116 REPORT— 1885. 
According to Stefan, it is necessary if two circuits have a potential 
that 
Qa+b+c¢—2d=0. 
But Stefan did not consider the couple exerted by one element of 
circuit on another. The couples acting on the element ds’ will be as 
follows. There will be a couple tending to increase 6’, i.e. a couple 
whose axis is at right angles to both ds’ and r, equal to dT /d6’, i.e. to 
Biss 
4 — {(1+k) sin 6 cos 6’ cos n—2 cos 6 sin 6'}, 
and another couple tending to increase 7, 7.e. a couple whose axis is along 
the line joining the elements equal to dT /dn, 7.c. to 
| aig 
r 
4 (1+£) sin 6 sin 0’ sin 7. 
We see that these will agree with the couples in Korteweg’s theory of 
pois ee: page G+), ~ porque GtD, 
T T , 
Let us return to the consideration of the energy of the circuits, and 
suppose that, instead of currents flowing along linear circuits, we have a 
distribution of them throughout space. If u, v, w be the currents in 
the element dz, dy, dz, then the part of the energy contributed by this 
element will be 
— A? {Uu+Vv+ Wu} "da dy dz, 
where 
v=3(([{a+Ht+a-H=> fue—H+ey—n+w@-9} } 
dé dy dé, 
with symmetrical expressions for V and W, where 
P= (@— fy? + (y—n)? + @— 6)? 
We may write the expressions for U, V, W in the form 
dw u 
=4(1-—k) — = Oh 
b>—270 m+ {il £ dyn dé 
db v 
mee ae ee oh 
v=ta-)% + [| 228 an ae 
eee Me er (ta dn dl, 
. dz er 
x dr dr dr\ 3; : 
where y = {\| (« di + v iy w 5) dé dy df 
If u, v, ware the components of the ordinary conduction current, e the 
volume density of the free electricity, then 
du , dv , dw de 
ao aig ae noe”: 
and if 7, m, n be the direction cosines of the normal to a surface at which 
