for Reflected and Refracted Light, 105 



divided opinions, whether the vibrations are parallel or perpen- 

 dicular to the plane ^i polarization, and on the decisive evidence 

 lately obtained in favour of the latter hypothesis. Some other 

 questions relative to the same subject still demand examination, 

 to which I propose now to refer. 



2. For this purpose it will be necessary briefly to premise 

 a recapitulation of the primary principles on which the several 

 investigations proceed, and which are fully discussed in my former 

 paper. These are, — 



I. The principle of vis viva ; (1) that the square of the velocity 

 multiplied by the vibrating mass is the true measure of force ; 

 (2) that the vis viva of the incident vibrations is equal to the sum 

 of the vires viva of the reflected- and refracted vibrations. Or, m 

 and m^ being the simultaneously vibrating masses of aether with- 

 out and within the medium, h, A', h^ respectively the amplitudes 

 (which are the measures of the velocities) of the incident, reflected, 

 and refracted vibrations ; — then the law of vis viva is expressed by 

 the equation 



II. The law of equivalent vibrations, which on MaccullagVs 

 view is expressed by 



(a) . . . A + A' =^y for vibrations j9erjt?ew«??cw/«r to the plane 

 of incidence, 



and {i and r being the angles of incidence and refraction) 



cos r 



{/S) . . . h + h' = h, r for vibrations jOflra//e/ to the plane 



cos z 



of incidence. 



III. On the principle adopted by Fresnel in the second case (/3), 

 the same law would be expressed by 



(a) . . . h — h' = hi for vibrations petpendicular to the plane 



of incidence, 



cos r 



{j3) , . . h — h'=zhi r for vibrations jo«m//e/ to the plane 



cos 6 



of incidence. 



IV. Maccullagh's hypothesis of equal density giving 



m sin 2i 

 m^ ~" sin 2r* 



V. FresnePs hypothesis of increased density giving 



m _ sin r cose 

 my sin i cos r 



VI. Maccullagh^s hypothesis of vibrations parallel to the plane 

 of polarization. 



