THE AERODYNAMICS OF A SPINNING SHELL. 
319 
shell, that is, the angle between the axis of the shell and the direction of motion of 
its centre of gravity. 
On each card there was marked, by methods which need not be particularised, 
(a) the vertical, ( b ) a reference point from which the point of aim for each round could 
be deduced. The probable error in the marking of the vertical was negligible 
compared to the other errors of observation. The probable error* in each co-ordinate 
of the point of aim was about 0 • 2 inches. 
Times of flight from the muzzle to each card were not directly observed, but 
the mean velocity of the shell over a suitable interval of the range was observed for 
each round with two standard Boulange chronographs. These were sometimes used 
as a pair—in these cases their readings were in good agreement—and sometimes 
separately, at opposite ends of the range, to determine the loss of velocity, and so an 
approximate value for the average coefficient of the drag. From the data so obtained, 
the muzzle velocity and the times of flight from the muzzle to each screen were 
calculated by the usual ballistic methods to a nominal accuracy of 1 f.s. and 
10 -4 second, respectively. It is improbable that any of these quantities are 
appreciably in error to the order of accuracy required by the rest of the experiment. 
A check on the calculated muzzle velocity is provided by the observations, for a 
discussion of which the reader should refer to § 4.1. 
§ 2.1.' Measurement of the Holes in the Cards. 
It is now necessary to deduce, from the position and shape of a hole in any card, 
the position of the axis and centre of gravity of the shell at the moment of passing 
the card. This can usually be done with considerable accuracy. It has been found 
that at all velocities less than 1600 f.s., and often at higher velocities, the hole has 
the form shown diagrammatically in fig. 8, and by photographs of actual examples 
in fig. 8 a. 
Inside the outer circumference ABA'IT of the hole, a considerable amount of 
bruised and partly torn card QQQ is left, which is still attached to the untouched 
part. It is found that, when the edges of this part are flattened out, they always 
define with some accuracy a circle of diameter 2 • 40 inches. A stiff paper circle of 
this diameter can be fitted to the hole with such certainty that its centre is seldom in 
doubt by more than 0*01 or at most 0*02 inches. 
in its tilted position. The dimensions of such a hole will only differ from those of normal impact by 
terms of order d (1 - cos r), where d is any dimension of the hole. Such second-order terms are completely 
negligible if t < 4 degrees. Thus in all cases the shell may be regarded as cutting the hole in the card 
as if the direction of motion of its centre of gravity is normal to the plane of the card at the moment of 
impact. 
* Throughout this paper “ probable error ” is used with its technical meaning, see e.g., Brunt, ‘ The 
Combination of Observations,’ p. 30. 
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VOL. CCXXI.-A. 
