the 

 unitoftime. - >>-'j;ri ,•(;;.., dou .:- ,r.....,:!i:;(,::. r ,■,,:,, ^■jj.ijjj 



Let ns now, adop{&^''ttii^VAJu6'bf' ^^^exIittiitie'a'li^ttle'artiWh^t- 

 rate a small portion of heated air, situated in other air which has 

 not been heated, would cool by radiation. If $ be the excess of 



jAs ;:. ;..: . V' _ , ... „,,•. ,, , . , ,,., 



c^, fl, ,Poiss(W>» Traite de Mecaniqve, yo\.i\. est.^T . The value deduced 

 from the observed velocity of sound is somewhat lai'ger, and is more likely 

 to be correct. I have employed the value 1 ".36 in order to avoid arguing in 

 a circle, becanse I am reasoning as if the received theory of sound were not 

 esteblishedviJpti -j^ii i^uiAai ^UOiL—4 ^'i-[^•l=.^ gauitili .B<ii,yo-u{ 



S Y 



1 



