Motion of a Spinning Projectile. 377 



82. It should not be difficult to devise experiments that 

 will give /and c with fair accuracy. I have myself found 

 values of /for the Mark VI. and VII. bullets by the follow- 

 ing experiment. 



The bullet was suspended, with its axis horizontal, by a 

 thin wire. The direction of the axis of the bullet was 

 observed when it was at rest ; then a puff of air was applied 

 at a small angle with the axis, and the direction of motion of 

 the bullet was observed. The bullet, of course, swings as a 

 pendulum, and it is easy to observe the plane of its motion. 

 We have thus all the angles necessary for the calculation 

 of/. In this way I found values of/ which had a mean value 

 about 4*2 for the Mark VI. bullet. My apparatus was 

 rather crude, and more refined experiments would probably 

 give a somewhat different value, but I believe my error 

 is less than 15 per cent. 



83. If /=4'2 for the Mark VI. bullet, and if equation 

 (115) is correct, then c = 0'38 inch approximately. With 

 these values of /and c the product of fc is practically the 

 same as if / were 4 and c were 0*4 inch, which are the 

 values used in equation (82) in calculating the upper limit 

 for N in order that the axis should be stable. 



84. Angular Deflexion of the Axis from the Line of Flight. — 

 The two components of this angular deflexion are [x — e) 

 and (y—rj). We need not consider the effect produced by 

 the wind, for we have already found that its effect is to 

 m;ike the shot point in the direction of the relative velocity. 

 Also, as we are here only considering the mean position of 

 the axis, we shall not take account of the rapid conical 

 motions indicated by the complementary function in equa- 

 tion (72). Therefore, for the rest of the motion, 



(x-e)-+i(y — r)) = z — f 



= 7^l ^r by e( i uation ( 49 ' 



= f ^ { ~Jr +Z ' T+ ( 2 +/) t2 - } < 116 ) 



by equation (93). For the Marks VI. and VII. rifle-bullets 



du 

 ~ 4:2fcu 



We will work out the deflexions when u has been reduced 

 to Jj?/ , which is about 350 feet per second for Mark VI., 



