344 MESSRS. R. H. FOWLER, E..G. GALLOP, C. N. H. LOCK AND H. W. RICHMOND : 
In the practical analysis of the results of rounds whose stability factor is less than 
or near 1 , it is convenient to use graphical methods. If the observed yaw is plotted 
against Qt, it is easy to read olf the observed values of a, the maximum yaw, and 
HT, the period. A chart was therefore constructed with suitable families of curves, 
according to (3.704l)-(3.7044), from which, when QT and a are known, s, b, c, and k 
can be read olf directly. 
Part IV. —Analysis of the Experimental Kesults. 
§ 4.0. Equations of Motion in Polar Co-ordinates. 
The theoretical results of Part III. will now be applied to the analysis of the 
observations described in Part II., which consist of determinations of yaw $ and 
orientation of yaw <p, for a shell fired horizontally over a range of about 600 feet. 
When the stability factor is greater than about 1 * 1 , the maximum yaw for the 
corresponding round never exceeds 7 degrees, and it is then possible to make use of 
the complementary function solution of equations of type a as given in § 3.6. These 
rounds give more valuable information than those which are less stable. 
We treat certain of the force coefficients as constants over the range of the 
experiments, and verify that the results of the theory agree with experiment when 
certain values are given to the force coefficients. In particular the spin is treated 
as constant. The way in which the coefficients vary with the velocity is determined 
mainly by firing shells with various muzzle velocities. The final results have been 
already described in § 1.2 above. 
The experiments determine the values, at definite time intervals along the range 
(§2.0), of the angle of yaw S and the angle cp turned through by the line in which 
the plane of yaw meets the cards. The measured value of <p is zero, when this line 
is vertical and increases from 0 to 27r radians in the direction in which the 
shell is spinning. It is, of course, ambiguous by an integral multiple of 27 t. Except 
where specially stated the yaw S is assumed to be an essentially positive quantity. 
When OA passes through the position OP, the yaw vanishes; the value of <p 
will change discontinuously by an amount ± 7 r, and dS/dt will change its sign 
discontinuously. 
It is convenient in Part IV. to express the solution of the equations of motion of 
type a in terms of the co-ordinates S and <p. The exact relations between the 
measured $ and <p and the'direction cosines (l, m , n) and (x, y, z) of § 3.2 are 
cos $ — lx + my + nz, 
tan <p = 
(nx — lz) cos ( ny—mz) sin 6 } 
mx — ly 
