154 Mr Love, Note on Kirchhoff’s theory of the  [Nov. 28, 
a= Be — (ar + ey) + (a+ 14) ~ He (tg Dy) 20 
re — (Ky + K,) yz + 0,K,y — 0, Be. 
U W 
b= ay ay a (A,@ ae KY) a (A,%, an K,%) maa (x, a ru) YZ 
— (r+ K,") 2e + (6, -—0,) KY — o,A,%- 
c=—2x,24+ a —2w,«,+[«,(o,-—o,) + rA,a] 2— 2x, («,y" — 2,2"). 
The functions w,, v,, w, are to be determined from the stress- 
equations. 
In the general case of an eolotropic solid the stresses are 
linear functions of the strains, and the equations contain differential 
coefficients of e, f, g, a, b, c with respect to a, y, z, these are linear 
functions of w, y, z. The equations also contain the differential 
Ou, OU, OW, 
Oe Oe Ox 
expressions for u,,V,,W,- It is important to observe that for the 
purpose of the approximation we may finally put 2, y=0 as it is 
only necessary to know the strain at all points of a line initially 
normal to the middle surface. The potential energy will be found 
by first integrating along one of these lines and then for all the 
lines. 
coefficients . On integrating we should find general 
In the general case u,, v, are not zero, and the best way is to 
calculate ge we 0@ ae a 
On ey en oy ion oy: 
or aS oR 
02° OB? OR” 
duce the surface-values of S, 7, #. If the solid be isotropic the 
work is much simpler. In this case u,, 1, =0 and 
te —2,) Ae (G7 Ga) ‘| 
then substituting we find 
equations for On integrating these we may intro- 
m—n 
m+n 
Y= = 
We find 
Thus the stress equation involving A becomes 
oR 
ap t Pat [le -2,) 
m—n 
m+ 2 
((*,—A,) 2 + (a, + o)} 
i) (ay ae My oF 2K,") 2 + 0, — eA = 0 ve (16). 
