NEWTON S PKINCIPIA. 179 



other as their magnitude and the accelerative forces of 

 their gravity conjunctly ; that is, as 101 to 100, and 

 500 to 501, or as 505 : 501. The difference, viz., four 

 parts, must be supported by the centrifugal force. Hence 

 the ratio of the centrifugal force bears to gravity the ratio 

 4 : 505. 



(3.) Newton now brings in the rule of proportion. If 

 a centrifugal force j$j cause a difference of elevation of 

 the two legs T ^Q, what difference will a centrifugal force 

 g-^g make ? The calculation gives a result |^, or the 

 diameter of the earth at the equator is to its diameter at 

 the pole as 230 to 229. The ratio of the difference of 

 these diameters to the equatorial diameter, is called the 

 ellipticity of the planet. 



This investigation of Newton is manifestly altogether 

 defective. He assumes not only that the spheroid is a 

 form of equilibrium, but that the ellipticity is always 

 proportional to the ratio of the centrifugal force to gravity. 

 These two assertions are indeed true, but they are not 

 self-evident. It was Maclaurin who first demonstrated 

 their truth. It is very remarkable in how wonderful a 

 manner Newton often arrives at correct results by means 

 the most inadequate. Of this there are many other 

 instances besides the present one. He guessed the mean 

 density of the earth he determined by analogy that the 

 velocity of waves varied as the square root of their 

 length. Another analogy led him to a curious result in 

 regard to the tides. 



2. NOTE III. 



3. Newton remarks that the force of gravity will not be- 

 the same at all points of the earth. For draw any radius 

 O P = r from the centre to any point P in the circum- 



N 2 



