366 Sir IS AAC N E W T O N’s Book IV.

parts is * about 60’ times less, because their distance from theearth’s centre is so many times less than the distance of themoon from it. The gravity of those parts of the earth thatare directly beneath the fun, and of thole opposite to it, is di-minished by a double quantity of what is added to the lateralparts ; and as the diminution of gravity of the one, and aug-mentation of the gravity of the other, conspire together inraising the water under the sun, and the parts opposite to it,above its height in the lateral parts ; the whole force that pro-duces this effect is to be considered as triple of what is addedto the gravity of the lateral parts : and is thence found to beto the gravity of the particles as i to 12868200, and to thecentrifugal force at the equator as 1 to 44527. The elevationof the waters, by this force, is considered by our author as aneffect similar to the elevation of the equatorial parts above thepolar parts of the earth, arising from the centrifugal force at theequator; and, being 44527 times less, is found to be 1 footand 11^ inches, Paris measure. This is the elevation arisingfrom the action of the fun upon the water.

In order to find the force of the moon upon the water, hecompares the spring tides at the mouth of the river Avon belowBrijlol (which are the effect of the sum of the forces of the funand moon when their actions almost conspire together,) withthe neap tides there (which are the effect of the difference ofthese forces when they act almost against one another,) andfinds their proportion to be that of 9 to 5 ; from which, afterseveral necessary corrections, he concludes that the force of themoon is to the force of the fun, in raising the waters of theocean, as 4,4815 to 1 ; so that the force of the moon is able,of itself, to produce an elevation of 8 feet and 7^ inches, and

* Princip. Lib. III. Prop. 36.

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