1880.] under the gravitation of its own parts. 13 



and therefore a state of steady motion is not possible if 



3a > c> a. 



Or, otherwise, since (f>=^r, 



., „ dyfr 2a 2 12 „ 



therefore — £ = — ^——^ - £, 



dt a 2 + c (o s 



, cZ<6 „ a 2 + c 2 6) „ 



, . fZ<f> dyjr 



and since -p- = -~- , 



., , 2a 2 O 1 a 2 +c 2 &) ft 



therefore , , „ — + 1 = « ~ = 0, 



a +c a a 2 - c 2 O 



or 



to a"-cV (a 2 -c 2 )(9a 2 -c 2 ) 



n 'a* + c*J 4(a 2 + c 2 ) 2 



and therefore 9a 2 > c 2 > a 2 for the roots of this quadratic in w : fl 

 to be imaginary, and therefore a state of steady motion impossible. 



Mr H. W. G. Mackenzie has pointed out to me a very simple way 

 of reducing the hydrodynamical equations to the form 



1^ + ^=0, l d / + B'y = 0, 14 + (fiM.a 

 p ax pay * p dz 



For the hydrodynamical equations are of the form 



- -f- + Ax + ax + hy + gz — 0, 

 p dx * 



Ify+By + hx + fy+fz^Q, 



--fi+Cz + gx+fy + yz = 0-> 

 p az 



and we see that the component accelerations in space of the 

 liquid particle at xyz parallel to the co-ordinate axes are respec- 

 tively 



