Page:Popular Astronomy - Airy - 1881.djvu/238

224 to find the proportion of eF to jK. Now taking CE as 95,000,000 miles, the circumference of the earth's orbit is 596,900,000 miles, which the earth describes in 365.26 days; and therefore the line Ee which is the earth's motion in one hour, is 68,091 miles. Adding the square of CE to the square of Ee, and extracting the square root of the sum, we find that CE is 95000024.402 miles; and therefore eE, the space through which the sun draws the earth in an hour, is 24.402 miles. For Jupiter, CJ is 494,000,000 miles; the circumference of its orbit is therefore 3,104,000,000 miles; which is described in 4332,62 days; therefore Jj, the motion in one hour, is 29,850 miles; and the length of Cj, found in the same manner, is 494000000.9019 miles; and jK, the space through which the sun draws Jupiter in one hour, is 0.9019 miles. Hence, the attractive force of the sun on the earth is to the attractive force of the sun on Jupiter, in the proportion of 24.402 to 0.9019. But if we compute from the rule of the inverse square of the distances, what would be the proportion of the force of the sun on the earth to the force of the sun on Jupiter, we find that it is the proportion of 24.402 to 0.9024. These proportions may be regarded as exactly the same, the trifling difference between them arising mainly from the circumstance, that I have only used round numbers for the distance of the two planets from the sun. And thus for these two planets it is true that the strength of the sun's attraction is inversely proportional to the square of the distance of the attracted body from the sun.

If I had compared any two planets, I should have arrived at exactly the same agreement. And generally, I may state (though I cannot at present