1878.] Films under the Action of Sonorous Vibrations. 



71 



or 



if 1 =i 



[ 1 PPP , 7 ,_ 2 A( g-w)A(g-w.)A(g-j ?) 



J-r- M /A 2*+i aw " 



where as above 



13 5 / 1\ 

 A( „ l) = 1.3.5--^-lW . 2-2-2--"l m ~2) 

 K 1.^.5 m -1 . 2 . 3 7. . m 



It is clear that, in order that this integral may be finite, no one of the 

 quantities m, n, and p must be greater than the sum of the other two, 

 and that m + n+p must be an even integer. 



I learn from Mr. Ferrers that, in the course of the year 1874, he 

 likewise obtained the expression for the product of two Legendre's 

 coefficients, by a method very similar to mine. In his work on 

 " Spherical Harmonics," recently published, he gives, without proof, 



the above result for the value of the definite integral j P m P m P„ciU. 



-i 



IV. " Experiments on the Colours shown by thin liquid Films 

 under the Action of Sonorous Vibrations." By Sedley 

 Taylor, M.A., late Fellow of Trinity College, Cambridge. 

 Communicated by J. W. L. Glaisher, M.A., F.R.S. Re- 

 ceived December 12, 1877. 



(Plates 5 and 6.) 



Professor Helmholtz remarks, at page 603 of the fourth edition of 

 his " Tonempfindungea," that a film of soapsuds and glycerine forms, 

 when caused to occupy the orifice of one of his "resonators," an 

 extremely sensitive means by which to make visible the vibrations of 

 the air within its cavity. 



While I was engaged in verifying this observation, my notice was 

 attracted to the parallel bands of colour which traversed the film, and 

 it occurred to me to examine whether the forms of these bands were 

 affected by the sonorous vibrations which agitated the film. A few 

 rough trials having convinced me that they were so affected, I at once 

 proceeded to submit the phenomena which presented themselves to a 

 closer examination. 



Having caused a film to adhere to the circular aperture of a Helm- 

 holtz resonator, and allowed the fluid to drain off until the interference- 

 colours became visible, I set' the resonator, nipple downwards, in a 

 stand, so that the film was exactly horizontal, and then stroked with a 

 resined bow a tuning-fork Of the same pitch mounted on its resonance 



