DYNAMICS. 



If S be the space described by the body in its own 



path, the space described by the perpendicular in 



the other line will be S cos /3. 

 Hence also if the velocity of the body in its own path 



is uniform, it will be uniform when reduced to any 



other direction. 



55. -The change which any variable quantity 

 undergoes in an infinitely small portion of time, is 

 called the Momentary Increment of that quan- 

 tity. 



Thus if S is the space described by a moving body in 

 the time t, and if V be its velocity, supposed vari- 

 able, at the end of the time t, if we suppose t to be 

 increased by an indefinitely small instant, the change 

 of S and of V in that instant are called their Mo- 

 mentary increments. 



The increments are denoted by the same letters that 

 express the variable quantities, with a point over 



them. Thus S, V, T, are the momentary incre- 

 ments of S, V and T. 



Though the variable quantities may decrease as well 

 as increase, the momentary change is called an In- 

 crement in both cases, but is accounted negative 

 when the quantity diminishes. 



56. Though the velocity of a body be variable, 

 it may at any point be taken as uniform for an in- 

 definitely small portion of time, and the increment 

 of the space will be, just as in the case of uniform 



motion 



