90 J'HILOSOPHICAL TRANSACTIONS. [aNNO 1764, 



weight of the water does; making the case analogous to the diminution of gra- 

 vity by centrifugal force. 



But it is likewise easily shown, that half this quantity of lunar force exerts 

 itself to depress the waters all around at the distance of 90 degrees from the 

 vertex; ^ therefore of the former fraction, that is ., „ ^ ;, ^ , ^ part of the force of 

 gravity, will be the total cause of the difference in height of the flood and ebb, 

 in an open and boundless ocean. Say therefore, if (in determining the figure of 

 the earth) -^i-^ of gravity, suspended by the centrifugal force, gave, for the dif- 

 ference of diameters ^-^, what will -^s^rrrr^ P^i't give? and the answer, in feet, 

 will be 8.887. 



4. In like manner, if we take 84" for the sun's parallax, and thence his dis- 

 tance from the earth 23468.6 semidiameters of the equator; we shall find that 

 his whole force to produce a difference of flood and ebb, is to his force at the 

 earth's centre, as 1 to 7823f. But the sun's distance being to the radius of the 

 moon's orbit as 387.34535 to 1, this last force will be to that of the earth on 

 the moon, as 387.34535 to 178.7234 (by cor. 2, prop, princip. l). And the 

 earth's force on the moon is to gravity as 1 to the square of 60.5883 ; whence, 

 adding these ratios, the sun's force to move the sea, will be to the force of gra- 

 vity, as the fraction whose logarithm is — 8.1778026 to 1 ; or gravity is to that 

 force as 1 3249445 to 1 . And therefore, by the same analogy as before, we 

 find the difference of flow and ebb, from the sun alone, to be 1.97824; 1 foot 

 114- inches. 



The solar force therefore, in raising the tides, is to the lunar, as 1 to 4.4924, 

 in a ratio somewhat less than that computed by Sir Isaac. The ratio likewise of 

 the sum of the forces to their difference, is but 7-869 to 5, instead of 9 to 5, 

 which he assumes from comparing the spring and neap tides at Bristol. And it 

 is indeed surprising how he could, from that datum, arrive at conclusions so near 

 the truth, as his very probably are. He tells us he used the ratio of 9 to 5, 

 only till a more certain could be procured. And therefore the foreign mathema- 

 ticians, who have censured him on that head, and on some other articles of this 

 doctrine, might have spared their reflections; at least till they could show that 

 their own deductions were more agreeable to nature and observation. 



6. Unity representing the force of gravity, d the sun's distance, the earth's 



force on the sun will be h, or the fraction whose logarithm is — 9.259021.8. 



And the solar force on the earth is (from the numbers in remark 4) to the force 

 of gravity, as 1 to 1673.I : whence the attractive forces (and masses) of the sun 

 and earth will be as 325172.3 to 1. Add to this the inverse ratio of their mag- 

 nitudes, collected from the sun's mean apparent semidiameter l6'6", and the 

 parallax 8^': and the density of the sun will be to that of the earth, as 1 to 4.068. 



