Theory of Surface Forces. 415 
denote by du, dv, and dn. For the potential energy of the 
agent, which presents mathematically the fluid, we have 
found : 
w =-^ f SS n3d ^ dz -wfS^ d!/dz *' ■ (2) 
where R denotes the force acting on unit of mass. 
This equation can be written : 
»=-4[ff{(£H£M£)>«- 
~£rM yHudvdn - 
The variation of W gives : 
du dv dn 
47r /JJJl^ ? ' B M ^ V ^ V ^ U ^ n J 
,(^YSVdudvdn (3) 
We put : dudv = d$ 1 , dudn = d$ 2 , dvdn = d$ z ; 
hence : 
§ 
■ U } du. 
"dn 
The integral refers to the whole space, and the surface- 
integral, being therefore null, contributes nothing to the 
value of BW. 
By the development of all the terms of the first volume- 
integral of (3) we get : 
SW 
- £r f {\^^ du dv dn (4) 
We will now consider the " parallelepiped curvilinear " 
constructed upon the differentials du, dv, and dn, which meet 
* " On the Theory of Surface Forces— I." : Phil. Mag. Dec. 1906, 
p. 559. 
2 F 2 
