LAW OF THE UNIVERSE. 235 



Now let A M N B represent the orbit of the moon ; A N the 

 arc described by her in a minute. Her whole periodic time 

 is found to be 27 days 7 hours and 43 minutes, or 39,343 

 minutes ; consequently AN : 2 ANB :: 1 : 39,343. 



But the mean distance of the moon from the earth is about 

 30 diameters of the earth, and the diameter of her orbit, 60 of 

 those diameters ; and a great circle of the earth being about 

 131,630,572 feet, the circumference of the moon's orbit must 

 be 60 times that length, or 7,897,834,320, which being 

 divided by 39,343 (the number of minutes in her periodic 

 time), gives for the arc A N described in one minute 200,743, 

 of which the square is 40,297,752,049, or A N 2 , which (by the 

 proposition last demonstrated) being divided by the diameter 

 A B gives A ??. But the diameter being to the orbit as 

 1 : 3.14159 nearly, it is equal to about 2,513,960,866. There- 

 fore A n = 16.02958, or 16 feet, and about the third of an 

 inch. But the force which deflects the moon from the tan- 

 gent of her orbit, has been shown to act inversely as the 

 square of the distance ; therefore she would move 60 X 60 

 times the same space in a minute at the surface of the earth. 

 But if she moved through so much in a minute, she would in 

 a second move through so much less in the proportion of the 

 squares of those two times, as has been before shown. Where- 

 fore she would in a second move through a space equal to 

 16 g ' T nearly (16.02958). But it is found by experiments 

 frequently made, and among others by that of the pendulum,* 

 that a body falls about this space in one second upon the 

 surface of the earth. Therefore the force which deflects the 

 moon from the tangent of her orbit, is of the same amount, 

 and acts in the same direction, and follows the same propor- 

 tions to the time that gravity does. But if the moon is 

 drawn by any other force, she must also be drawn by gravity ; 



* It is found that a pendulum, vibrating seconds, is about the length 

 of 3 feet 3j inches in this latitude ; and the space through which a body 

 falls in a second is to half this length as the square of the circumference 

 of a circle to that of the diameter, or as 9.8695 : 1, and that is the propor- 

 tion of the half of 3 feet 3 inches to somewhat more than 16 feet. 



