THE AERODYNAMICS OF A SPINNING SHELL. 
347 
The curves of fig. 11 were calculated from formula (4.06), assuming and 
constant, and p u p 2 proportional to t. They show the type of curve on which the 
observed values of 0 may be expected to lie. 
§ 4.1. Analysis of the Experimental Results. 
It is now necessary to make use of these results to analyse the experiments. The 
analysis was carried out by graphical methods. The observed values of S and 0 were 
plotted on separate diagrams, examples of which are shown in fig. 12, against the 
abscissa Qt, Q being determined from the muzzle velocity and the observed moments 
of inertia. The constant factor Q was inserted to make the independent variable of 
zero dimensions; the values of the variable Qt, at given distances down the range, 
are also independent of small changes in the muzzle velocity. The observed values 
of S are sufficient to give a good determination of curves showing the relation 
between § and Qt, except in the neighbourhood of the minima (3, where rapid changes 
of curvature occur when /3 is small .* These curves give approximate values of the 
periods from minimum to minimum, and also the best determination available of the 
values and times of occurrence T„ of the maxima a. By drawing smooth (non¬ 
periodic) curves through the values of a we determine aj as a function of Qt. 
* When f3 is small it may be convenient, in a preliminary plot, to change the sign of 8 in each alternate 
period, so as to obtain smooth curves with 8 passing through zero periodically. 
