THE TIDES. 



on the waters to be the same as if they were collected at H, it will be 

 evident that the moon's attraction on the solid earth will be less 

 than its attraction upon the waters which lie on the nearer side of 

 the earth in the proportion of the square of 60 to the square of 59, 

 that is, as 3600 to 3481, and consequently the difference of the 

 two attractions will be to the whole attraction exerted by the 

 moon upon the earth as 119 to 3600, or what is the same, as 1 to 

 30|. Thus it appears that the moon's power to raise a tide on the 

 nearer side of the earth is little less than a thirtieth part of its 

 entire attraction on the earth. 



By the same method of calculation, the power of the sun to 

 raise a tide may be ascertained. The pun's distance from the 

 centre of the earth is just twenty-four thousand semi-diameters 

 of the earth, and its distance from the waters, on the nearer side 

 of the earth is therefore twenty-three thousand nine hundred 

 and ninety-nine semi-diameters. It follows, therefore, that its 

 attraction on the waters on the nearer side exceeds the attraction 

 on the earth, in the proportion of the square of 24000 to the 

 square of 23999, that is, in the proportion of 576,000000 to 

 575,952001, and consequently the difference between its attrac- 

 tion on the waters, and its attraction on the solid earth, under the 

 waters, has to its entire attraction the proportion of 47999 to 

 576,000000, or, what is the same, that of 1 to 12000 ; so that 

 the sun's power to raise a tide is about the twelve-thousandth part 

 of its whole attraction on the earth. 



It appears, therefore, from this reasoning and calculation, that 

 the moon's power to raise a tide is about the thirtieth part of its 

 entire attraction, while the sun's power is the twelve-thousandth 

 part of its attraction. If the entire attraction of the moon were 

 equal to that of the sun, it would therefore follow very obviously 

 that the moon's power to raise a tide would be greater than that 

 of the sun, in the proportion of 12000 to 30, or what is the same, 

 of 400 to 1. But the proportion in favour of the moon's influence 

 is not nearly so great as this, because the entire attraction of the 

 moon is much less than that of the sun. Let us consider in what 

 proportion it is less. It is demonstrated by astronomers, that the 

 mass of the sun is 28,394880 times greater than that of the 

 moon. If the sun, therefore, were as near the earth as the moon 

 is, its attraction would be 28,394880 times greater than that of the 

 moon. But being at a distance 400 times greater than that of 

 the moon, its attraction is diminished in the proportion of the 

 square of 400, or 160000 to 1. Its actual attraction will, 

 therefore, be found, relatively to that of the moon, by merely 

 dividing 28,394880 by 160000, which gives 177. 



6. Since, therefore, the moon's power to raise a tide would be 

 134 





