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From A draw any number of right lines Ab, &c. cutting T B produced, in b. On these take always edeb, and d will be a point in the curve.

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For draw the chord e C; and join b C, and d C.

bA=b C,... LbAC = Lb CA.

The Ae C, is an in a semicircle; ... e C is to A b.

ed=eb, ... dC=bC; and ▲ dbC= L bd C.

The sum of the angles of the ▲ Ab C =180°.

LbAC=4bCA; LAb C + 2 2 b AC, = 180

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C F is a side produced of the ▲ AdC.

... LdCFL AdC + L dAC, 3 ▲ dAC.

=

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Q. E. D.

The curvilinear area Bd ATC B, is=3 ▲ PB C. = □ Pm n'x;
Rad+Tang 60'

=3

2

Rad

The area of the curve A d BƒF CT A, is = 3 ▲ Ph C,=□ Pyx z, 3 Tang 60. = Rad x

2

And the entire area Ad BƒFW A is = Rad × 3 Tang 60'.

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On PB produced, take Bm=BP; also Bh=TC ; and hy = {h P. Draw the s P x; mn; h C and

yz.

PC AQ= CA. As BPC and Q BA are = and similar. The 4 BCA 34 BCP, and from what has been already stated in the former demonstration, (No. 32, page 408,) it is sufficiently evident that the curvilinear area BdATCB is generated by the triplication of the ▲ PBC, expanding on its vertex C, until PC coincides with AC; in like manner the area BƒFC B is generated by the triple expansion of the ▲ Bh C.

=

Bm BP..□ Bm nT A PBC. ...□ Pmnx=3 ▲ PBC; = area Bd ATCB. hy=&h P, . '. □ hy z C = ▲ Ph C = ▲ P x C. The area BfFC B, is = 3 ▲ BhC: myzn, 15

2

... The area of the curve Ad BƒFCTA, 3 A BhC+3 A PBC 3 Tang 60° 3 = Pyzx, = Rad × = 1 x √3 +√. =√√√ 6·75, =2.59807621.

2

=

And the area of the entire curve A d BƒF WA, being of course double the last quantity, is Rad × 3 Tang 60° = Rad X 3 Rad3. ✓ (AT A F3.) = √ (1 × 27) = 5·19615242.

Q. E. D.

Ships' Rudders.

MR. EDITOR,-By a pamphlet published many years ago, and lately put into my hands, it appears that an old officer has been hard at work for the last fifteen years to bring about a reform in the Rudder, by reducing it upon the principle of the fish's tail (tapering), &c. &c. &c.

As I am not without a hope of commanding a gun corvette soon, and should wish to have her efficient in every way, particularly in this most essential point, I beg to offer, for the solution of scientific and nautical judges, this, as it appears, difficult and knotty point; the grand objection being," that a tapering rudder would require to be put over many degrees more than the old parallel-sided one."

Hamoaze, 20th Sept. 1831.

A YOUNG OFFICER.

Postage-a Tax on Foreign Service.

MR. EDITOR,-I have ever considered it not only illiberal, but a hardship, that while on foreign service, any friends or relations with whom I correspond, are subject to a heavy foreign postage.

Why should military officers detached on duty for years from their native country, or naval officers, whose letters (from their locomotive service) frequently do not reach them till they have ceased to interest, be subject to this tax on their services? for a tax on service it undoubtedly is, as naval or military officers on home service can communicate with their relatives for a postage they pay with pleasure.

Foreign postage also prevents much useful information and interesting occurrences reaching the public from abroad, as no editor can pay for the numerous subjects submitted for his favour, and very few can boast of the friend who would unhesitatingly pay a heavy postage for a letter not for his perusal, and which postage must be paid in England.

Your Journal being ever ready to point out the grievances of the United Service, I feel assured that you will favour these few lines with insertion in one of your future publications, where they cannot fail to meet the eyes of those in whose keeping we are.

Oct. 3rd, 1831.

I am your most obedient servant,

A TAR.

CORRESPONDENCE.

Naval Courts-Martial.

MR. EDITOR,—I should conceive no man of common feeling could have perused the minutes of a court-martial lately held at Portsmouth, on a midshipman of H. M. ship Etna, without being disgusted at the cruel treatment that officer experienced by command of his captain; or without blushing, if a naval officer, that such conduct should have passed without a comment from the officers who composed the Court.

As one who blushes for the errors of that service of which I am proud of being a member, I cannot but attempt to assign a cause, and at the same time offer a remedy for the partiality of naval courts-martial.

A captain who appears either as prisoner or prosecutor, is, in nine cases out of ten, on intimate terms with the officers (captains) who compose the Court, and who are naturally lenient to their friend and brother officer when he appears to answer charges as a prisoner, and, when in the character of prosecutor, are, in all probability, prepossessed, from having heard his (the prosecutor's) statement of the case, and conceive themselves bound to support him for the preservation of discipline.

Thus it is, Mr. Editor, that we so rarely find captains brought to a court-martial, and still more rarely that they are found guilty when tried; or that charges preferred by them are not (at least in part) proved.

Not being of the opinion of some of our old sons of Neptune, that to maintain discipline, commanding officers must be supported in glaring acts of oppression, and cannot be amenable to their subordinate officers for such acts, without infringing on the absolute authority so necessary to the efficiency of our men-of-war; still, being so strong an advocate for undeviating obedience to all just orders, as to have gone by the name of "Strict Discipline," I may, without fear of a charge of lukewarmness for that discipline, propose that a court-martial should be composed of an equal proportion of captains, commanders, and lieutenants; the inferiors' opinion being taken first, as is the case in the army, where the system works well. What captain could object to a Court composed of two-thirds of his own rank? Who, holding the rank of lieutenant, could be so absurd as to imagine the third of his rank could uphold him in a breach of the printed instructions? And what midshipman would not bow with greater satisfaction to the decision of a Court thus composed, than one as at present?

Oct. 4th, 1831.

I am, Sir, your very humble servant,
STRICT DISCIPLINE.

Provision for Officers Families.

MR. EDITOR, The object of the present communication is to direct the attention of the officers of the navy and marines to the opportunities now afforded them (by institutions formed for their exclusive use) to make provision for their families, the number who have availed themselves of such opportunities being comparatively small. It is no discredit to the services to say, that they are composed of men not, generally, in affluent circumstances; yet there are few who would experience much inconvenience by making a small sacrifice quarterly for the benefit of their families, and to relieve them from the necessity of applying to charitable institutions for their future support that there are too many in this situation already, the reports of the Naval Charitable Society alone afford a most lamentable proof.

The late regulation of the Admiralty, as it respects the widows pensions, will in the course of a few years render it imperative on a large proportion of those officers who may be husbands or fathers, to make that provision for their families which will be denied them by their country; and as many of the present day cannot leave their's in affluence, I would ask whether a small sacrifice made while they have the power to do so, which would add to the comforts of those who are nearest and dearest to them when they are

no more, would not impart a degree of consolation when their heads are reposed on a dying pillow?

A sailor has ever been deemed a thoughtless improvident being, but surely an intercourse with landsmen for upwards of fifteen years, where he has had opportunities almost daily for observing the worldly wisdom by which he is surrounded, ought to have given an improved bias to his character, and I think it must be a source of gratification to many, that such a result appears in the formation of several benevolent institutions emanating from their own body. It is true that one such institution, conducted on right principles, would be sufficient for the whole service; but as no human effort can at once approach perfection, the errors and failings of one have given rise to others. The last so formed is the Portsmouth Royal Naval Society, established in March last, and to which I would call the attention of your readers, who may be interested in such institutions, by detailing a few of its leading characters.

It professes to be an improved model of its predecessors, and designed more particularly for the poor man, not admitting of speculation by the rich at his expense; each member being limited to not more than two shares. It embraces every rank of officers in the navy and marines, from the wardroom door upwards, and also the candidates for such rank, in the second-master, assistant-surgeon, passed midshipmen, and passed clerks, who may make a provision for any of their relatives permitted by Act of Parliament. There is no probation required; hence, no anxious fears can be felt by its members respecting the continuance of such an uncertain tenure as life.

The widows and wives of officers may make provision for their children on as liberal terms as the welfare of the society will admit, which has been formed and conducted on the most rigid principles of economy; thereby ensuring to the widow and orphan all the benefit that such a society can impart. These are its most prominent features, but many others of minor importance will be found on comparing its rules with others of a similar I remain, Sir, your most obedient servant, A NAVAL OFFICER.

nature.

October4 th, 1831.

Notes from Jamaica.

MR. EDITOR,-If you consider the following suggestions deserving a place in your useful and entertaining Journal, please insert them in any manner you think proper. I have the honour to be,

Your obedient servant,

AN OFFICER SERVING IN JAMAICA.

The

1st, The necessity of regiments on service in the West Indies having a complement of four officers a company, which can easily be effected, by allowing but two officers a company to remain with the reserve. service companies are nearly double the strength of the reserve, and yet, from the number of officers sick, on leave, &c. &c. a regiment out here scarce ever musters one-third its complement, and consequently the duty is very severe on the few remaining. The reserve companies are at present over-officered; it is a frequent occurrence to have more officers than men on parade.

2nd, The propriety of having officers' barracks, particularly at home, completely furnished; not, as at present, with but a table and chair. There ought to be in each quarter a bedstead and mattress, a kettle, a few plates, cups, &c. I am convinced it would be much more convenient, and then one half the allowance of baggage would be sufficient, and consequently so much saved to the country.

3rd, That officers employed on the staff, recruiting, &c. should be selected from the half-pay: it would be a means of giving them something to do, without any extra expense to the country; regiments would be more effec

tive, and it would do away with a great deal of jealousy which at present exists, in consequence of officers on the staff being appointed to regiments who never join or do any duty with their corps, but who enjoy all the care of their staff situation, the comfort of a good climate, and all the chances of promotion, while others are obliged to do their duty.

4th, The propriety of adopting one facing and one sort of lace for all regiments of the line. I cannot discover the necessity of retaining those trifling differences, for, with those exceptions, the soldier throughout the line is dressed exactly uniform; good conduct, discipline, &c. ought to be the only distinctions. Why not, as well as in the navy, have the crew of each man-of-war dressed with various facings, lace, &c.

5th, The necessity of altering the subscriptions paid by officers, viz.— twelve days pay to the band and eight days pay to the mess-fund. To say, twelve days to the mess and eight days to the band, or dividing the difference, ten days pay to both-the mess-fund, in this country, particularly requires the addition; whereas, on the contrary, that of the band increases unnecessary proportion.

Jamaica, 9th May 1831.

Antiquity of the Royal Cork Yacht Club.

MR. EDITOR,-A correspondent who addressed you on the subject of "Yacht Clubs and Regattas" in a late Number, proved the Cork Yacht Club to have been in existence in the year 1782. The following extract from a little work which has lately fallen into my hands, shows that this club was in a high state of perfection nearly forty years prior to the period mentioned by your correspondent:

"I shall now acquaint your Lordship with a ceremony they have at Cork, where we are returned. It is somewhat like that of the Doge of Venice's wedding the

sea.

A set of worthy gentlemen, who have formed themselves into a body, which they call the Water Club, proceed a few leagues out to sea once a year, in a number of little vessels, which for painting and gilding exceed the King's Yachts at Deptford and Greenwich. Their Admiral, who is elected annually, and hoists his flag on board his little vessel, leads the van, and receives the honours of the flag. The rest of the fleet fall in their proper stations and keep their line in the same manner as the King's ships. This fleet is attended with a prodigious number of boats; which, with their colours flying, drums beating, and trumpets sounding, forms one of the most agreeable and splendid sights your Lordship can conceive."* The Cork Yacht Club would therefore appear to be the parent institution of the kind in these realms. Your constant reader,

Value of Half-pay Commissions.

PADDY.

MR. EDITOR,-In your very excellent article of August on the subject of Half-pay Officers, you do not appear to have taken any notice of a grievance much complained of;-namely, the deduction of the regulated difference (received by officers going on half-pay) from the regulated price of their half-pay commissions.

As I cannot permit myself to believe that the Ministers of this great state (either past, present, or to come) would descend to commit a wilful act of injustice and cruelty to a body of meritorious, and by no means overpaid, individuals; but are led to it by a belief, although, as I shall presently show, a very erroneous one, that they are doing, as they are in duty bound to do, that which is correct and honest between these individuals and the statepermit me to explain the matter :

Tour through Ireland, by two English Gentlemen. London, printed for J. Roberts, in Warwick-lane, MDCCXLVIII. page 118.

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