298 MESSES. E. H. FOWLEE, E. G. GALLOP, G. X. H. LOCK AND H. W. EICHMOND 
knowledge of the force system acting on any shell at high velocities, except when 
the shell is moving “nose on, ” i . e ., when its axis of symmetry and the direction of 
motion of its centre of gravity coincide.* 
Cranz (cf. (5)) and Charbonnier (cf. (2)) make little progress in the treatment of 
the general equations of motion. Prescott (cf. (6) ) makes an appreciable advance 
in the reductions of the general equations of motion to a tractable form, which is not 
too restricted in application, and gives an exact solution of his reduced equations in 
the simple case in which all the components of the impressed force system vary as the 
square of the velocity of the shell. We understand, also, that the problem of the 
initial motion of the shell has been recently treated by M. Esclangon and M. Garnier, 
of the French Artillerie de Marine, with results that are closely analogous to ours, 
but we have not seen their work. 
We therefore propose, in this paper, to give in Part III. a detailed account of 
the complete equations of motion of a spinning shell, moving through air, and to 
justify as far as possible the reduction of these equations to various useful approxi¬ 
mate forms, some of which are classical. To do this, it is of course necessary to start 
from certain a priori assumptions as to the nature of the complete force system. 
These assumptions, which are far less restrictive than any that have hitherto been 
used, are carefully analysed when they are introduced. We then, in Part IV., submit 
the theoretical results so obtained to the test of the experiment described in Part II. ; 
we are thus able to justify to some extent our a priori assumptions, and to obtain 
numerical results of some precision as to the more important components of the force 
system acting on the shell, in the general case. These numerical results, with a 
general description of the actual motion of a shell, will be found in Part I. 
We have seen that the information to be obtained by comparison of the observed 
and calculated values of the drift is of very limited value. Two alternative methods 
are available, both of which are employed in this paper :— 
(1) The complete force system on a model shell at rest in a uniform current of 
air may be determined by observations in a wind channel, t 
(2) Certain components of the force system on a shell moving at high velocity 
may be deduced from the measurements of its oscillations just after leaving 
the muzzle. 
The highest velocity obtainable at present by the first method is 80 f.s., but by 
means of the “ square law ” (see § 1.01) the results may be extended to velocities as 
* In this case the force system has only one component of practical importance, namely, the resistance 
of the air, acting in the opposite direction to the relative motion of air and shell. This force component 
is here called the drag, in conformity with aerodynamical usage. The numerical values of the drag are 
known with fair accuracy for certain external shapes of shell and ordinary atmospheric conditions. 
f For a full description of the construction of the wind channels at the National Physical Laboratory, 
and their use in measuring forces on model aircraft, see Cowley and Levy, “ Aeronautics in Theory and 
Experiment.” 
