12 FERGUSON'S LECTURES. 



LECT. And also by comparing the forces which retain Jupiter's 

 - ^ v ^ x ^ moons in their orbits, with their respective distances 

 from Jupiter. These forces will be explained in the 

 next Lecture. 



The velocity which bodies near the earth acquire in 

 descending freely by the force of gravity, is proportional 

 to the times of their descent. For, as the power of 

 gravity does not consist in a single impulse, but is always 

 operating in a constant and uniform manner, it must 

 produce equal effects in equal times; and consequently 

 in a double or triple time, a double or triple effect. 

 And so, by acting uniformly on the body, must ac- 

 celerate its motion proportionably to the time of its 

 descent. 



To be a little more particular on this subject, let us 

 suppose that a body begins to move with a celerity 

 constantly and gradually increasing, in such a manner, 

 as would carry it through a mile in a minute ; at the end 

 of this space it will have acquired such a degree of 

 celerity, as is sufficient to carry it two miles the next 

 minute, though it should then receive no new impulse 

 from the cause by which its motion had been accelerated : 

 but if the same accelerating cause continues, it will 

 carry the body a mile further ; on which account, it will 

 have run through four miles at the end of two minutes ; 

 and then it will have acquired such a degree of celerity 

 as is sufficient to carry it through a double space in as 

 much more time, or eight miles in two minutes, even 

 though the accelerating force should act upon itno more. 

 But this force still continuing to operate in a uniform 

 manner, will again, in an equal time, produce an equal 

 effect ; and so, by carrying it a mile further, cause it to 

 move through five miles the third minute : for, the 

 celerity already acquired, and the celerity still acquiring, 

 will have each its complete effect. Hence we learn, 

 that if the body should move one mile the first minute, 

 it would move three miles the second, five the third, 



