and the Laws of Plane Waves propar/ated throiyh them. 137 



(38) represents a body wl.ose molecules act in the line joining them a wave of 

 normal compression is always possible. This will be rendered more evident by 

 considermg the conditions at the limits. 



Let the limiting sui-f\ice separating two bodies be the plane (.•, y) then the 

 equations of condition (11) will become, for the function (38), 



^'<-o+Q'< + Pp'o^A"a,'J+Q'X' + P"^'J; ^'„ = ^'„'. ^ ' 



These equations are equal in number to the unknown quantities, provided nor- 

 mal waves be included, because the unknown quantities of the problem are the 

 intensities of the reflected and refracted waves ; it is impossible, therefore for 

 exclusively transverse waves to be produced by reflexion or refraction in such 

 a body as (38) defines: in order to obtain unknown quantities whose number 

 shall be equal that of the necessary conditions of the mechanical problem we must 

 introduce normal vibrations. The conditions at the limits deduced from (39) are 



P'X'^=P"X'.'; rf, = .U, (44) 



f = f • 

 The additional hypothesis made by Professor Mac Cci-lagh, that the densitv 

 of the medium is the same in the two bodies, reduces these equations to four 

 Accordingly, with this hypothesis, there is no necessity to have recourse to normai 

 waves, as there will be four intensities to be determined in the transverse waves 



From these considerations it appears, that the e.perimma crucis between 

 the rival theories of light must be sought for among the laws of reflexion and 

 refraction ; but unfortunately these laws are not known with sufficient accuracy 

 to enable us to decide the question. Mr. Gkeen's theory contains the common 

 kws of reflexion at the surfaces of ordinary media as first approximations, while 

 Professor Mac Cullagh's system has the advantage of giving these laws as exact 

 results ; nothing, however, but more accurate experiments can decide whether 

 the approximation or the exact result be most in accordance with the truth • and 

 as these experiments involve considerations of the intensity of li^ht, it wou'ld be 



VOL. XXII. J ° 



