322 MESSRS. R. H. FOWLER, E. G. GALLOP, C. N. H. LOCK AND H. W. RICHMOND: 
To determine the value of 0,* it is necessary to measure the angle between AA' 
and the vertical recorded on the card. The direction of AA' must be determined by 
eye from the considerations that it is (l) the greatest diameter, (2) the axis of 
symmetry of the hole, and (3) that it must pass through 0, which is located as the 
centre of a paper circle fitted into the inner hole. 
By proceeding in this manner it was found that the values of § could be nearly 
always determined with confidence by at least one method and often by both. When 
both methods were available the agreement in the resulting values of S was in 
general good ; the average difference between them in all cases for shells of type I. 
(99 in number), in which both measurements were available and both appeared to be 
a priori reliable, was 0*20 degrees. These cases were simply taken as a sample. 
The general features of the agreement were the same for all types. We may 
therefore fairly assert that the probable error of any determination of S is some¬ 
thing less than 0-2 degrees. The use of the measurement OA' is of special 
importance for small values of S, and in fact alone makes their accurate determination 
possible. 
The probable error in the determination of 0 is not quite so easy to estimate, as there 
is no alternative method of determining 0. The method is clearly theoretically sound, 
and the errors can only arise from faulty estimations of the symmetry of the hole. 
By making a number of independent determinations for the same hole, with proper 
precautions against a biassed judgment, and comparing their consistency, it appeared 
that the probable error of any determination of 0 was less than 2|- degrees, unless 
the yaw was small (less than 0*8 degrees, say). As the yaw approaches zero, the 
errors in the determination of 0 increase rapidly until, when the yaw is less than 0-2 
degrees, 0 cannot be determined at all. 
Proceeding in this manner the values of S and 0 were tabulated for each round for 
the values of the time corresponding to the position of each card. If the above 
estimates are correct it is doubtful if the accuracy obtained could be much improved 
on without a radical change in the method of recording the position of the shell. 
2 . 11 . When the yaw has been determined, and the position of the centre of gravity 
on the axis of the shell is known, its position along A A' can be calculated from the 
dimensions of the shell. The position of AA' on the card is well determined, and so 
the position of the centre of gravity can be located with respect to the reference 
point, and so with respect to the point of aim. This part of the determination is 
considerably more accurate than the location of the reference point on the card. 
The path of the centre of gravity for a small number of rounds was measured up in 
this manner; the results of the discussion (§4.2) are mainly null, in agreement with 
theory. The measurements were therefore not completed for every round and are 
not given here. 
* The angle 0 denotes the angle between the plane of yaw OAP and the vertical plane through OP. 
See fig. 10, p. 332. 
