NEWTON S PRINCIPIA. 



193 



rection, we may wholly omit those perpendicular. The 

 only force acting along the axis of x is the resolved part 

 of the resistance in that direction. This is 



x v cos. 



But we know that v= -= and cos = ~r. Hence the moving 

 at as 



force is 



dx 



By similar reasoning that parallel to y is 



i 

 &quot;&quot; * dt 



Hence just as in Art. 2., the equations of motion are 

 d* x dx 



m 



dt* ~~ *dt 

 d y 



- (1.) 



We have met with both these equations before. The mo 

 tion parallel to x is manifestly the same as that in the 

 second case of Art. 2. We can therefore write down our 

 results at once, viz. 



V COS = -= = V COS a . e m 

 a t 



and 



m IT /I 



x = V COS a . ( 1 g 



- (2). 



The motion parallel to y is the same as that of the third 

 case of Art. 2. Hence 



