152 Mr Love, Note on Kirchhoff’s theory of the [Nov. 28, 
The equations must still give 7,=0, for the only terms in on 
Ox 
which are linear in y are —7,y—7,0,y, and there is no term in 
Ow “48 
a which is lmear in w In like manner, writing o,, v, 7, for 
g) 
g,, U, T, and interchanging a, y we find 7, = 0. 
Again, the terms in od which are linear in yarex,y+X,0,Y—A,@Y, 
Ox 
and the terms in oe which are linear in ware —),@—2,o,2. Hence 
we find «,(1+¢,)—-Aw=—A,(1+¢,). Or since o,, o,, @ are all 
small we have \,=—«,(1+o¢,—¢,)+A,%, which gives XN, = — K, 
approximately as ‘before, and also gives us a second ‘approximation 
to the value of 2,. 
Using the second approximation to , in terms of the first 
order, and the first approximation in terms of the second order, 
we find 
a) 
aA [z+ w, ap gA,e + K, cy +Za,y | +o, 
u 
aoe [et+tu,—$r\,@ +n,cy+hny]io 
+ {k,(o,—o,) +A,a} 2. 
pRB Gets OWENS be, 
The condition —— ann Paice gives 
d, (4,24 ky) =K, (A,2— KY), 
which requires TON re AU staid noch ace eee eee (12). 
Hence, 
U=U +r, 20 —K,y2+0,0+ ay+[k, (o,-0,) +22] y2 
+ w, (A,e— Ky) — pra" — $x, KY? 0... (13), 
where uw, is an unknown function of z, w, is a known function of z 
which for an ie oe is 
m 
m+n 
“Thm — my) 2+ (a, +0,) 2%, 
and the term in 2’y, which has the coefficient 4(—2,«, +2,x,), 
and that in y’«, which has the coefficient 4 («°A, + «,7) ‘have dis- 
appeared. 
* The notation for the elastic constants is that of Thomson and Tait, 
