ON RIFLED GUNS. 15 



*-*.«. *(v>+!£) 



in which A is the resistance, in pounds, on a square foot of cross section of the projectile for 

 a velocity equal to one foot a second; V, the velocity which would make the two terms of the 

 binomial factor equal to one another; and R the entire atmospheric resistance. For spherical 

 balls, A = 0,000514; and for pointed missiles one-third less, or 



A = 0,000342 

 and 



Vi = 1427 feet. 



While the actual velocity of the projectile increases rapidly from the point of starting to 

 the mouth of the piece, the decrease in the elastic pressure shows a diminution in the acceler- 

 ation. The law which connects the actual velocity of the missile with its distance from the 

 point of starting may, with reasonable approximation to the truth, be assumed to be that 

 which connects the ordinate of a parabola of suitable parameter with its corresponding abscissa, 

 the curve being referred to its vertex and axis. This would give 



Y* = 2 P y; 

 at the mouth of piece y = l; and F==V = initial velocity. Whence 



\ 2 = 2]>.l, 

 or 



V 2 



2 P - r 



which substituted above gives 



/V 2 



This substituted in Piobert's formula gives 



R - A -'-' J \ Y -T + v 1 -n) 



whence, denoting the work of the atmospheric resistance by Q'", 



or 



Q'» = A.n.f?.l.V>.(i_+l^) 



2.9561684 

 6.8455760 

 3010300 

 9 3010300 



9 403S044 



0.7534 



(327) 



