330 
PliOFESSOK A. K. FORSYTH ON THE 
Similarly 
and therefore 
Again, we have 
and therefore 
7 ^ + <t>J/ V + 
<±_ cx cy c2 
dn -j- A 
+ fo=. 
d-cj) __ + '2(l),,y4>.,4u + -</>■! - 0 . 7 <^; H~ 
drd <p,~ dr ({>/' dr 
Hence 
(-) j d~(f) _ 
A, did ~ Ai^ Ai Ai^ ’ 
that is, 
d^ _ , /1 I _Lv'^^iY 
\dnj did ^ \y\dnj '11^ VvJ ydn) 
and theref ore 
AiI o/i , 1 
Ay ” did ^ " \K, ^ VJ dn ' 
33. Let U, V, W denote (^onr ^uoi respectively ; then the directions of the lines 
of curvature, through tlie j^oint x, y, on the surface (j) = constant, are given hy the 
et] nations 
(/U, U, d:c =0, 
f/V, V, dy 
c/AV, AV, dz j 
U dx + A" dy + AA^ dz = 0 . 
Ijet /, in, n denote the direction-cosines ol either line ; then 
a/ + li??i + gu, U, / = 0, 
h/ + Inn + fv?. A", m 
gl + fin + ca, AA^, ii 
U/ + Yrn + AAhi = 0. 
