312 Prof. 8tokes'^ Examinaiign of the possible effect of 



the exception that the last term Qutsid? the brackets w:ould have 

 been replaced by ,^ ,,-.■. 



''f'' "•* «i' «« n f ;. M,^,.|T,!v, 



'If now we take the case next in order of simplicity^ in which the 

 'motioji is symmetrical about a centre, and put r for the distance 

 'of any point from the centre, v,v shall get for the determination 

 «0f ?•« the same partial differential equation as (7.), with the ex- 

 cerption that a; vAW be replaced by r. To obtaiir, therefore, the 

 ihtegi-al corresponding to (13.), it will be sufficient to replace x 

 by ?• and divide the second member by r. This integral woidd 

 apply to the case of the disturbance produced by a vibrating sphe- 

 rical body, in which the motion is supposed to be symmetrical 

 with respect to the centre. And in the more general case of a 

 vibrating body of irregular form, or a musical instrument, or any 

 other source of sound, the conclusions would doubtless be the 

 same as to theii- leading features. ■ ^,.,( j,,r.^, ,,* 



There remains a more important point to be considered before 

 we apply the foraiula (13.) to the vibrations of air within along 

 tube. At first sight it might seem that the radiation of heat 

 within a tube must take place in a manner altogether different 

 from that in which it would take place in free aii'. But a little 

 consideration will show, I think, that such is not the case. Of 

 the heat radiating from any pai'ticle of aii- which has been shghtly 

 heated by condensation, any particular ray is incident on the 

 side of the tube, where it is partly absorbed, partly reflected, 

 and, it may be, partly scattered. The reflected ray, or any one 

 of the scattered rays, is again incident on the side of the tube, 

 ■w'here a good portion is absorbed, and so on. The small quan- 

 tity of radiant heat which remains after three or fom* reflexions 

 may be regarded as insensible. Now since radiant heat travels 

 with a velocity equal to, or at any rate comparable with, that of 

 light, we may neglect as altogether insensible the time which 

 any portion of heat, once become radiant, takes to be absorbed. 

 jMoreover, we may neglect the small portion of heat reabsorbed 

 by the air itself, because a ray of heat has only to traverse a 

 length of air comparable with three or four diaineters of the tube 

 before it is absorbed by the tube. Hence we may conceive a 

 small periodic flux of heat as taking place across the inner sur- 

 face of the tube. Now it follo^vs from the mathematical theory 

 of he^t, that when a periodic flux of heat takes place at the sm-- 

 face of a solid, the corresponding variation in the temperature of 

 the solid near the surface is verj' small if the period \)e very 

 small. If we suppose the flux expressed by the sine or cosine 

 of an angle proportional to the time, the expression for the fluc- 

 tuation of temperature -will involve in its coefficient the square 



