20G Captain Noble on the Pressure required to ' ;. 



mence at zero, it will be found more convenient to make the 

 plane of xy pass through the point where the twist would be 

 zero were the grooves sufficiently prolonged. Let the axis of x 

 pass through one of the grooves ; and, for the sake of simplicity, we 

 shall suppose the rifling to be given by one groove only. Let the 

 axis of z be coincident with that of the gun ; let A P (see fig. 1) 

 be the groove or curve described by the 

 point P, and let P [x, y, z) be the point 

 at which the resultant of all the pressures 

 tending to produce rotation may be as- 

 sumed to act at a given instant. Let the 

 angle AON=f 



11. Now the projectile in its passage 

 through the bore is acted on by the fol- 

 lowing forces : — 



1st. The gaseous pressure G, the re- 

 sultant of which acts along the axis of z. . 



2nd. The pressure tending to produce 

 rotation. Calling this pressure R, and . 

 observing that it will be exerted normally /^ 

 to the surface of the groove, we have forge 

 the resolved parts of this pressure along 

 the coordinate axes, R cos A, R cos jjl, and R cos v — X, fi, and v 

 being the angles which the normal makes with the coordinate 

 axes. 



3rd. The friction between the stud or rib of the projectile 

 and the driving-surface of the groove. This force tends to re- 

 tard the motion of the projectile ; its direction will be along the 

 tangent to the curve which the point P describes. If fi x be the 

 coefficient of friction, and if «, 0, <y be the angles which the tan- 

 gent makes with the coordinate axes, the resolved portions of 

 this force are ^R . cos a, yu^R . cos /3, ^ t R . cos 7. 



12. Summing up these forces, the forces which act 

 parallel to x are X = R . {cos\— -fj { cos a}, ^j 



„ y „ Y=R. {cos /z-/^ cos/3}, j> . (1) 

 „ z „ Z — G + R . {cos v—z^cos y};J 

 and the equations of motion are 



M ** 



* dt* 



R{cos v<— \i x cosy}, 



Yx-Xy 



(3) 



p being the radius of gyration. Equations (1), (2), and (3) are 

 identical with those I formerly gave. 



13. Now, in the case of a uniformly increasing twist, the 



