236 Mr Greenhill, On the rotation of a [Mar. 24, 



The dynamical equations are 



1 dp dV du du du 

 p ox ox ot ox oy 



1 dp dV dv dv ^^ _ A 

 p dy dy dt dx dy ' 



Now since the axes are rotating with angular velocity to + to', 



du / a^ — If A , , ,, 



and ?/ = (ft) + ftj'j X, since xy refers to a point fixed in space. 

 Therefore 



du a , f.a^ — b^ 



dt ^ ' o? + h'' 



Similarly, 



dv ^ , ,, a^ - 6^ 



Therefore the dynamical equations become 



1 dp dV a^ — Jf { (c^ — 6^\^ 1 



and therefore, integTating, 



a constant. 



The surfaces of equal pressure are therefore similar cylinders, 

 and similar to the external surface if 



« \ — ^ - 2&) (ft) + 0) ) -^ — ^2 + <y 2 , 72 - 



2\2 



