If two lines are divided in such a way that any point on one corresponds to one and only one point on the other, the lines are said to be divided homographically, and any relation between the segments which gives the variable point on one corresponding uniquely to a variable point on the other is a homographic equation.

These equations are of two types:

(α), which contains the term xx', may be said to be of the second order, and (β), in which the term xx' is wanting, may be said to be of the first order.

The graphic methods in use are open to the objection of requiring an improvised graph, depending on the constants of the equation. To obtain even a 5 % approximation, the construction of such a graph demands calculations far in excess of those involved in Horner’s method.

There are some problems in elementary mathematics that the average student is apt to consider as matter for memorising without any great effort being either useful or advisable at understanding them. Experience in teaching elementary statics shows that the theory of stability is an example of such a problem. The average student often does not appreciate the principle of the method generally adopted to investigate the stability of the equilibrium of one body resting on another. He is not generally in a position to grasp the significance of an “infinitesimal displacement,” or the meaning of “proceeding to the second order of small quantities” when the equilibrium is “neutral” to the first order. He is further puzzled by the fact that what appears to be neutral equilibrium becomes, when higher orders of small quantities are taken into account, stable in one case, unstable in another, whilst remaining neutral in a third. These difficulties can be overcome if we adopt a slight modification of the treatment given in the text-books. The object of this article is to explain the method used by the author for lecturing purposes, and not to obtain new results.

Mr. Hatton in the March number of the Gazette (p. 43) has given an interesting discussion of the “geometry at infinity” with the object of reconciling Euclid's definition of parallel straight lines with Desargues' conception of lines “meeting at infinity.” There seems to me, however, still to be considerable confusion, and the young geometrical student who finds difficulty in grasping the statement that all the points at infinity in a plane lie on one straight line will scarcely be reassured when he is informed that two planes may under certain circumstances intersect in a region which is neither a straight line nor indeed a curve.

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.

The news of the sudden decease of the above named gentleman, who was a mathematical master at the “Shop” for a period of more than a quarter of a century, will be received with feelings of profound regret by many officers of the Royal Artillery and Royal Engineers.

Mr. Jackson left evening study (7.15) on the 17th October in his usual health, but was picked up unconscious just outside the West Lodge at 7.30 p.m., and conveyed to the Plumstead Infirmary, where he died the morning after without having regained consciousness.

Nothing was known of the sad occurrence in the “Shop” until after his death. So passed away one who was universally respected and esteemed, and who was held in great regard by all who knew him, both from his refined and gentle character and high intellectual attainments.

Although books of mathematical tables have appeared by the dozen in recent years, most of them show little or no evidence of originality in the matter of arrangement. One of the most common characteristics of such tables is that much space is taken up with unnecessary repetition, as when both logarithms and antilogarithms, squares and square roots, or sines and cosines of all circles from 0° to 90° are separately tabulated, while the information supplied in other directions is defective, as when logarithms of reciprocals are omitted and tables of squares fail to give the correct values of the squares of integers.

The Annual Meeting of the Mathematical Association was held on Friday, 5th January, 1917, at the London Day Training College, Southampton Row, London, W.C., the President, Professor A. N. Whitehead, Sc.D., F.R.S., in the chair.

OH, wad some power the giftie gi’e us
To see oursels as others see us,
It wad frae mony a blunder free us,
And foolish notion;

in which case it is probable that wars would cease. During the last few years we have had glimpses of ourselves through the spectacles of the Central Powers; occasionally through the telescopes of the French, the Italians, or the Russians, and in the near future we are likely to get a good many pictures of ourselves as we appear to the last-named people. We are apt to think that our own view of ourselves is the only true view, and all other images are in error just as they differ from our own standard. Naturally other nations adopt the same course, and we are free to believe that in many cases their vision of themselves is far more at fault than our own self image. In this respect a study of Alice and her standards might be not without profit to the nations. When we want to see ourselves, or, at least, our faces, we usually employ a mirror, and what we see depends very much on the mirror we use. Sir George Greenhill was the first professor of Applied Mathematics at the Eoyal Indian Civil Engineering College, Coopers’ Hill. He told us that at the end of the first session a reception was held and the science departments were on view. A young lady entering the physical laboratory and seeing an inverted image of herself in a large concave mirror naively remarked to her companion, “They have hung that looking glass upside down.” But those who fixed the mirror were not to blame, as the lady would have discovered had she advanced past the centre of the curvature. The reply of modern mathematics to the prayer of Eobert Burns is the Theory of Relativity I have some doubt whether Burns would have appreciated the answer. As a rule, we use a plane mirror to inspect ourselves. This reverses certain spatial relations which can be expressed best, perhaps, by stating that it presents a right-handed screw as a left-handed screw and vice versû, or changes a wine screw into a beer screw, as Clerk Maxwell would say, referring to the tendrils of the vine and the hop.