MOTION. 9 



pose a body moves over one thousand yards in ten 

 minutes, its velocity will be one hundred yards per 

 minute; because one hundred is the quotient of 

 one thousand, divided by ten. If we would com- 

 pare the velocity of two bodies A and B, of which 

 A moves over fifty-four yards in nine minutes, and 

 13 ninety-six yards in six minutes, the velocity of A 

 will be that of B in the proportion of six (the quo- 

 tient of fifty-four divided by nine) to sixteen, (the 

 quotient of ninety-six divided by six.) To know 

 the space run over, the velocity must be multiplied 

 by the time: for it is evident, that if either the ve- 

 locity or the time be increased, the space run over 

 will be greater. If the velocity be doubled, then 

 the body will move over twice the space in the 

 same time; or if the time be twice as great, then 

 the space will be doubled : but if the velocity and 

 time be both doubled, then will the space be four 

 times as great. 



It follows from this, that when two bodies move 

 over unequal spaces in unequal times, their veloci- 

 ties are to each other, as the quotients arising from 

 dividing the spaces run over by the times. If two 

 bodies move over unequal spaces in the same time, 

 their velocities will be in proportion to the spaces 

 passed over. And if two bodies move over equal 

 spaces in unequal times, then their respective ve- 

 locities will be inversely as the time employed; 

 that is, if A in one minute, and B in two minutes, 

 run over one hundred yards, the velocity of A will 

 be that of B, as two to one. 



If a body in motion tend always to the same 

 point, its motion is said to be rectilinear, or in a 

 straight line. If it continually changes its direc- 

 tion, it is said to have a curvilinear motion. 



