give Rotation to Rifled Projectiles. 209 



Prom (4), kr<j> = z*, 



•• hr - it-* 9 -it' 



kr -dt*— i -\f'd? + \dt) J ' 



and substituting this value of -~ in (12), 

 R= 



2Mp 2 



{**'}■ 



kr i f k - sin8 _ S T 



\ v^ 2 (sin 8)»+ A 2 */4s a + A 8 J 

 or, for brevity, 



or, substituting the value of -^ derived from (10), 



. JG.z Hz/ 2-z.sinS fi l k \ 9 '\\ 



I'M "M V /4* 2 (sin^p+T 2 + VZz^+JV + V J ' 

 and from this expression may be deduced 



(ArV + 4/o a g a )8in8 2^( /3 2 -r 2 ) ' ' ' ^ ; 

 v / 4^ 2 (sin8) 2 + F + V4F+I 2 



18. Equation (14) gives the pressure acting between the 

 studs or rib of the projectile and the driving-surface of the 

 groove at any point of the bore, and for any inclination of the 

 driving- surface ; but, as before stated, in the Woolwich guns 

 the normal to the driving- surface (that is, the line of action of 

 R) may, without material error, be considered as perpendicular 

 to the radius. 



If in (14) 8 be put =90°, the equation is simplified; and the 

 resulting expression gives the total pressure on the studs for the 

 Woolwich guns. 



Putting then 8 = 90°, (14) becomes 



2p** / 4>z* + k ( *(Gz + Mv' i ) 

 R ~kr*(k-2fi 1 z)+2p< i z{2z + f j, 1 ky ' ' ( 15 ' 



19. Compare now (14) and (15), the equations giving the 

 Phil. Mag. S. 4. Vol. 45. No. 299. March 1873. P 



