Motion of a Spinning Projectile* 



335 



resistance in pounds, V the velocity in feet per second, 

 I and Zj a pair of constants depending on the size and weight 

 of the shot. 



8. For similarly-shaped shot with the same mean density 



W 



-J- is proportional to the area of the section of the shot 



perpendicular to the axis, h being the length of the shot. 

 Since R, is also proportional to this same area, it follows that 



W . WW 



-7- is proportional to -r~ or -j-' and therefore that I and Z x 



are each proportional to h. Moreover, because E and W 

 have the same dimensions as each other, it follows that Ig 

 and l^g have the same dimensions as V 2 , and consequently 

 that I and l± have each the dimensions of a length. Thus 

 for all different but similar shot / and / x are the same pair of 

 multiples of h. 



9. In finding the equation to the trajectory the assump- 

 tion will be made that the area presented to the air by the 

 shot in its flight is constant, which amounts to assuming 

 that the shot always travels nose foremost with its axis 

 exactly in the direction of the line of flight. The extent 

 to which this assumption is in error will appear in the latter 

 part of the paper where the motion of the axis is investi- 

 gated. 



Fig. 2. 



10. Let X denote the angle that the line of flight makes 

 with the horizontal t seconds after the shot has left the 

 muzzle ; u and v are the horizontal and upward vertical 

 components of the velocity V ; X and Y the displacements 



2 A2 



