Uniform Motion. 1 5 



pie, what is the ratio of the velocities of two bodies which des- 

 cribe the known spaces s, /, in the times t, t respective^ ; by call- 

 ing v, v', the velocities of these two bodies respectively, we shall 

 have 



v =s -, and -' = -;-, 



whence 



s s' 



v : v' : : - : 



that is, the velocities are as the spaces divided by the times. 



In a word, if it is proposed to compare the velocities, the spaces, 

 or the times, the principle above laid down, will give the express- 

 ion for each of these particulars with respect to each body ; we 

 have therefore only to compare together these expressions. For 

 example, if we would compare the spaces, the fundamental prop- 

 osition v = , gives s = v i ; we have in like manner for the 



second body s f =vV; whence 



s : s' : : v t : v' t', 

 that is, the spaces are as the velocities multiplied by the times. 



26. Of these three things, namely, the space, time, and velocity, 

 if we would compare two together, when the third is the same 

 for each body, we have only to deduce from the same funda? 

 mental theorem, the expression for this third particular, with 

 respect to each body, and to put these two expressions equal 

 to each other. If, for example, we would know the ratio of 

 the spaces when the velocities are the same, we should have 



s , , s' 



v = 7? and i = y ; 23. 



s s' 



whence, since by supposition v = v, we have = 7 , and ac- 

 cordingly 



s : s r :: t : t'; 



that is, the velocities being equal, the spaces are as the times. It will 

 be found in like manner that, the times being equal, the spaces are as 

 the velocities ; and that the spaces being equal t the velocities must be 



