255 
It is then shown, by the aid of the auxiliary ellipsoid, whose 
equation is 
(A—L)2* + (B—M)y* + (c—N)2* + 2(a, + Bi + yidy2 
+ 2a + 2 + y2)vz + 2a; 4+ Bst+ ys)zy= 1, (6) 
that the function v, and the surface (5), may be referred to a sys- 
tem of rectangular axes, for which the following relations exist : ° 
RAF 14=0; &+3,4+3.=0; 842,43,=0; (7) 
the Hebrew letters denoting what the Greek become after 
transformation of coordinates. The possibility of these equa- 
tions in every case amounts to a proof of the existence of three 
axes at each point of a body, which are intimately connected 
with the molecular constitution of the body round the point. 
The equation of equilibrium of a solid body is then shown 
to be 
§§§(xBE-+ v8y 4.282 d= 0 —§§6( 88+ a,8n+ R 8 )dedydz, (8) 
where 
OBES pa a 
B= A + wy at Mis +2(azae+ "ede + *“aedy) 
ae + eas * “any + Pra) 
ae ag 
ey ass dy ee w+ + 2(aoe “dady p vet 4 Maa) 
dn 
a= 2 3% wa PP 7 4N 4 i+ (Pst ts Bat + B an) 
ae at 
tBap trae + wae + 20 at Leds * Vapi) 
dé aE 
. +35" + 1 + age + Sed “\xdz + 'aeay) 
ot + abv = 
n= i + ne wee = ae + Veda) 
yl a =) 
ey" seh Pa ee Nini * “dedy 
dy 
at Pe t+ ant at Bo b+ 2(y, a Fe Bey + Lagi)" 
VOL. I. x 
