It is, I think, of happy augury that it should have been found possible to arrange a joint meeting of members of the local branches of the Classical and Mathematical Associations, as well as members of the Yorkshire Natural Science Association, to hear a few words about Greek science. No doubt the classical or humane studies can stand by- themselves and so (in a way) can the study of science based only on good English: but I venture to think that they are both much stronger when they stand side by side and support one another. The idea that there is any necessary antagonism or opposition of interests between them is surely unfounded, and there is room for both in our system of education. It is a mistake to suppose that in our school education there is not time for the one or the other; the question is really one of using the time that there is to the best advantage. No doubt schoolboys in the past have wasted much time in the perfunctory learning of Latin and Greek. It has often been remarked that, while a boy was more or less continuously learning Latin and Greek from the age of nine or ten till he went to the University, a girl who only began Latin and Greek at, say, fifteen or sixteen managed to catch up the boy and take a place alongside him in Part I. of the Classical Tripos. It was therefore probably the inefficient or uninteresting way in which the boy used to be taught Greek and Latin that caused the waste of time. If the subjects were made sufficiently attractive and the bogey of compulsion were removed, there is no reason why the boy of good ability should not during his school years acquire a good working knowledge of both classics and science, as well as of the indispensable amount of modern languages. And, if the boy’s interest can be aroused sufficiently to make him take kindly to Greek and Latin on the one side and mathematics and science on the other, I am clear that each branch will help the other and be better done.

The principal ideas are due to Von Staudt and Luroth. There is also a paper by Prof. Mathews, though it does not go far enough; and a recent treatise in English on the subject makes no reference at all to the question. It may be useful therefore to put down a brief account of the leading ideas of the two writers first mentioned, together with some simple developments.

1. The dynamics of aeroplane motion is a comparatively new subject, and one that arouses interest in all students of mechanics. Although a full study of aeronautics involves the use of complicated analysis, yet some really useful information about aeroplane motion can be obtained with quite simple mathematics. It is the object of this paper to draw attention to such methods and results. It will be seen that some of the investigations can be understood by mere beginners in mechanics; others are more suitable for such students as have had considerable experience of mechanics.

The Course described here has been evolved at Northallerton Grammar School during the past nine years. The field-work and plan-drawing are done during Geography lessons, while the calculation of area, height finding and resection are undertaken by the mathematics classes. Many mathematical ideas are involved throughout the Course, which acts as a connecting link between the two subjects. The ages given are only approximate.

Wonderful progress has been made in mathematics during the last thirty years, which have been so productive of memoirs, treatises, journals, encyclopedias, societies, and international congresses, that even an expert is in considerable danger of being overwhelmed by the never-ending torrent. The flow is indeed so great that every one must feel how little he knows, and regret that neither the time nor the energy at his disposal will allow him to explore or even to obtain second-hand information of many of the interesting subjects that are brought to his notice.

The theory of unicursal plane curves affords so many interesting exercises that teachers may like to have a short collection of formulae and theorems about these curves, reduced to the shape which appears to be most convenient for applications.

I propose to consider adjustments which improve the teaching of two subjects that are related as are geography and mathematics. Obviously there is much in mathematics with which geography has no concern, and there is much in the geography course on which mathematics throws no light. But there is some material more or less common, and it is desirable to see in which department or by which master or mistress it should be introduced.

Together with our fellow-students of the Courses in French, Geography and History, we assembled on the evening of the 30th July at the University Lecture Rooms, Palace Green, Durham, and were welcomed on behalf of the University by the Dean of Durham and Canon Cruiokshanks, who promised lis that everything should be done by the authorities to make our visit to their historic city a pleasant one, a promise which it is needless to say was amply fulfilled.

Selection plays an important part in the life of the individual. It is a fundamental process which he must be able to apply in order to understand the world into which he is born. An individual placed amidst any set of circumstances does not assimilate the whole of them. He does not act like a camera plate, which reproduces automatically every feature of an external situation. The complex mental image which he forms from his surrounding circumstances is not an exact copy of the original environment.

5. We shall now apply this method to a few typical cases.

(i) The equation y 1=x 2+y 2

gives y 2=2x+2y 2(x 2+y 2).

Hence, y 1 is always positive; y 2 vanishes along the curve

r 2=-cot θ,

in which x=r cos θ, y = r sin θ. Hence, in Fig. 5(a), the curves have the form) above the dashed curve (the locus of inflexion), and ( below this curve.