14 Statics. 



the space passed over in any portion of time denoted by *, we 

 shall have 



this is one of the fundamental principles of mechanics. 



24. The equation i? = , gives not only the measure of the 



velocity, but also that of the time and space. Indeed if we con- 

 sidered t and s as unknown quantities successively, we shall 

 have, by the common rules of algebra, 



Thus, to find the time we divide the space by the velocity ; and, to find 

 the space we multiply the velocity by the time. 



If, for example, it is asked what time is required to describe 

 200 feet, when the body in question has a uniform velocity of 5 

 feet in a second ; it is evident that it would require as many sec- 

 onds as there are 5 feet in 200 feet ; that is, we should have the 

 time sought, or the number of seconds, by dividing the space 200 

 by the velocity 5 ; we shall find for the answer 40 seconds ; or, 

 in other words, a number of seconds equal to the quotient arising 

 from dividing the space by the time. 



In like manner, if it is asked what space would be described 

 in 20 seconds by a body moving with a constant velocity of 5 

 feet in a second ; it is manifest that it would describe 20 times 5 

 feet ; that is, it is necessary in this case to multiply the velocity 

 by the time. 



Thus, although we have here employed algebraic characters, 

 it is not because they are necessary to the investigation of these 

 fundamental truths, but because, by means of them, the proposi- 

 tions, and their dependence, the one upon the other, are more con- 

 cisely expressed, and more easily remembered. Indeed it will 

 be seen by the above example, that the first principle, expressed 

 algebraically, being once fixed in the mind, the two others are 

 rendity deduced from it by the most familiar rules. 



25. It will be easy now to compare the uniform motions of 

 two, or of a greater number of bodies. If it is asked, for exam- 



