fidence in a sound constitution, rigid self-denial, and abstemious habits. Yet we are fragile and feeble beings the best of us. The steamer in which I sailed up the Mississippi was snagged, and sank just as I left her. Ten steamers have met with the same fate within these few months on the Ohio and Mississippi, besides many accidents from boilers bursting, &c. I left squatters, swags, sawyers and the knives of keelmen at Memphis, and travelled across Tenessee and Kentucky, by way of Nashville to Louisville, as a sailor in blue jacket and trowsers, among "hand and scull men-gaugers of eyes and rifles, and buck-shot." I am now on my way, by Pittsburgh, to Lake Erie, Niagara, Montreal, Quebec, New York, Philadelphia, &c., and may be in England in the beginning of December. Louisville, Falls of Ohio, I am, yours, &c. A. J. E. REVIEWS AND CRITICAL NOTICES. CAVENDISH; OR, THE PATRICIAN AT SEA Although, in our sober judgment, this production be not calculated either, to benefit the service, or reflect credit on the taste or feeling of the writer, it will doubtless be recommended to the general reader by its lively incidents, smart and vituperative style, and the harmless extravagance of caricature in which it indulges. Some notes on Naval Reform are appended; to these, as the only practical portion of the work, although penned with undue bitterness of party spirit, we shall turn our attention in an early Number, and extract from them any suggestions which may strike us as tending to the honour and improvement of the Naval profession. THE LOG-BOOK OF A MIDSHIPMAN, illustrative of the Voyages and Travels of Capt. Basil Hall, R.N. A New Game. By N. Carpenter.-Such is the title of a very amusing little toy, which has been sent to us by the author; and we willingly notice so ingenious a production. It falls, indeed, more within the range of our critical notice than might seem, at first sight, to be the case. Capt. Hall, in the title-page of his Fragments, lately published, professes to write chiefly for the use of young persons, but we know well enough that he must likewise have wished to engage the attention of his brother officers. In the same spirit, although this Journal is devoted chiefly to the edification of the grown-up members of our United Services, we feel the strongest interest in the amusement, as well as instruction, of those immense shoals of small fry, which, like the followers of an oriental army, attend the march of the papas and mammas amongst us. We are certainly no encouragers of marriages amongst half-pay officers, but as it does so happen, in spite of Malthus, that the population of half- pay children goes on in a much greater ratio, alas! than the means of subsistence of their worthy parents, we feel it our duty, in the absence of more substantial aid, to contribute, as far as we can, to the domestic happiness of our brother officers' families; and, accordingly, we venture to recommend this game, which, at the cost of three shillings and sixpence, is calculated to afford our young friends at least that amount of amusement, and of a very innocent kind. The game is played with a pool, counters, and a tee-totum, like the renowned game of the goose-only the scenes are taken from the parts of Capt. Hall's 66 Fragments," in which he describes his adventures when a Midshipman. There are twenty coloured representations of cockpit adventures, including, of course, Old Shakings, the dog, and his mourning friends, the pigs. We have also the Bell Rock Light-House, Lord Duncan, and the Middy's own Papa, Sir James Hall, rigged up like a fox-hunting squire, besides the Halifax Tailor undergoing the amputation of his long tail, and sundry others. To those who have not read the work from whence the scenes have been borrowed, of course, this game will possess a minor degree of interest. But we can hardly imagine a better puff for the book; and Capt. Hall ought, and we dare swear does, consider the appearance of this toy as a very high compliment to his literary character. We doubt not, Miss Edgeworth's chief delight as an author has sprung from the consciousness of giving daily pleasure to myriads of young folks. We cannot flatter the Captain with such a consummation to his labours in juvenile literature, but, in the mean time, we wish him joy of his having succeeded in setting a tee-totum a spinning, aud we hope his second series of Fragments, which, we understand, is in the press, may prove equally fortunate. We have recorded our favourable opinion of the former Volumes, an opinion enhanced by an occasional recurrence to their pages, and confirmed by the general voice. EMINENT BRITISH MILITARY COMMANDERS-Cabinet Cyclopædia, Vol. 25. -Mr. Gleig, though a prolific writer, executes whatever he undertakes with equal care and ability. The work under notice, will add to his well-earned reputation. In the present volume, the Lives of Sir Walter Manny, Sir Francis de Vere, Cromwell, and Marlborough, are preceded by a luminous view of the mili. tary systems recognised in England from .the earliest to the present time. The opening article of our present Number will show how fully we concur with Mr. Gleig and the writer whom he quotes, in the opinion that "the greatest curse that can befal a nation, is the loss of its military spirit," and that "he must be a very short-sighted politician, who sees not that the best means of guarding against aggression or insult, is to hold ourselves at all moments ready to repel it." EARLY ENGLISH NAVIGATORS Edinburgh Cabinet Library, Vol. 5.—A most interesting and well-executed Volume, comprising the Lives and Adventures of those eminent British Navigators, Drake, Cavendish, and Dampier, honoured names in the records of Naval enterprise and discovery. A well-written summary of discoveries in the South Sea prior to Drake's voyage, is prefixed. -- GALLERY OF THE SOCIETY OF PAINTERS IN WATER COLOURS. The First Part of a series of Engravings to illustrate this beautiful branch of the Fine Arts, contains three finely-executed subjects. The View at Venice is exquisite; pity that the artist, (Prout, engraved by Goodall,) could not have managed to afford us a glimpse of the just concealed Bridge of Sighs, of mysterious and murderous memory. POLAND-BY HARRO HARRING.This volume, a translation from the German, is of a desultory and anecdotical character, presenting some lively sketches of the country it treats of, entering much and amusingly into its military details, and giving a revolting, though, it is to be hoped, a prejudiced picture of the Russian Vice-Regal Court. A Work, to be entitled THE CABINET ANNUAL REGISTER, is about to appear (for the year 1831), and be continued upon a plan similar to that of the popular "Libraries." The design is good, and deserves success. INSTRUCTIONS FOR THE APPLICATION OF LIGHT DRILL TO SKIRMISHING IN THE FIELD, &C. BY MAJOR C. LESLIE, 60th Rifles. Of this treatise, intended as a supplement to the general regulations for Light Drill, and amply illustrated by plates, we can only at present say, that it evinces a degree of zeal and industry creditable to the officer who compiled it. Since the war, the importance of light movements in the field has been duly appreciated; and we shall at all times be ready to direct attention to suggestions tending to improve and extend the practice of Light Drill. The HARMONICON has closed the year with an excellent number. Having "music in our souls," and duly eschew. ing "treasons, stratagems, and plots," we commend a publication which ministers so capably to the study and enjoyment of Harmony, whether social, vocal, or instrumental. A work consisting of "Observations on the Enlisting, the Discharging, and the Pensioning of Soldiers, by Henry Marshall, Esq. Deputy Inspector-General of Hospitals," is in the Press. GENERAL CORRESPONDENCE. TO THE EDITOR OF THE UNITED SERVICE JOURNAL. Admiral Brooking to Sir Robert Seppings. MR. EDITOR,-Should the following be not too late for insertion in your next Journal, you will oblige a constant reader, and Palestine Cottage, Plymouth, 24th Nov 1831. Your humble servant, S. B. SIR ROBERT, Unpleasant as I feel the alternative to which I am driven by your letter, (at least by a letter sanctioned by your signature,) wherein I am told I have bent my thoughts on a trifle, and worked myself up to I believe it a matter of importance, I would beg to remind you, that it is more than fifteen years since I proposed to reduce the rudder to one-half or one-third at the back, and that you condemned the principle in the following words: "The surveyors cannot recommend its adoption, as the rudder must be put over many degrees more than is at present necessary, before the same effect would be produced." Allow me further to remind you, that next April it will be ten years since an investigation took place of the above and other suggestions of mine by seven officers of rank and experience, and in their report thereon were the following words:" Our opinion is, that it would be desirable to make experiment of both the rudders, (the above and that for working in a grooved stern-post,) by trying them on ships now employed on the home station. The officers, &c. &c." Again" A majority of the officers, indeed I (Sir Alexander Cochrane, President,) may say that all were agreed in that respect, that reducing the rudder by tapering towards the after end would be advantageous.” I forbear, Sir Robert, making any further comment, than by stating (with all due respect to your scientific judgment, and highly responsible station,) that had experienced seamen, instead of surveyors, been my judges in 1816 as in 1822, not one ship belonging to His Majesty would years ago have been without a reduced tapered rudder, working in a grooved stern-post; and I must look to you now, as an act of justice to myself, and as a duty to the service, to second me in my intended application to be allowed to try my plans, of the rudder and sail, on some vessel on the home station. Much, much as may be said on the subject, I conclude, Sir Robert, Your obedient servant, SAMUEL BROOKING. Suggestions on Promotion in the Navy. MR. EDITOR,-The officers of the British Navy are divided into three classes: 1st. Men promoted after short service by interest, who know nothing about their profession. 2nd. Officers promoted after very long service, who are disgusted and good for nothing. 3rd. A few experienced officers, less fortunate than the former, and more so than the latter. The sale of commissions would correct these evils. Midshipmen, Lieutenants, and Commanders, who have served the established time, might be promoted by purchase. This class would be composed of influential men, who now receive their promotion for nothing. The one vacancy in three at present chiefly given to influential men, should be bestowed on Midshipmen who have served nine years, Lieutenants who have served seven, and Commanders who have served six and upwards. Such a regulation would give us young Admirals, young Captains of line-ofbattle ships, and a certain number of experienced officers, without costing the Government anything. One-half of the appointments should be given to those who purchase, and the other half to those who do not. This would satisfy all parties, and benefit the service. I have the honour to be, Sir, a conscientious nobleman's son, who was two years at college and four in a flag-ship, two years a Flag-Lieutenant, and little more than one a Commander, and now A CAPTAIN. Major W. Mitchell, on the Trisection of an Angle, and the Mathematical Principles of Field Movements. MR. EDITOR,-In the 17th Number of your valuable Journal, you favour the public with the translation of a notification published at Vienna, and signed by Major Wermerskirch of the Imperial and Royal Army, in which, it is made known that he has discovered the solution of the problem, "How to divide an acute angle into three equal parts.” After showing, on the authority of a celebrated mathematician, that the trisection of an acute angle has ever been represented as an impossibility, the writer asserts that the trisection can be performed; "that he will carry on his proof both analytically and synthetically, but that, considering the difficulties opposed to the communication of such a discovery, he should have suffered it to remain in eternal oblivion (!) had not the love of truth, and the undeniable utility of the discovery, decided his adoption of an opposite course." All universities and academies which desire, and are able to make use of this new discovery, are therefore requested to apply, by letter post-paid, to a particular address at Vienna. A year having elapsed before I, in this remote part of His Majesty's dominions, received the number which contains the notification alluded to, I had no other means of rescuing “from oblivion" here, a discovery which many of your readers at home may now be acquainted with, than those of the rule and compasses, and having discovered a solution of this celebrated" problem, and not feeling any difficulty (like the Austrian Major) in communicating publicly the solution of a problem which puzzled both ancient and modern mathematicians; I now subjoin a figure, with the construction, and a solution founded on the ancient analysis, having also combined the most obvious deductions in two corollaries; by means of which I consider it not improbable that the other celebrated problem of antiquity, the quadrature of the circle, may be solved by some of those who have sufficient leisure for such speculations. H M TO TRISECT AN ANGLE. Let A CB be an angle of which the trisection is required. On C, as a centre, describe the circle ADEB, and produce A C, and BC, the sides of the given angle to the opposite circumference ; extend the chord E B to G; bisect the arc AB in F by drawing CF parallel to E B, and extend the chord D F till it meets the production of EB in H; join C H, cutting the arc A B in I, through D draw DL parallel to CI, cutting the same PECA MOCAL FIRM arc in L, and join CL; then the lines CL and CI will trisect the angle AC B. For let K be a point in the extended radius C I, ph such, that B K shall be equal to the radius CI, and DonorsCarives on K as a centre, with the radius KB describe the equal circle BZM, produce DB to the opposite circumference at Z, draw BM parallel to CH, and da te join K Z. Because HBZ is an equal angle, whose with me vertex is in an equal circle, the arc H Z is equal to DE (Eucld. III. 26). DE is equal to A B, there * See Legendre Eléments de Geomètrie, also Leslie's Geometry, &c, &c, fore H-Z is also equal to A B, and the angle HKZ is equal to the given angle AC B. Because BK is equal to BC, the angle B KC is equal to ICB; and B M being parallel to CH, the angle BCK is equal to Z B M, consequently B KC is also equal to Z B M; but an angle at the centre, on the same base M Z would be double of Z B M, which is at the circumference, or of BKC which is equal to Z B M (Eucld. III. 20); wherefore the arc MZ is double of I B, and H M being equal to IB, ÍB is equal to one third of the whole are HZ, and is therefore, in fact, one third part of AB, which is equal to HZ. LD being parallel to IC, the angle LDC is equal to IC B. LCB being double LDC, is, therefore, double also of ICB, consequently LB is equal to M Z, which is double of IB; the remaining portion AL of the whole are given A B, must therefore be equal to the remaining portion H M of the whole arc H Z, and H M being equal to IB, AL is equal to IB. Therefore the lines LC and IC trisect the given angle A CB. Corollary 1.-Hence, if the sides of a given angle be produced to the opposite circumference of a circle, and the chord of the outward segment (BE) be extended till it is intercepted by the production of the chord of an arc (FAD), which shall include the opposite segment (A D) and half of the given angle; then a line from the point of intersection (H) passing through the centre of the circle will intercept one third (FI and DN) of each of the remaining portions (FB and DE) of the circumference. Corollary 2.-Hence, also, if two equal circles intersect each other, and one straight line (CH) is drawn through the centres of both, and another straight line D Z through one centre (C) and one point of contact (B) to the circumference of the other circle, then the angles which stand on the arc (HZ) of that circle intercepted by those lines will be-at the point of contact (B) one half-at the centre of the other circle (C) one third-and at the opposite extremity (D) of that diameter, one fourth, of the angle at the centre (H K Z) on the arc H Z. In order to connect my subject more directly with the professed objects of your interesting periodical, I avail myself of this occasion to notice some of the mathematical principles on which the field movements of the army depend. The diameter of a circle being in the proportion of 7 to 22, the length of the radius must be to the arc of the quarter circle as 7 to 11, or, in other words, the extent of front of any division is in that proportion to the distance the man on the outward flank must march to complete the quarter circle. It is laid down that the number of wheeling paces of 33 inches contained in the are of the quarter circle, described by any division, is equal to the number of files composing its front; no doubt, because 7 is to 11 as 21 is to 33-21 inches being the space occupied by each file, and 33 inches the wheeling pace. Now, as there are several rates of marching, it is obvious that the acceleration of the wheeling paces should be proportioned to each rate, so that while the marching divisions take 7 paces, the wheeling one should still complete 11, and, consequently, that one rate of wheeling time cannot apply both to slow and quick march; it is remarkable that the wheeling time of 120 paces in a minute is inapplicable to either slow or quick time, for a front of 75 paces of 30 inches would be composed of 107; files, so that while the succeeding division of an open column marches 75 paces of 30 inches, the flank man of a wheeling division of equal strength must take 107, say 108 paces of 33 inches, which is exactly the quick time, not the wheeling time, which would be 120. Again, while a division in open column marches 108 paces, the flank man of a wheeling division of equal strength should take 154 paces of 33 inches, say 150 paces, which is the double quick time Hence it appears, that the different rates of marching are in such proportion to each other that quick time is, in fact, the wheeling time for an open column marching at slow time, and that double time is the wheeling time for an open column in march at quick time: that the rate of |