336 Mr. J. Prescott on the 



corresponding to these component velocities, the displace- 

 ments being measured from the muzzle o£ the gun. The 

 values of quantities at the muzzle of the gun will be denoted 

 by a suffix 0, thus V , u . The letter a will be used to 

 denote the whole angle through which the line of flight has 

 turned in t seconds, so that a=X — X. 



11. The equation for the horizontal component motion 

 when V> 1060 is 



W du ^ _ W V 2 u 



-n = — K cos X— r = 



g dt g I V> 



that isj 



du uV , . 



rfF = -T (D 



When V< 1060 then l± must take the place of / in (1). 



Now in a low trajectory V differs very little from u, so 

 that equation (1) can be written 



00 



I 2 



dt ~ I 

 and the integral of this is 



i-H (3) 



U U t ' 



Again, since 



du _ du dX. _ du 



di - dX~di ~dX u ' 



equation (2) is equivalent to the equation 



du u 



dX~"~r 



...... (4) 



the integral of which is 



I 



, u X 



°%<u T; 



or _f 



u = u e l 



12. The component acceleration perpendicular to;the curve 



and towards the lower side is V — and the component 



force in the same direction is W cos X. 

 Hence 



w v ^ WcosX=w « 



g dt V 



