342 Proceedings of Royal Society of Edinhurgh, [may 21 , 
Monday, ^Ist May 1888. 
Dr JOHN" MUEEAY, Vice-President, in the Chair. 
1. Exhibition of Photographs. 
A series of Photographs of the Nice Observatory, presented by 
M. Bischoffsheim through the Astronomer-Eoyal for Scotland, were 
exhibited. 
The following Communications were read : — 
2. Note on the Hydrodynamical Equations. By Professor 
Cayley, Hon. F.E.S.E. 
d d d d 
Writing for shortness D = ^ + u-^ + v-^ + , then if from the 
hydrodynamical equations 
“'-K''-::). 
without the aid of the equation, 
dy dv dio „ 
dx^ dy^ dz ’ 
np 
we eliminate V - - , we obtain equations not equivalent to those of 
Helmholtz, 
( ,d d Au dv Aw . 
dv dw dw du du dv i i 
= as usual), but which, 
transforming them by means of the omitted equation, agree as they 
should do with his equations. But the form of the equations 
obtained directly by elimination as above, is an interesting one, 
which it is worth while to give. 
We have 
■r^fdv dw\ ^fdv dtv\ d^ 
- ■^) > 
d d d 
, d\ (d,v dw\ 
