254 



where. 



d,i , di: dl dl dl dn 



az ay ax dz dy dx 



It may be observed that the function v cannot be the 

 same as the function used by Professor MacCullagh for light, 

 which is a function of the quantities. 



dri 



dK 



dK 



dK 



d^ 



dri 



dz 



dy' 



dx 



dz' 



dy 



dx' 



and that, consequently, if the latter represent light, that the 

 molecules of the luminous ether cannot act on each other in 

 the line joining them ; in fact, the two functions mutually 

 exclude each other. 

 From (2) is deduced 



SSS(xSg + Yg^ + zgO^»^= (4) 



SlpBHdydz + llpSndxdz + ^IpKdxdy 



which will give the well-known equations of hydrostatics, and 

 the conditions at the limits of the fluid. 



If the function v, be transformed by changing the direc- 

 tions of the axes of coordinates, it can be shown that the 

 transformation is the same as the transformation of the sur- 

 face 



Ax'^ -\r By* + cz" + 6(l2/222 -f Ma;V + n.tV) (5) 



+ ^yzi^ayX^ + ^xf + Ti^O + ^xz{a^x' + 3)3,«/^ -}- 72^^) 

 + ^xyia^x"- + jSs?/^ -f 37322) = 1 . 



This surface may be called the characteristic surface of the 

 function Vi, as, if it possesses any geometrical properties which 

 simplify its equation, a corresponding simplification will take 

 place in the function \\. 



