AND THEORY OF THE HEAVENS. 119 



magnified by the telescope, must yet find it very distinctly 

 perceivable by the eye. But this is not actually the case, 

 and the theory might seem to be prejudicially affected 

 thereby. A thorough examination wholly removes this 

 difficulty. According to the hypothesis of Huygens, which 

 assumes that gravitation is everywhere the same in the 

 interior of a planet, the difference of the diameters is in 

 a twice smaller ratio to the diameter of the equator than 

 what the centrifugal force has to gravitation at the poles. 

 For example, in the case of the earth the centrifugal force 

 of the equator is ^i~9 tn f gravitation at the poles ; and 

 hence according to Huygens' hypothesis the equatorial 

 diameter is 5Ts*h greater than the axis of the earth. The 

 cause is this : since, according to the hypothesis, gravitation 

 in the interior of the globe is as great at all the points 

 near the centre as on the surface, but at the same time 

 the centrifugal force diminishes with the approach to the 

 centre, the centrifugal force is not everywhere ^l^th f 

 the gravitation ; and the whole diminution of the weight 

 of a liquid column in the plane of the equator, for this 

 reason, amounts not to -aiirth but rather to the half of 

 it, i.e. -g-fgth. On the other hand, in Newton's hypothesis 

 the centrifugal force, which causes the axial rotation, has, 

 in the whole plane of the equator down to the centre, 

 an equal proportion to the gravitation of the place ; 

 because in the interior of the planet (if it is assumed to 

 be of uniform density through and through) this force 

 diminishes with the distance from the centre in the same 

 proportion as the centrifugal force, and consequently the 

 latter is always g^th of the former. This causes a lighten-, 

 ing of liquid columns in the plane of the equator, as also the 

 rise of them by ai-gth. And this difference of the diameters 



