354 Mr. J. Prescott on the 



*=(/-!) 5=f ; (44) 



J=(/-l)^ + /f (45) 



These equations are all linear in as, y, e, 77, and these 

 angular deflexions are the result o£ a, a, and /3. It is clear, 

 then, that each produces its own effect quite independently 

 of the others. Thus the wind, to which j3 is due, produces 

 its effect independently of the effect produced by the rota- 

 tion (c ) and the acceleration (a, ) of the line of flight in the 

 plane of the trajectory. Then we may consider the effect 

 of the wind by itself, dropping a and a while we do it. 



45. Dropping a and a from (38) and (39), it is clear that 

 these two equations, as well as equation (40), are then 

 satisfied by 



# = 0, 6 = 0, y ~ a constant, rj — t/ = j3. . . (46) 



We have to show that these values will satisfy equation 

 (41) also; and we need not use any particular expression 

 for R, as it will be seen that the result is independent of the 

 law of resistance. We shall eliminate R from (41) by 

 means of the equation 



W du _, 



g dt 



From this last equation and (41), by division, we get 



- u £=</- 1 >&-9)+/& 



The values in (46) make the right-hand side of this 

 become /3, that is,- , while the left-hand side becomes 



d{y+P) _ i d/3_w_ 

 an du u 



which is the same as the right-hand side. At the muzzle 



r) = and /3= -, so that the constant value of y is . 



