( 254 ) 
Now we have: 
[vr wdt= yo tet fu ears [yet ar oo oe 
By partial integration : 
fulton one [CG 
d ; , af 
Because w and = become!) zero at infinite distance from the 
H 
agens, the surface integral becomes zero and so: 
dw dy? 
—~ d& = — Es dr 
if! ad dx? d He dx 
> dw 
By substituting in equation (14) this expression for fy ae dt 
x 
and the corresponding expressions for the other surface integrals of 
(15), we find: 
et pal eee 2 
Ba rrd ble a sh [war 
( dy? dw dy 2 dy 2 | 
oe (2) + DD) 1S 
The energy in the unity of volume becomes therefore: 
Be Fg fond an een 
Sf I= (Ze) dE 
Let us put: 
mEt) 
then we may also write: 
R? — q° w° 2) 
= pe, ae . e hd . . . . (16) 
Saf 
1) If the members of the last equation are added to those of the corresponding 
equation for the other axes, we may consider the surface integrals together as being 
one surface integral over a sphere. If r=, this integral becomes 0. 
2) g J has the dimension of a force, for g is the reverse of a length. 
