300 ON THE CONDITIONS OF FLUID-MOTION. 



Substituting the required form of a-, we get 



t + V6T+2V6(S + V€T)=a-VP.. . . (2) 



Now act upon this with v (which will not affect either S 

 or e), and afterwards take the vector and scalar parts, thus 



V (Ver + 26V - 2eSeT) = Va — V ''P, 

 or 



2e — 4e^= Va— V^P; 

 therefore 



2e=Vvaj and 4e''= V^P — Sva-. • (s) 



The first of these equations gives the required condition ; 

 if the forces acting are conservative, Yvci=o, and e must 

 be constant in direction and magnitude, the magnitude 

 and pressure being connected by the second equation. The 

 case here considered is the general case of the possibility 

 of a quantity of dead water accompanying a moving solid, 

 and includes that of fluids in relative rest upon or within 

 the earth. 



Considering the possibility of a fluid interior of the 

 earth, it must be observed that, owing to precession and 

 nutation, the axis of the earth is not constant in direction, 

 and that, therefore, the condition is not truly satisfied. If, 

 however, the shape of the earth gives a stable form for the 

 fluid, the viscosity of the fluid will tend to mitigate any 

 departure from the apparent rigidity after such motion has 

 once been established. 



Precession must also prevent the absolute rest of fluid 

 contained in a vessel upon the earth^s surface ; and it is pos- 

 sible, though highly improbable, that in this way precession 

 might be demonstrated as Foucault^s pendulum demon- 

 strates the earth's rotation. 



