The present investigation fills a gap in the applications of the formal methods of rigid dynamics to the study of the motions of aeroplanes.

The principal methods for the approximate solution of dynamical problems together with their aeronautical applications may perhaps be conveniently classified as follows:—

It will be seen that this order of development, which was contemplated by me long before the realisation of artificial flight, was that required at that time to answer the questions, whether an aeroplane could fly without upsetting, how it could be steered in a curve, and how it could be adapted for use in boisterous weather.

The solution of Laplace's well known formula giving the relation between the height above datum level and the pressure and temperature of the atmosphere, may be rapidly accomplished by means of a d'Ocagne alignment chart, an example of which is shown in Fig. i. Its use may be best explained by means of an example. Let the initial temperature (t0) and pressure (p0) be 20° C. and 29 inches of mercury, and at a certain height (z feet) suppose they have fallen 10 temperature (t) 0° C. and pressure (p) 20 inches. The ratio of the pressures and the mean temperature Place a straight edge across the chart so as to cut the right hand (R) scale at 1.45 and the left hand (T) scale at 10. The cut of the middle (z) scale gives the required altitude, namely, 10,000 feet.