256 Mr. A. E. H. Love on the Oscillations of a Rotating 



may be, provided it is not faster than once in 3 hours ; so 

 that if the length of the day was ever about 4 hours the den- 

 sity must have been such that, as the spheroid contracted, and 

 rotated faster, the period of free oscillation coincided with that 

 of the semidiurnal tide before the length of the day was 

 3 hours. 



2. Suppose a mass of liquid enclosed in an ellipsoidal case, 

 whose equation is x^/a^ + y^/b^ + z^/c^ =1, to be rotating as if 

 rigid about the axis z with angular velocity ^, and let an 

 additional angular velocity O about the same axis be im- 

 parted to the case, and let the case be made to change form 

 but so as to remain ellipsoidal and of constant volume ; the 

 velocity-potentials of the motions set up in the liquid by these 

 two motions of the case are 



n 



!_52 



and 



'■ + P 



xy, 



^a^'^WA 



A', y, z being the coordinates of a particle of the fluid referred 

 to the principal axes of the elli})Soid at time t, these axes 

 rotating with angular velocity f») = ^-fO. The velocity- 

 components of the fluid-element which at time t is at {x, ?/, z^ 

 are 





(I) 



w= -z. 

 c 



If U, V, W be the rates of change of the coordinates of a 

 fluid particle at {x, y, z), we shall have 



TT « , 2a^ „ 



V=v— G).r= jy — 



'W=io ■=■ - z. 



26^ 

 a2-t-62 



O^, ^ • • • (2) 



3. The Eulerian equations referred to the moving axes are 



