The subject of this Paper is one that presented itself in a piece of work of a practical nature. The development of aeroplane flight naturally suggested the investigation of the motion of a body in a resisting medium. In general this problem was too difficult for solution. One therefore looked for legitimate means of simplifying it. One simple type of motion allied somewhat to aeroplane motion was that of a plane lamina moving in air under the earth’s attraction. Even here difficulties arose in the solution of the resulting equations of motion; yet further simplification was not quite permissible, for care had to be taken that the simplified problem did bear some relation to the actual problem presented by nature.

In the Report of t h e Education Reform Council, published in 1917 under the title “Education Reform,” it is suggested on page 83 that for boys of 14 to 16 years of age attending a secondary school it is desirable that the mathematical course should be directed towards an elementary use of calculus methods, so that those who remain at school to a later stage may be able to use effectively the elements of infinitesimal calculus. On the next page it is further suggested that boys of 16 to 18 years of age who take up mathematics and science may pursue the study of differential and integral calculus, including the easy parts of differential equations, and apply these with advantage to higher algebra, trigonometry, co-ordinate geometry, solid geometry and mechanics; that the co-ordinate geometry requires a muchbroader treatment than that commonly adopted—a treatment in which the calculus is freely used and in which some “geometrical” conies, when elegant and convenient, is dovetailed into the analysis.