364 Mr. J. Prescott on the 



62. Stability of the Mark VII. bullet.— For stability of the 

 axis in this case 



N . 7T 2 6d 2 12100 



that is, 



< 



or 



fW+'6d J $ c ' 



ttJ 6 x 0-303 2 2100 

 / 4(l-2) 2 -f3(0-303) 2 ~8^~' 



N < <r ( 79 > 



If /were 4 and c were 0*4 inch, then we should get. 

 15^8^12 



that is, <42 (80) 



Actually, for this bullet, 



N=33, 



and the fact that the bullet is stable for this value of N 

 shows that 



fc< (^||^) 2 ^et, or < 2'6 inches. . (81) 



In the case of the Mark VI. bullet, for which 1 = 2600, 

 the result corresponding to (80) is 



N<42x^/g°°or <46-7, . . . (82) 



and the result corresponding to (81) is 



fc< 3-22 inches. ...... (83) 



63. Particular Integral of Equation (ol). — Equation 

 (51) can be satisfied by an infinite series of powers of T 

 beginning with the first power. Thus, assuming that 



^ = (/-1)||h 1 T + H 2 T 2 + H 3 T 3 + }, (84) 



equation (51) gives 



T{2H 2 + 3.2H 3 T + 4.3H 4 T 2 + } 



+ (/+l-2^T){H 1 + 2H 2 T + 3H 3 T 2 + j. 



-/(r + 2imT){H 1 + H 2 T + H 3 T 2 + \ 



= l-2troT. 



