of homogeneous Ellipsoids. 
3 5 6 3 
co-ordinates are a', b', c' (which is plainly within the solid) are 
as follows : 
where x',y', %' are the three co-ordinates of a point in the sur- 
face of the ellipsoid, whose semi-axes; are h, h' , h" . To deter- 
mine the attractions of the given ellipsoid upon the given 
point, we have now only to apply the theorem demonstrated 
in § 3 ; and so. 
5. If we examine the expressions (5) for the attractions of 
an ellipsoid upon a point placed within the surface, it will 
readily appear that the coefficients, into which the co-ordinates 
of the attracted point are multiplied, are homogeneous func- 
tions of 0 dimensions of the semi-axes of the solid, these quan- 
tities rising to the same dimensions in the numerators of the 
functions, as in the denominators : and hence it is easy to in- 
fer, that the values of these coefficients depend only on the 
proportions of the semi-axes to one another, and not at all 
upon their absolute magnitudes. Therefore, if we conceive 
two ellipsoids of the same homogeneous matter, similar to 
