40 



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 mi 

 nutes, or 39,343 minutes; consequently A N : 2 AN B 

 ::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 num 

 ber 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 AN 2 , which (by the propo 

 sition last demonstrated) being divided by the diameter 

 AB gives A n. But the diameter being to the orbit 

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

 Therefore A n = 16.02958, or 16 feet, and about the 

 third of an inch. But the force which deflects the moon 

 from the tangent 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. Wherefore she would in a 

 second move through a space equal to 16^ nearly 

 (16.02958). But it is found by experiments frequently 

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



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

 of 3 feet 31 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 proportion 

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



