360 MESSRS. R. H. FOWLER, E. G. GALLOP, C. N. H. LOCK AND H. W. RICHMOND : 
As the value of the couple T is only known to be small, it is necessary to assume 
that N is constant. The principal steps in the calculation of the drift Z, by means 
of (4.203) and (4.204), for the trajectories at 30 degrees and 50 degrees, are given in 
Table YIIIb. for the gun rifled 1 turn in 30 diameters of the bore. For a different 
rifling the drift (N constant) is proportional to N. 
It is only necessary to estimate roughly the effect of the complementary function 
on the motion of the shell since the total effect is always fairly small. The periodic 
term Hj-m'Z, is obviously smaller than 4vy 1 a ] /Q 2 (l —a-) 2 in absolute value, where a x 
is defined as in §4.0, equation (4.041). The initial value of the coefficient of a x is 
1-25 feet for the gun rifled 1 turn in 30 diameters of the bore; both a x and its 
coefficient diminish rapidly. Taking a x — 0*1 radian as an extreme case, 
| Hi + iL x | <1*5 inches. 
The actual value in practice is probably always <0*5 inch, which is small. It 
explains why no evidence of helical motion was obtained in the jump card experi¬ 
ments. The constant value of |H 3 -mZ 3 | is equal to the initial value of |H 1 + iZ J | 
and is also negligible. There remains only the term H 2 + ?'Z 2 . This is equivalent to 
an angular deviation of j K] (c^) 0 +K 2 (c£ 2 ) 0 1 > which is less than 2ko.JQ (l —a-). The 
coefficient of a x for the gun rifled 1 turn in 30 diameters of the bore is 1*8 x 10~ 2 , so 
that for a value of a x of 0T radian the angular deviation is of the order 0° 6'. This 
is of the same order of magnitude as the angular jump likely to be due to changes of 
form and position in the gun and mounting under firing stresses. When it varies 
from round to round in magnitude and direction, it will account for an irregularity 
of the corresponding amount in the observed positions of the shells at any time. 
When, as may sometimes be the case, it remains fairly constant from round to round, 
it will cause systematic errors in the position of the shell at any time. It is probable 
that anomalous values of the drift, sometimes observed at short times, are due to this 
cause. Practical results, however, more often fully justify the use of the particular 
integral alone to give a mean value of the drift when the initial disturbance is only 
known to be small. 
The results of the above calculations of drift will now be compared with observa¬ 
tions of the Z co-ordinates of the bursts of shells, fired at Portsmouth, at corresponding 
elevations, in February and April, 1918. For this purpose use is made of the azimuth 
of the shell burst Z/X ; the quantity A = Z/X£ is tabulated, since its value varies 
slowly along the trajectory (Table IX.). The agreement between observation and 
calculation is as good as could be expected, in view of the uncertainty in the wind 
effects, and provides important evidence as to the correctness of the whole theory. 
4.22. The Damping of the Angular Oscillations and the Effect on the Head 
Resistance. —We have now obtained the complete motion of the centre of gravity of 
the shell by use of the equations of type a for the two standard trajectories; we 
have, in so doing, assumed that the velocity of the shell is the same in the plane and 
