Haughton — On Complete Tidal Equations. 233 



a force, but a couple, tending to turn the fluid round the centre. 

 Thus, 



-^ is a, force acting in the direction of the radius vector ; 

 or 



~i is a couple, acting always in the moving meridional plane, and 

 whose axis moves perpendicular to that plane ; 



3^ is a couple, acting always round the axis of rotation, and 

 parallel to the equatorial plane. 



It is evident that if D'Alembert's equations (2) are satisfied — 



1°. YoT forces acting along the radius vector; 



2°. For couples acting in the meridional plane in every possible 



position of that plane ; 

 3°. For couples actiug always round the axis of rotation ; 



complete Dynamical Equilibrium will be secured. 



"We may discount all the mechanical consequences of the rotation 

 by introducing the centrifugal force, leaving only the geometrical 

 consequences of the rotation, in the problem. 



The geometrical effect of the rotation is expressed by writing 



(ji' = nf + cf)', 



where n is the angular velocity of the earth's rotation. 



The components of the velocity of any particle along B, S, T, 

 are — 



^ dO' . , / d<h' 



The centrifugal force affects the directions H, S, only, and does 

 not enter into T. 



The centrifugal force in the direction of H is, obviously, 



dt- \ dt ) 



r 



From this, and from the first three equations (2) we find, at 

 sight — 



dp „ <?¥ rd6'^ . _/ d<i>'\ ,,, 



