292 NEWTON S PRINCIPIA. 



The force of the sun, therefore, to raise the tide, will 

 be 128^200 9- But the centrifugal force has been shown 

 to be g- The latter raises the water to a height under 

 the equator exceeding that under the poles by 85,472 Paris 

 feet. Hence, the sun s force is -j^th part of the centri 

 fugal force, and will raise the water , or 1 Paris foot 

 and 11^ inches, about two English feet. 



If the mass of the moon had been known in Newton s 

 time, he might have made a similar calculation to deter 

 mine its force to raise the tides. But he was obliged to 

 deduce this mass from the height of the tide itself. &quot; Be 

 fore the mouth of the river Avon, three miles below Bris 

 tol, the height of the ascent of the water in the vernal and 

 autumnal syzygies of the luminaries (by the observations 

 of Sturmy), amounts to about 45 feet ; but in the quadra 

 tures to 25 only. The former of these forces arises from 

 the sum of the forces of the sun and moon, the latter from 

 their difference.&quot; 



If, therefore, L and S are supposed to represent respec 

 tively the forces of the sun and moon while they are in 

 the equator as well as in their mean distances from the 

 earth, we shall have L + S to L S as 45 to 25, or 

 L to S as 7 to 2. Newton remarks that the observations 

 at Plymouth by Colepress gave a ratio 41 to 23, a propor 

 tion which agrees tolerably well with the former. He, 

 however, prefers the former result, because the observa 

 tions were made on larger tides. This reasoning proceeds 

 on the supposition that the earth is without rotation, and 

 in that case there would be high water immediately under 

 the luminary. But this is not the case ; it does not occur 

 until three hours after the transit of the luminary. Nei 

 ther does the highest tide occur at the syzygy, but about 

 three days after. Newton attributes this to the &quot; force of 

 reciprocation,&quot; which the water once moved retain a little 



