THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
749 
to the energy function, before conducting the variation; and we must subsequently 
determine the function of position X so as to satisfy the conditions of the problem. 
The result would now come out 
(oy + T, Jf-g + c% + = 
'jL tL !L\ V 
d.r’ fh/’ 
with the condition that V is constant over the surface of the conductor : where 
and would represent so to speak an electromotive pressure uniform in all directions. 
The introduction of such a quantity would make the equations too general for tlie 
facts of electrostatics ; on this ground alone we might assume T to he null, and 
therefore V to be subject to a characteristic equation 
— 11 —] 4- I — 0 
civ \ civ J cly \ dy) dz \ "cfz j 
This investigation may remain as an illustration of method ; but it is not required, 
when we bear in mind the constitution of the medium. Since 
(/ ^0 = curl (^, 7), C) 
we must have (/, g, h) circuital ; so that the characteristic equation for V is Involved 
in the data, without the necessity of any appeal to observation ; while tlie intro¬ 
duction of tlie quantity d would be illicit, and would have to be annulled later on. 
42. If we assumed that the energy-function contained a term 
the conditions of electromotive equilibrium would come out 
and 
(lc~h dldy dcdf cWh db-cj da^f\ 
dy dz dz (lx dx dy J 
cl . o' 
’ dy ' dz j 
where 
{mc^h — nb^g, na^f—IcVi, IWg — ma^f) = — {1, m, 
