THE AERODYNAMICS OF A SPINNING SHELL. 
335 
To include the effect of these components we add to the right-hand side of (3.105) 
-/uB{[A . A'] —(A . 0) A + 0}+AN y (A cosS-X), 
and to the right right-hand side of (3.113) 
N\[A . X]. 
Equations (3.104) and (3.112) (type a) are unaltered. As a result, the following 
additions must be made to the right-hand side of succeeding equations :— 
To (3.202), +AEW+ ANy (m—y). 
To (3.203), — hBm'+ ANy (n—z). 
To (3.212), -Nx(z-n). 
To (3.213), -N\(w- 2 /). 
As the total effect of the extra components /?, y and X is certainly small in any 
practical case, we have neglected all terms other than those of the lowest order in S. 
Equations (3.206) (3.215), when modified by the inclusion of these extra terms, become 
(3.501) ^(,+cf)-(iQ-A)| (,+cf)-(|-iQy) , = ; 
(3.502) ?={ K -iN\)i/c. 
3.51. The Additional Terms in Equations of Types (3 and y. —The additional 
terms in the equations of type /3 can be written down in a similar manner. The 
following additions must be made to the right-hand sides of the equations :— 
To (3.302), 
To (3.303), 
To (3.305), 
To (3.306), 
+ yrn cos S — h ( nV — In') / Q. 
+ y?i cos S—h (lm f 
+ N An. 
—NXm. 
The terms in h are negligible, as they are O (hS'/Q 2 ) compared with the principal 
terms —nw—10', so long as w/Q is not very small. The principal application of these 
equations is to the motion of a shell near the vertex of a trajectory at an elevation 
of 70 degrees, where the velocity becomes small while the spin probably remains 
large. Under these circumstances the terms y and A arising from the spin rise in 
importance relatively to the terms a and k representing the ordinary force 
components. The inclusion of the extra terms y and A in these equations is at 
present of no practical importance, as we have no definite information as to their 
value. 
The corresponding terms could be added to equations of type y by the same 
VOL. CCXXI.-A. 3 A 
