254 The Eev. Samuel Haughton on the 



three unequal diameters, the least being the axis of revolution, and the greatest 

 being directed towards the central body. 



The components of attraction of the fluid mass upon a particle at its sur- 

 face* are 



Ax, By, Cz ; 



where 



ZMf 3Mf d.\L _ 33^ d.X'L 



^- a? ' a' d\ ' a' d\' ' 



M denoting the mass of the fluid, a the least semi-axis of the ellipsoid, / the 

 dynamical measure of attraction of two units of mass at the unit-distance, 



" Jo/l-t-Wi/l-f-X'V ' 



'^ — 5 ) "■ — 2 > 



the equation of the ellipsoid being 



X' y' z' , 

 a' c 



Let the axis of rotation be the axis of «, and the axis of y be directed towards 

 the central body ; if u denote the distance from the centre of the sun to any 

 particle of the planet, 8 the distance between the centres of the sun and planet, 

 E the mass of the central body, and w the angular velocity ; it is easy to see that 

 the equation of the surface, deduced from hydrostatical principles, will be 



but, neglecting small quantities, 



E E (^ Zy\ ,E. 



E E{l-y) _2Ey 



therefore, the equation of the surface becomes 



• Vid. Ddhamel, "Cours de Mecanique," Tom. i. p. 198. 



