PROFESSOR M. J. M. HILL ON A SPHERICAL VORTEX. 
Also by (XT.) 
221 
xfj = 
A ^ _ z)= _ Az 
(XVII.). 
Art. 5. The Pressure. 
Substituting the above values of r and iv in equations (IV.), they become 
- ~ »■ (•2r- - a}) = - |( ^- + V 
' or \ p 
8P , 8kP d/p 
I 
, ^ . (XVIII.). 
Z + ^(^-Z)3--(.-Z)=-^J^ + V 
Therefore 
P 
2P / . 2^’2 4/i;- , 
+ V = -{z-Z)A-~{z-Zy zy 
+ an arbitrary function of ^.(XIX.). 
Art. 6. The Molecular Rotation. 
If 2&) be the molecular rotation, 
Therefore 
2(ii = - — 
0 T 
dz 
djv ^ 
0r ^ c2 ' 
<j) 
M , Ic , 
+ jl’'- 
(XX.) 
Hence the molecular rotation varies as the distance from the axis of symmetry. 
The vortex lines are circles, whose centres are on the axis of symmetry, and whose 
planes are perpendicular to it. 
Art. 7. P'urther simplification ofi the Particular Pntegral 
Amongst the surfaces given by making X constant in XV., there is one, viz. :— 
V - ^)- 
— 1 
ft- 
c- 
= 0 , 
which breaks up into the evanescent cylinder 
P = 0 
(XXL), 
