382 
PROFESSOR M. J. M. HILL ON THE MOTION OF FLUID, PART 
and reasoning as in Art. 3 it follows that 
A=K(\, f) +jVb?/ 
But -(—— C ^\ is a function of g. 
r\dr clz ] 
Therefore 
1 /d 3 A 1 dA , d* A\ r 
therefore 
a \ dr 2 r dr dz 
tF(X, t) 
f rbr 
’ b\ , 
‘(A? 
9. For a vortex of invariable form which moves parallel to the axis of 2 . 
\=L(r, z—Z) 
where Z is a function of t only. 
As before 
— = — Z and --- = 0 
X- bt 
() -^ z 
w 
=z-A^=-1^( K (m)A z 
Therefore the equation in A. becomes 
..2 ■ 
5 lie SK 
i.e., 
therefore 
1(£ 1+ * I *W 0) = H (x. 
?’ 3 Ids 3 fZ?’ 3 r dr) \ tX J (A)?' 
The current function is 
K(X, t)--Z 
To obtain it directly from the preceding article, it would only have been necessary 
to put 
A 
X." 
= -Z 
rK' 
