168 Dynamics. 



269. Therefore the velocities and the times are each as the square 

 roots of the spaces described from the commencement of the motion. 



270. The principles here established are equally applicable 

 to the case of motion uniformly retarded, provided that by the 

 times we understand those which are to elapse, and by the spa- 

 ces those which are to be described, from the instant in question 

 till the velocity is destroyed. 



271. From the equation s = | gt 2 , the quantity g by which 

 we have understood the velocity that the accelerating force is 

 capable of producing by its action, exerted successively during 

 a second of time, is what we call the accelerating force, since we 

 must judge of this force by the effect which it is capable of pro- 

 ducing in a body in a determinate time, an effect which is noth- 

 ing else but the communication of a certain velocity. 



Of free Motion in heavy Bodies. 



272. It is the kind of motion we have been considering, to 



which the motion of heavy bodies is to be referred. But before 



applying to this subject the theory above developed, it will be 



proper to make known a few facts concerning gravity, in addition 



74. to those heretofore given. 



As to the magnitude of the force of gravity, it is different, 

 strictly speaking, in different latitudes, and at different dis- 

 tances from the centre of the earth in the same latitude. But 

 the quantities by which it varies, as we depart from the equa- 

 tor, are very small, and do not in any manner concern us at 

 present. The same may be said of the variations it under- 

 goes, according as we rise above, or descend below, the mean 

 surface of the earth; they cannot become sensible, except 

 by changes of distance much more considerable than any to 

 which we are accustomed ; so that for the present we may regard 

 gravity as a force every where the same, or one which urges 

 bodies downward by the same quantity in the same time. 



This force is to f-e considered also as acting, and acting 

 e.qually at each instant, upon every particle of the matter about 



