produce Translation and Rotation in the Bores of Rifled Guns. 203 



to those shown in fig. 1, and a third rifled polygonally, and if 

 we suppose that the shot in each case are of the same weighty and, 

 further, that in each case the velocity-increments at the moment 

 under consideration are equal, then the pressures upon the base 

 of the shot will be as follow : — In the case of the 



Smooth-bored gun, pressure = G; 

 First rifled gun, pressure = G + 



R 



Polygonally-rifled gun, pressure 



\/\+k* 



M+i); 



= G + KJ 



\/l + V 2 



+ 



. 7T 



sin — 

 n 



. >■ (28) 



\A 2 +(-!) s J 



We shall now give examples of the cases we have been dis- 

 cussing to exhibit numerically the above results. 



Let us suppose that two seven-inch guns are rifled — the first 

 according to the method shown in fig. 1, with a pitch of one turn 

 in 294 inches, the other octagonally, with a pitch of one turn in 

 130 inches. It is required to determine in each case the pres- 

 sure on the driving-surface in terms of the pressure on the base 

 of the shot. Now, in the first case, from (13), 



Pressure on driving surface = ^—r- f- — - — ^ — - — — . G, 



hr(k— ffcj) +27rp 2 (/* 1 A:H-l) 



where 



tt=3-14159, p=r*/i = 2-475, £=13-3697, A=294, 

 r=3-5, ^, = -1666, 

 whence we obtain 



R=0375G (29) 



In the second case, from (26), 

 Pressure = 



27T/0 2 



/*i 



v/l + * 2 



(2wp**-rA) + 



sm7r 



\A+( sin 



7 T~^ \ ,G ' 



.( 27rp 2 sin — H rhk ) 



where 



tt=3-14159, 



, 2 + cos — 

 J. n 



p= y^c 2 . -_ = 2*350 (c = length of side of polygon), 



1 — cos — 



