give Rotation to Rifled Projectiles. 211 



pebble-powder at various points of the bore, and the corre- 

 sponding values of R. It will be remarked how high the 

 pressure on the studs is when that on the base of the shot is a 

 maximum, and how rapidly the strain decreases as the shot 

 approaches the muzzle. 



Table showing the pressure on the studs in a 10-inch British- 

 service gun rifled with a uniform twist } calculated from (17). 



Travel of shot, 

 in feet. 



Total pressure G 

 on base of shot, 



Value of C. 



Value of R, or 

 total pressure on 



in tons. 





studs, in tons. 



0-000 







•04426 







0-333 



1547 



>> 



68-5 



0-945 



1077 





47-7 



1-834 



781 



>> 



34-6 



2-723 



621 



H 



27-5 



3-612 



510 



>» 



22-6 



4-500 



424 



>> 



18-7 



5-389 



356 



yt 



15-8 



6-278 



305 



>> 



13-5 



7167 



268 



n 



11-8 



8055 



240 



>» 



10-6 



8-944 



220 





9-7 



9-833 



205 



>> 



9-1 



24. The results in the Table show the pressures required to give 

 rotation, if the 10-inch gun be rifled on a uniform twist. I turn 

 now to the rifling as it actually exists, and which is defined to 

 be a parabolic twist, commencing with one turn in 100 calibres 

 and terminating at the distance of 9*833 feet with a twist of one 

 turn in 40 calibres ; and first to determine the equation to the 

 parabola. 



Let the origin be at the point where the twist vanishes when 

 the curve A B is sufficiently prolonged — that is, at the vertex of 

 the parabola. Let O z and O y 1 be the axes of coordinates ; let 



Fig. 2. 



53 L'/ 



O A!=z l} OB'=^; let tan 0, be the tangent of the angle which 

 the curve- makes with O z at A, and tan q be the correspond- 

 ing tangent at B. 



P2 



