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go back to his clockmaking and regard his college course as mere waste of time. And I really do not see how I could have advised otherwise.

Professor Hobson, Sc.D., F.R.S., has recently published a tract on Mathematics from the Point of View of the Mathematician and of the Physicist.' Should this tract fall into the hands of a non-mathematical reader, it would only confirm the common impression that mathematicians do not stand in need of the world's goods, but that they can spend all their time in revelling in quadratic forms, imaginary quantities, and the like unworldly abstractions. Even Sir G. Greenhill made a similar suggestion in saying that we could take our leisure in studying the stability of aeroplanes, while practical men had to neglect these precautions and get up at once into the air. There never was a bigger mistake. Mr. Harper and I had to wait about ten years before doing anything at the subject, owing to teaching duties. The whole of the mathematical problems connected with aeroplanes could have been cleared up, in fact wiped off the board, so to speak, long before the first manned flights, by anyone who had plenty of time and leisure to think about the matter.

One object of this article is to contradict these misleading suggestions and to point out that mathematicians are, after all, human beings who ought to earn enough money to eat and drink and be clothed, and perhaps to marry and bring up families ; on the other hand, they often find this impossible under existing conditions, and no one outside a small mathematical circle—perhaps

а not everyone in that circle-realises the fact.

Although this article has already grown to a considerable length, it seems desirable before concluding to refer to a cognate question leading to very opposite conclusions, which would require, for its adequate discussion, another equally long article-namely, the value of mathematics to a non-mathematical specialist. I will only refer to two cases in point.

At the discussion on this paper before the Mathematical Association, a letter was read from a former fellow-student of mine at Cambridge, now occupying an important official post in the Survey Department of the Egyptian Government. If I remember rightly, he used to be regarded as taking a very 'back seat' behind the students of that time who were training as mathematical specialists. But his letter seems to show that he finds the 'outlook' gained by his mathematical studies to be of the greatest possible value



in deciding a large proportion of the questions involved in his official everyday correspondence. He specially refers to Taylor's Theorem, considered in its broad and general aspect. I take it that what he means is something of this kind : while the statement and proof of this theorem must necessarily be associated with a large quantity of algebraical symbols in our text-books, the theorem itself indicates broad and far-reaching relations between cause and effect in associated phenomena, and when a small change occurs in one of the conditions of a problem he is enabled by this means to appreciate the effects of this change.

This and other similar instances seem to indicate that beneath the mass of formulæ of our text-books there is a kind of substructure of fundamental truths which enable conclusions to be drawn perhaps partly by intuition-without doing any algebra at all, and that it is when this substructure is reached that the nonmathematical specialist begins to realise the value of his mathematical knowledge. Shortly after this letter I received an application from a surveyor

a in Central Africa for advice and tuition in connexion with Jordan's classical treatises, and it was some time before I could find an English mathematician competent to give the necessary assistance which he required for his professional duties.

All the changes which have recently taken place in mathematical teaching are calculated to develop the 'outlook' value of the teaching and to minimise the mere algebraical drill with meaningless symbols which has proved such a blind alley to would-be mathematical specialists in the past. The campaign is a difficult one. There is much inertia to be overcome. The traditions of Cambridge forty years ago and more still filter down into our school examinations, and boys who do not intend to do any mathematics after leaving school are still required to work G.C.M.s and L.C.M.s which they will never want to make use of afterwards, even if they become mathematical specialists. But this spirit is passing away. If we can only prove to the world that a course of training under an English mathematician of the first rank is the most valuable asset in the education of a non-mathematician, we may hope to secure a material improvement in the income and prospects of the mathematical specialist.


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'The bombardment of Kagoshima by the British Squadron in 1863, and Shimonoseki in the following year by the combined squadrons of England, France, America, and Holland, were serious incidents ; strictly speaking both were unwarranted. But ... these bombardments of the sacred shore of Japan by foreigners, unfortunate as they were thought to be at the time, produced lasting effects_namely, that even the most anti-foreign patriots came to recognise the futility of offering armed resistance to Powers which were armed with modern engines of war.'—Count OKUMA, Fifty Years of New Japan.

From 1863 to 1912 is a small period in the history of the world, but during those fifty years what marvellous changes have taken place in Japan. In all her long history, the year 1863 may be pointed out as the turning-point which brought about a complete revolution in regard to the relations of Japan with the outer world, and the gradual changes which led to representative government at home. Events that occurred in 1863-64 are fresh in the mind of the writer, who at that time was serving as a midshipman on board H.M. 17-gun-sloop Perseus. It is his hope that, aided by notes from official documents placed at his disposal, he may be able to set down a brief account of some of these events which will be read with interest.

Probably few Englishmen are aware that Japanese guns were ever discharged at British warships, and that our Navy ever bombarded Japanese ports and strongholds. Possibly from a desire to bury the memory of our quarrel with our Ally, references to the bombardment of Kagoshima in 1863 and of Shimonoseki in 1864 have been kept in the background. Silence on this question cannot be desired by the Japanese, who, for the first time, then exemplified to the outer world those qualities of courage, self-reliance, mental grasp, determination, and patriotism which have since been appreciated and admired by the nations of the world. They never showed more markedly than in those days their characteristic thirst for knowledge and their methodical ways of acquiring it. On examining a watch the Japanese thought little of the gold case


or the exterior value. His question was, What makes it go ? On seeing marine steam-engines for the first time he expressed no extreme surprise ; he asked the same question-What makes them move ? Nor would any reply satisfy him till all that happened to the water converted into steam, and doing its work as steam, with all the results in detail, had been fully explained.

At this period there were two Courts at Yeddo (now Tokio), the capital—that of the Mikado, who was supported by the Old Nobles, and that of the Taicoon, or Taikô Sama (My Lord the Taikô) supported by powerful feudal Barons, who were known as Daimios. Secular affairs were dealt with by the Taicoon, whereas the Mikado was the Spiritual head of his people. The Daimios owned and governed large districts, and were supported by an army of retainers of gentle birth, who were entitled, according to rank, to wear one or two swords. Tradesmen were little thought of. Three treaty ports were open to foreigners--Yokohama (only a few miles from Yeddo), Nagasaki in the South, and Hakodadi in the North. In these places there were to be found representatives of most countries who engaged in trade; and to meet the demands of a Western civilisation there houses, offices, warehouses know as godouns, and even clubs.

Inside these settlements good feeling prevailed between foreigners and Japanese, and the latter, with their courteous and polite bearing, might well have been described as born gentlemen. Foreigners, however, were not permitted outside a limited area surrounding this settlement, and, generally speaking, trade in those days was despised in Japan, especially by the Daimios and their military retainers. To them trade development meant the opening up of the country, difficulty in levying taxes in their districts, and the introduction of democratic ideas. And, in fact, to proceed outside the treaty limit was to invite assassination by the retainers of the hostile Daimios.

To come to the events which led up to military action by Western Powers, the Japanese authorities had notified that on a certain day the all-powerful Daimio Matsudairu Shiuri No Daiboo, Prince of Satsuma, would pass along the Tokiado, a high road en route to Yeddo, on a pilgrimage to the two Courts, and strangers were cautioned to avoid this road. But there was a confusion of dates, and it happened that a party of Englishmen-Messrs. Charles Lennox Richardson, William Clarke, and William Marshall, merchants, with whom was a Mrs. Borradaile-were riding together, and met the Prince's retinue. Mr. Richardson was murdered, and the other gentlemen were severely wounded, whilst Mrs. Borradaile, thanks to a good horse, escaped. The consequence of this was that a British squadron assembled shortly after in Yokohama Bay.

And, from a personal point of view, what happy days those were ! Diplomacy was at work, and results were patiently awaited. In the meantime a new joy was appreciated by officers and menthat of practically living in a new world. For at that time only two or three Japanese had ever left their country, and few from the outside world had seen Japan. From the two or three Japanese who returned from abroad, pressure or honour had demanded suicide or the ‘hara-kiri,' which tradition says was duly performed. We, for our part, found ourselves enjoying a glorious climate, fresh invigorating air, ravenous appetites, and the best of food. We had long days on shore, which we spent in riding Japanese ponies, walks, convivial meetings at a young but comfortable club, and flirting with primitive, bright, fresh little maids! What more could a British sailor want ?

As regards the more serious work in hand, from time to time reports reached us of intended attacks on the settlement by unfriendly Daimios. Guard boats were, therefore, drawn up at night in front of the town, and at a given signal these were to take all foreigners to the men-of-war; one alarm of this kind, when it was eventually discovered to be false, caused much amusement.


An indemnity of 100,0001. and an apology was demanded from the Government, and a further indemnity of 25,0001. for the relations of the murdered man and those injured. It was also demanded that the murderers should be handed over for execution. The Government consented to the required indemnity and an apology, but pointed out their inability to control the powerful Prince of Satsuma, and suggested direct dealing with him. In consequence, on August 11, 1863, at 10 P.M., a squadron of seven ships anchored in Kagoshima Bay. It was composed of H.M.S. Euryalus, 35 guns, 510 men ; Pearl, 21 guns, 275 men ; Coquette, 4 guns, 90 men; Argus, 6 guns, 175 men; Perseus, 17 guns, 175 men; Racehorse, 4 guns, 90 men ; Havock, 2 guns, 40 men. Admiral Augustus L. Keyser, C.B., was in command and had on board his flagship H.M. Chargé-d'Affaires Lieut.-Col. Neale, who was accompanied by six gentlemen of his staff, including

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