where, 
=o ue ae. tie _d dy 
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, 
in: Oi. Ahn, Ge inethe in 
i ae ae de ag ae 
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(xdE + ¥dn + 28Z) dm= (4) 
Wp 0& dydz + Spendxdz + Sp do dady 
I 
= sf o& ae 7" a P dn)de dy dz, 
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’ + By* + cz* + 6(Ly?z? + Ma®z* + Nay?) (5) 
+ 4y2(8aa? + Bry? + 2) + 402z(aox* + 3B.y? + yz") 
+ 4ay(a;a? + Psy? + 3322) = 1. 
This surface may be called the characteristic surface of the 
function v,, as, ifit possesses any geometrical properties which 
simplify its equation, a corresponding simplification will take 
place in the function y,. 
