450 THE MATHEMATICAL PRINCIPLES [BoOH III tion to the force of the sun, and this proportion is to he collected from the proportion of the motions of the sea, which are the effects of those forces. Before the mouth of the river Avon, three miles below Bristol, the height of the ascent of the water in the vernal and autumnal syzygies of the lu minaries (by the observations of Samuel Sturmy} amounts to about 45 feet, but in the quadratures to 25 only. The former of those heights ari ses from the sum of the aforesaid forces, the latter from their difference. If, therefore, S and L are supposed to represent respectively the forces of the sun arid 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 as 9 to 5. At Plymouth (by the observations of Samuel Colepress) the tide in its mean height rises to about 16 feet, and in the spring and autumn tluheight thereof in the syzygies may exceed that in the quadratures by more than 7 or 8 feet. Suppose the greatest difference of those heights to be 9 feet, and L -f S will be to L — S as 20 £ to ll