Chuzzlewit again) at the eleventh hour. On the other hand, he could give us, without any such half-hearted compromise, a Ralph Nickleby, surely as complete a scoundrel as any in literature. With Scott I fancy the spirit of clannishness prevailed over conviction, since I can recall, anyhow on the moment, no instance of a typical uncle occurring in his pages. Thackeray, obsessed with his mothers-in-law, treated the fellow with a comparative but still contemptuous leniency, as witness the cases of Major Pendennis and Sir Brian Newcome. Yet, at the best, they had but a grudging silence or a damning with faint praise to award him. It is true that both the jovial Ingoldsby and the moral Mrs. Elizabeth Turner have a passing word of approval, each in characteristic style, for the man's trick of moralising on occasion, as is evidenced in the following lines:—

And :

I remember, I remember,

When I was a little boy,
One fine morning in September
Uncle brought me home a toy.
I remember how he patted

Both my cheeks in kindliest mood;
'Then,' said he, 'you little Fat-head,
There's a top because you're good.'

One day her uncle brought a toy,
That round and round would twirl,

But when he found

The litter'd ground,

He said, 'I don't teetotums buy

For such a careless girl.'

I must insist for myself, however, that I recognise nothing in either of these cases but a bid for a sister-in-law's approval, whether with a view to a subsequent loan, or at least to a bed and dinner, is not permitted to appear.

And now, having confessed, I must 'hedge,' or the game is up. Bad as are the examples I have quoted, it does not do to generalise from particular instances. We must not venture the statement that all uncles are inherently vicious. If we were to, there are Uncle Toby, and the single gentleman,' and the most lovable the Knight of La Mancha himself, to name no others, to refute it. There is nothing, I believe, which structurally or mentally dif ferentiates an uncle from any other form of relation; indeed, he is not infrequently the most attractive member of the family group. The demoralisation which, perhaps in the majority of cases, has overtaken him, is due, I am sure, to the equivocal nature of his

standing. This, operating upon a very keen and self-conscious intelligence, has effected in him that yeasty effervescence which counts for moral unstability. The laws of primogeniture have been for ever placing him in a false position. Think, for instance, of his having to address that offensive little cub his nephew as ' Your Majesty' on state occasions. Of course an uncle may be a king himself, and very often is; but how is that to better the situation of the uncrowned ones? If years,' they might say, 'are the measures of merit, and the two or three which divide me from my elder brother are represented by the disproportion between a kingdom and a competence, why should my brother's child rank for me above the whelps in my kennel?' It is this resentful grievance, no doubt, which lies at the root of avuncular depravity. The creature is for ever brooding his enforced insignificance. He knows that his title to the small authority he possesses is so little esteemed that he is often obliged to share it with intimate friends of the family, whose years forbid, or whose kindness deprecates, a manner of address either more familiar or more formal. And what is the consequence? He goes to places where social distinctions are less observed, and morals therefore slacker, and makes himself a by-word for reckless unobservances. At intervals he comes home, ravages the sideboard for 'nips' at all unconscionable hours, boils his tea in a billy over the drawing-room fire, slaps valuable relations on the back, and is only blessed if he ends by dying, as I have known him to do, with his dropsical legs in a footbath and a pipe in his mouth.

I am not, however, defending the uncle; I am merely touching on some causes which are possible to account for his reputation. That that is, on the whole, a villainously bad one, we have much testimony (though unobtrusive, as I say) by those whose business it is to assay the relative values of the bad metals of the world. Even his title has been degraded to a significant use; for do we not consign our pledges to mine uncle,' contriving in that phrase a suggestion of something which is both brazen and underhand? Now, being regarded somewhat as a nameless and unattached vagabond, he has come cynically to develop the character attributed to him. He hangs, in short, on his bad name, and even seeks that distinction of being exalted, for the first and the last time in his life, above his fellows. The observant jurors of literature have long seen to it, in their quiet way, that he shall be accommodated.

BERNARD CAPES.

ENGLAND'S NEGLECT OF MATHEMATICS.

FROM time to time references have been made in the Press regarding 'England's Neglect of Science,' and the British public is now being slowly but surely provided with the statistical and other information necessary to enable it to appreciate, if it will, the national importance of scientific work, and its influence on international competition in the world of commerce and industry.

There are, however, growing indications of a serious danger lest, it the English nation does awake to a sense of its duties to science, the most important and fundamental of all the sciences may be entirely overlooked. It will, I believe, come as a great surprise to many people to learn that among the sciences neglected in this country, mathematics probably occupies the foremost place. There appears to be a widespread popular belief that science is one thing and mathematics is something quite different, and it will be asked how can it be possible to say that mathematics is neglected in England when a subject bearing that name forms a large portion of the curriculum of every school in the country?

The deplorable position which Great Britain at present occupies in the mathematical world is the outcome of causes which have been at work for a considerable time, and the gravity of the situation which has thus arisen is so serious that no effort must be spared to enlighten the public on the subject of England's neglect of mathematics and the consequences that this neglect may involve.

There are few people in this country whose knowledge of mathematics extends beyond what may be described as 'School Mathematics,' and the select few who can be correctly styled mathematicians are so overwhelmed by the magnitude of the work which lies before them that it is rarely possible for them to take any steps to arouse popular interest in their subject. Consequently, if the question is asked, 'What is the use of mathematics?' ninety-nine persons out of every hundred will probably reply that mathematics is of no use in itself, but that its study affords an excellent mental training in developing the brain.

Now, there are many other subjects of study to which the same answer would apply with equal force. Of these I like to choose

philately as an instance, because no one would at the present time seriously contemplate introducing the study of postage stamps into our schools and universities. Yet if the subject were regarded from an educational point of view it would certainly develop the pupil's powers of observation, give him practice in accurate measurement, and teach him many facts in contemporary history and geography by a method which might not inappropriately be described as 'heuristic."

Happily it is not necessary at present for the mathematician to defend himself in the educational world against the rival claims of the philatelist. But claims for increased recognition are being pressed by specialists in almost every subject that can be regarded as part of an educational system, and if the mathematician is not to be crowded out in this competition, he must rely on much more powerful weapons of defence than arguments based exclusively on the mental training afforded by the study of elementary mathematics.

Personally I consider that far too much importance is at present attached to the mere examination value not only of mathematics but also of other subjects, especially in their elementary stages. Thus has arisen a state of affairs in which A teaches B a subject in order that B may pass an examination and obtain a certificate which B regards as a qualification for teaching the same subject to C. Neither A, B, nor C is likely to form any true appreciation of the value of a subject taught in this way. Each of them will, in the words of Socrates, think himself wise where he is not, and he will regard his education in much the same light as a Limerick competition-a means by which he can earn money by answering certain examination questions.

It is to the practical aspect and the research aspect of mathematics that we must turn if we want to find the true answer to the question 'What is the use of mathematics?' These two aspects are inseparably bound together under the single heading The Practical Value of Mathematical Research.' The brains of the mathematician constitute a mine of wealth, not perhaps for the mathematician himself (especially in a country like England), but for the world at large. He is the custodian of a priceless treasure with which he has been endowed in order that he may advance civilisation and render possible those improvements which conduce to the happiness and welfare of mankind. The mathematician who is content to live on a starvation income and to shut

himself up in his study, covering pages of foolscap with long formulæ, may, unknown to himself, be a pioneer who is building up for posterity the foundations of a great industry. The mathematical researches of the past form the basis of nearly every advance in practical science of the present time, and culminate in the commercial successes of the future.

I suppose it will now be generally admitted that a certain amount of mathematical knowledge is essential for the requirements of modern applied science, and the estimate commonly formed of the extent of this knowledge can possibly be described as 'B.Sc. Mathematics.' The present article deals with a much more extended aspect of mathematical science, which may be described as 'Research Mathematics,' and compared with which B.Sc. Mathematics' is a mere drop in the bucket. Research mathematics is such a vast subject that no single human being can form an adequate conception of more than a very limited portion of it. It would be much easier for a linguist to learn to speak all the languages of the world than for a mathematician even to understand the whole literature of mathematics. The specialist in Theory of Groups cannot be expected to know much about Hydrodynamics, and to the specialist who takes up astronomical problems such as the lunar and planetary theories, a paper on Theory of Numbers or Multiple Algebra may be absolutely unintelligible.

What, then, is the practical use of all the pages of papers which these specialists turn out when one specialist cannot read another's papers? And admitting that applied mathematics may be of some practical value, how can research in pure mathematics ever lead to any useful results?

Let us in reply give a simple illustration. When mathematicians first began to solve quadratic equations, they soon found the square roots of negative quantities occurring in their solutions. Now, a negative quantity cannot have a square root, and a natural inference is that the problem cannot be solved. This explanation would have quite satisfied any 'practical man' of the sixteenth century. He would consider that the study of such problems was unpractical and opposed to common sense, and that it would not pay. Not so, however, the research mathematician. He said: Square roots of negative quantities occur in my problems, therefore I must find out all I can about them.' Thus arose the study of imaginary quantities which in the course of time became the centre for a large mass of mathematical literature. What has been