THE AERODYNAMICS OF A SPINNING SHELL. 
359 
freed from the unnecessary restriction that / L // M and N should be constants.* We 
have thus justified the use of the plane trajectory as an approximation to the true 
motion. The leading terms in (X—X x ) and (Y—Y x ) can be calculated if required. 
The effect on the motion of a change in initial conditions is obtained from the 
complementary function. Equation (3.655) gives the value of £ corresponding to the 
general initial conditions £ 0 = 0 , )? 0 = a, >/ 0 = bQ, where a and b may he complex. 
Substituting in equation (4.201) the part of £ arising from the complementary 
function, it appears that H + iZ is made up of three parts 
(a) A periodic term 
(b) A term 
H 1 + iZ Y 
4*^-5 / K]??! K,„ \ 
G 3 V(l+<x) 2 (l-<x) 2 / 
H 2 + iZ 2 — — {Kj (^) 0 + K 3 (f 2 ) 0 | 
cv £3 dt, 
which is the effect of a variation in the direction of projection, as mentioned in 
§ 3.64. 
( c) A constant term H 3 + ?'Z 3 equal to the initial value of H 1 + iZ 1 with its sign 
changed. 
4.21. Numerical Residts as to Motion of Centre of Gravity. —-The only data as 
to the forces on the shell required for the calculation of the drift are the value of 
/l//m as a function of v/a. This is derived from the results of the jump card 
experiments for vja >0*7, and from wind channel experiments for v/a <0*7, and is 
shown plotted in fig. 15. 
* Prescott obtains a solution of the equations of motion in the form of a series of which the first term 
is also equivalent to Mayevski’s formula. (See Introduction, p. 296.) 
3 P 
VOL. CCXXI.-A. 
