342 Mr KELLAND, ON THE TRANSMISSION OF LIGHT 



15. Now if we had taken the three axes of x^, y^, %^, as those of 

 co-ordinates in the commencement, we should have had the extra 



term (supposing ai = 0) 2 " sm'-^ m each. 



Our equations then arise from making this quantity vanish. 



Let V, v be the velocities of transmission of the vibrations respec- 

 tively perpendicular to the front of the wave. 



Then v' = 2-2i^-,-^j sm'-^. 



These values of the squares of the velocity depend (it is supposed) 

 only on the direction of vibration, provided that direction be perpen- 

 dicular to the direction of transmission : the quantity 



is in fact the force due to the displacement /3, , and the position of /3, 

 in the front of the wave defines its value. Now this displacement 

 may be resolved into three parallel respectively to x, y, z, and Fresnel's 

 hypothesis is, that the force put in play by that resolved part bears 

 the same ratio to it as it would were the vibration one simply in that 

 direction. 



16. This supposition amounts to the following : 



That if we take the expression 2-^sin-— ^, and transform the 



expression ^y\ into an equivalent one in ^x, Sy, Sz ; placing before each 



kSx 

 of the terms, not the expression sin^ — — -^ , but an expression of the same 



form corresponding to a transmission at right angles to the axis belong- 

 ing to that term ; the expression will be unaltered. 



