168 — Prof. Maxwell on the Theory of Molecular Vortices 
We have in general, for the force in the direction of 2 per unit 
of volume by the law of equilibrium of stresses*, 
d d d 
X= 7 Peat dyP* ae zee . . . . . . . (3) 
In this case the expression may be written 
d (poe) de dp, 
X= 7 da iki aga 
d(wy) eS . 
d(u) 
ani nee aa 
ne 
4- 
zs dz ie 
d 
Remembering that aes ee Was de ata +6? +97), this 
becomes 
sa aa Ag? 43 d d Dae ; 
K=ai(£ (mex) + dy HP) + aS (uy) +3 he Lg + 6? + 7°) 
pS dB du 1 i= dy\ _ dp, 
we (5. a) +HY Ga \de 7 da). deen 
The expressions for the forces parallel to the axes of y and z may 
be written down from analogy. 
We have now to interpret the meaning of each term of this 
expression. 
We suppose «, 8, y to be the components of the force which 
would act upon that end of a unit magnetic bar which poits to 
the north. 
/ represents the magnetic inductive capacity of the medium 
at any point referred to air as a standard. pa, wB, wy represent 
the quantity of magnetic induction through unit of area perpen- 
dicular to the three axes of a, y, 2 respectively. 
The total amount of magnetic induction through a closed sur- 
face surrounding the pole of a magnet, depends entirely on the 
strength of that pole; so that if dw dy dz be an element, then 
which represents the total amount of magnetic induction out- 
wards through the surface of the element dx dy dz, represents 
the amount of “imaginary magnetic matter” within the element, 
of the kind which points north. 
The first term of the value of X, therefore, 
LP ad d ) 
ape(S.net oS om pth 
may be written 
ame bk) ita elt.niqe i 
* Rankine’s ‘ Applied Mechanies,’ art. 116. 
