The algebraical transformation

should be introduced into dynamical instruction at an early stage, and interpreted as the resolution or rearrangement of the left-hand side, the kinetic energy of two bodies, say railway trucks, of weight W1 and W2 tons, moving on the same line with velocity U1 and U2 feet per second, into (A) and (B) in the right-hand side.

An account of singular solutions of differential equations of the first order is given in every text-book on differential equations. The theory of singular solutions of differential equations of higher order is not usually given in elementry treatises. It is discussed by Goursat (American Journal of Mathematics, xi., pp. 329-372), who bases his discussion on the theory of singular solutions of simultaneous equations ot the first order. From the didactic point of view a more elementary treatment may be acceptable, and an attempt is here made to indicate how singular solutions of a given equation of the second order may be found by simple means.

In his interesting article on Newton in the July Gazette Dr. Rouse Ball had space only for a slight reference to Newton’s views on what we should now call the Foundations of the Differential Calculus. The subject “ involves,” as Dr. Rouse Ball has remarked, “ some awkward questions of philosophy which before Weierstrass’s researches were usually slurred over.” Some of the logical difficulties incident to Newton’s method of approach were clearly seen and pointed out by a contemporary, the celebrated Bishop Berkeley, in a tract which drew much attention at the time, and was followed by a considerable controversy.

The inhabitants of the three kingdoms which constitute Great Britain did not come into contact with the civilisation of the ancient East. Nor, as far as we know, did they have the advantage of direct relations with the Greeks—that race, beloved of Nature, which succeeded in placing all the sciences and all the fundamental arts on so secure a basis as to defy for two thousand years any attempt at radical innovation.