XVII.-Burrow's Diary.

Origin. This periodical probably owed its origin to the successful efforts made by Mr. Carnan, the proprietor, to dispossess the Stationers' Company of the exclusive privilege of printing almanacks, which they had monopolised 170 years. From the article " Almanac" in the Penny Cyclopædia, we learn that "James I. granted a monopoly of the trade in almanacs to the Universities and the Stationers' Company, and under their patronage astrology flourished till beyond the middle of the last century, but not altogether unopposed." Swift, it appears, under the immortal name of Bickerstaff, directed the points of his satiric humour so effectually as to stop the mouth of the original Partridge, though "he could not destroy the corporation under whose direction the almanac was published;" but in the year 1775, "a blow was struck which demolished the legal monopoly. One Thomas Carnan, a bookseller, whose name deserves honourable remembrance, had some years before detected, or presumed the illegality of the exclusive right, and invaded it accordingly. The cause came before the Court of Common Pleas, in the year above-mentioned, and was there decided against the Company. Lord North, in 1779, brought a Bill into the House of Commons to renew and legalise the privilege; but after an able argument by Erskine in favour of the public, the House rejected the ministerial project by a majority of 45. The absurdity, and even indecency, of some of these productions was fully exposed by Erskine; but the defeated monopolists managed to regain the exclusive market, by purchasing the works of their competitors." Mr. Carnan justly prided himself in having been so successful in this "expensive suit in law and equity," and never failed to preface his almanacs with an announcement of the decision. Lord North's attempt to restore the monopoly was also annually noticed, under the head of "Uncommon Notes;" nor did he fail to remind some ungrateful vendors, "to whom they were indebted for the double profit which they had for some years enjoyed from the sale of almanacs.'

The first number of this almanac was

published under the title of the Ladies' and Gentlemens' Diary; or, Royal Almanack for the year of our Lord, 1776: the name was pluralised in the three succeeding numbers; but in 1780, the "gentlemen" were discarded, and the work was issued under the designation of the Ladies' Diary, until its discontinuance in 1788. In the preface to the first number, the editor observes that, “As almanacks are becoming necessary to people in every station of life, and consequently have a more extensive sale than almost any other publication, it is evident that, when founded upon proper plans, and well-conducted, they must be of general utility, and that there can hardly be a greater public nuisance than one conducted in a contrary manner." This was too pointed a hit for the “ Palladium author" to pass by unnoticed, and accordingly we find the compliment returned with interest in the next number of that notorious work; but as the wary Captain" chose to cover himself with the shield of a correspondent's name, no notice was taken of this "passage of Arms." The preface further observes, that "the only Almanack that has hitherto appeared on anything like a rational plan is the Ladies' Diary; but this performance, though good in its kind, being particularly confined to a number of short questions and answers (and many of these trifling ones), it seldom happened that there was room to treat any useful subjects thoroughly, and never to draw results, or to deduce practiçal rules from them; the consequence of which was, that many useful dissertations and curious detached pieces were lost for want of an opportunity of making them public, and that the Diary contained a number of little articles of which few were curious, and fewer still of any real use." Hence the editor inferred the necessity for the present work, of which the third part "is intended for Dissertations and Essays on Philosophical, Mechanical, or Mathematical subjects.' These good intentions were carefully carried out during the publication of the first half-dozen numbers, but at the end of this period most of his ablest correspondents appear to have forsaken him, and subsequently the work became far

inferior to the corresponding portions of the "Old Ladies' Diary," which this work at one time was vainly intended to supersede. Indeed, from the whole of that portion which bears the name of Mr. Burrow on the title-page, it is evident that no friendly feeling existed between the editor and Dr. Hutton. The preceding remarks, quoted from the preface, are evidently intended to depreciate that Ladies' Diary of which the Doctor was editor; and in several of the earlier mathematical papers (as will hereafter be seen) his mistakes, real or supposed, are pointed out in no very courteous terms: but at the close of the Diary for 1781, "the learned and ingenious Professor Hutton, Esq." is openly charged with "getting and keeping" Mr. Burrow's letters; an accusation which few, perhaps, will be disposed to consider as literally true, especially when it is known that, notwithstanding his eminence in geometry, Mr. Burrow was subject to the infirmity of a violent, and, at times, ungovernable temper.

Editor.-Reuben Burrow, Esq., late Assistant-Astronomer at the Royal Observatory; author of "A Restitution of the Geometrical Treatise of Apollonius Pergæus on Inclinations," &c., &c.

Contents.-The usual contents of each number were an improved calendar for the year, with "such Tables as temporary occurrences" rendered "useful or necessary;" new queries, rebusses, enigmas, charades, paradoxes, &c., with answers to those proposed in the preceding year; new mathematical questions and solutions; dissertations and essays on philosophical and mathematical subjects, &c., &c.

Among the queries are found many of an interesting and instructive character, several of which have since, in substance, found their way into works of greater pretensions. The enigmas appear to attain to the full average merit of such productions; and it may be worth observing, that amongst the contributors of this department are frequently found the names of Professors Bonnycastle and Dalby, Reuben Burrow, the editor, and Samuel Rogers. With regard to the last-named gentleman, an esteemed friend (whose suggestions are always important), starts the inquiry, "Can this be the banker of Lombard-street? At the time when 'Samuel Rogers' appeared in

Burrow's Diary, the poet would be from 17 to 20 years of age. Nothing there done would be miraculous at such an age; but all would show good talent. Those beautiful lines 'To a Tear,' which were published with the first edition of his 'Pleasures of Memory,' bespeak a philosophical accuracy of conception rarely traceable in a poet :

'The very law that moulds a tear, And bids it trickle from its source: That law preserves the earth a sphere, And guides the planets in their course!' All this, I grant, is not positive evidence, but it removes, at least, all improbability."

To the above suggestion no reasonable objection can be offered; but when we further consider that Mr. Rogers received a most careful private education-became confirmed in his determination to be a poet at the age of nine, after reading Beattie's "Minstrel"-and published his first work, the "Ode to Superstition," at the age of 24, there is nothing improbable in the supposition that the youthful bard amused himself in the interim with composing an enigma, a rebus, a charade, or even a solution to a mathematical or philosophical question; since the greatest authors of those times did not consider it beneath their dignity to scribble in the newspapers, or occupy the "Poet's Corner in a periodical publication. The "philosophical accuracy of conception " observable in the preceding quotation has many parallels in "The Pleasures of Memory," published by Mr. Rogers in 1792, and were it necessary or desirable to pursue the reverse process in order to infer the poet from the philosopher and mathematician, the contributions to this Diary would furnish many important and almost conclusive illustrations. A careful examination of all that appears in this publication, together with certain portions of his earlier works, has led to the full conviction that "Mr. Samuel Rogers, of London," and the author of " Italy," are one and the same individual; and hence (with all probability) we may add one more to those illustrious names whose early efforts have been preserved, and whose aspiring geniuses have been encouraged by these unobtrusive and far too frequently ephemeral productions.

The "Mathematical Essays" constitute a valuable portion of the work; and

* It is much to be regretted that, since the discontinuance of Leybourn's Repository, no efforts whatever have been made to establish a journal which should have for one of its chief objects the re-publication of the many excellent and valuable mathematical papers which at present lie scattered over the different volumes of the transactions of various societies, in the magazines, and in the many now almost forgotten periodicals which have been published in England during the last hundred years. Archæological, historical, ecclesiastical, medical, chemical, and other publishing societies exist, and appear to obtain sufficient support:-these societies reprint and issue annually many scarce and valuable works in their different departments, thereby diffusing abundant information amongst their members which would otherwise, in many instances, be sought in vain. What, then, prevents the establishment of a mathematical publishing society, which shall have for its principal object the collection and re-publication of papers on mathematical subjects? It may be objected, as the Rev. T. P. Kirkman well observes, in a late number of the Manchester Courier, "that there are no readers, no purchasing public, to secure an author, whatever be his fame, or a publisher, whatever be his influence, from ruinous loss, in bringing out such books as are not intended for schoolboys or undergraduates;" and hence the impracticability of such a project might be easily inferred. Notwithstanding the literal truth of many of these remarks, as applied to mathematical treatises in general, the proposal appears to be worth the consideration of those who have sufficient leisure and opportunities to give it a trial; and though difficulties of a peculiar character will undoubtedly present themselves, it is to be hoped they will not be found of such a nature as to prevent the carrying out of so desirable an undertaking.

distant ordinates. By Mr. Reuben Bur

rów.

Art. V. A new and exact method of finding the time and longitude at sea; of very great use to navigators, &c., with remarks. By Mr. Reuben Burrow.

Art. VI. A new and very useful lemma, necessary in constructing geometrical questions relating to the maxima and minima, &c. By Mr. Reuben Burrow.

... In introducing this subject to the notice of the reader, the author remarks, that "Euclid has demonstrated that the sum of any two sides of a triangle is greater than the third side; and from this proposition Mr. Simpson has solved the very useful problem of finding à point in a line given in position, from whence lines being drawn to two given points, their sums shall be the least; but

do not know that it has ever been shown that the difference of any two sides of a triangle is less than the third side, though this is equally true and useful. I shall therefore demonstrate it in the manner that Euclid has done the other, and then deduce a lemina from it similar to that of Mr. Simpson's."

Proposition.

"Let ABC be any triangle; the difference of any two sides AC, AB is less than the third side, BC."

Lemma:

"Let DS be a given line, A and B two given points; it is required to find a point, P, in the line DS, so that AP— PB shall be the greatest.

This paper was reprinted in the Gentleman's Mathematical Companion for 1810, and both cases of the proposition have since been treated by Leslie in his Geometrical Analysis, B. iii., prop. 33. See also Potts's Euclid, prop. i., page 293; and Simpson's Geometry, prop. 1., p. 186. Notwithstanding the apparently close connection of the two cases, Mr. Burrow appears to have been the first to infer the extension of the proposition alluded to in the introductory observations.

Art. VII. A method of finding the latitude at sea from having two altitudes of the sun or a star, and the intermediate timé. By Mr. Reuben Burrow.

At the close of this paper, the author announces that, "in some future number will be given a method of find

ing the latitude from three altitudes and two intervals of time, by means of the tangents, with other useful problems; also several new theorems very useful and necessary in constructing spherical problems, together with the doctrine of spherical loci, a subject not hitherto considered." The method of finding the latitude here alluded to was given by the proposer in the 68rd question of this Diary, to which reference may be made; but it does not appear that he ever pub lished anything relating to spherics. Perhaps his removal to India would derange most of his plans, and render it impossible for him to carry out many of his intended researches; we may however suppose, with considerable probability in our favour, that the announcement here made would have its effect in inducing Messrs. Howard and Lowry to turn their attention to the subject to the former of whom we are indebted for the best treatise on spherical geometry at that time extant; and to the latter, as Professor Davies justly remarks, "we owe every important spherical theorem that can be set down to the credit of Englishmen during at least a century past.'

"

Art. VIII. A solution of a very difficult problem which was proposed in the Ladies' Diary for 1750, but never answered in any of the following Diaries. By Major Henry Watson.

Problem.

"To find three numbers such, that the sum and difference of every two of them shall each be a square number."

*.* This question is No. 311, in the Ladies' Diary for 1750, where it was proposed by Mr. Landen. No solution was given to it in the next Diary, but by a process "too tedious to insert," Mr. Charles Bumpkin found "three numbers answering the conditions of the question." In Leybourn's Edition of the Diaries, vol. ii., p. 19, it is stated that a solution may be seen in Ozanam's Dictionary, and there is another in Euler's Algebra, pp. 436-9, Hewlett's Edition. Dr. Hutton published three different solutions to the question in his re-publication of the Ladies' Diary in 1775; one by Mr. Landen, another by Mr. Wildbore, and the third by himself. These were transferred by Mr. Leybourn thto vol. ii., pp. 19-22 of his edition, to which he also added a fourth solution.

An elaborate investigation is also given in vol. iv., pp. 343-351 of the same work, by Mr. James Cunliffe, of the Royal Military College, and in the same place the present article is reprinted from the Diary for 1776.

THOMAS WILKINSON.

Burnley, Lancashire, Aug. 30, 1849. (To be continued.)

ON THE MASTING OF SHIPS.

There is nothing connected with our ships so little understood as the principle upon which to place the masts; consequently their positions, and thereby those (horizontally) of the centre of effort of the sails, are very irregular; and yet there can be but little hope of satisfactory results, at least uniformly so, until this principle be determined; for if the correct place be not "hi" (it is only a chance shot), the properties of the ship will be materially injured, and the constant changing, which a desire to place them correctly will entail, must be at tended with considerable expense.

I am aware that men will be found who will say that they can place the masts in the exact position they ought to occupy, but it is evident that such statements are not to be relied on, for since there is little or nothing known about resistances, there can be no data for calculations.

No work mentions this subject in a satisfactory way, therefore it should be discussed.

Chapman is evidently wrong in his theory; the assumption upon which it is founded could only be true under one condition out of every variety of speed, form, &c.

The position of the centre of effort of the sail (vertically) depending in the navy rather upon the moment of stability, and upon the convenience arising from classifying masts and yards than upon the form, we should look to the necessity of adapting the form to this point, rather than lose the advantage of a large area of sail which it affords; that is, so to form the ship, as that she will require the centre of effort of sail equally high with that which this classification would give it.

The finest bow below, commencing to rise far aft, requires the highest point of sail; the short and fullest bow below, the lowest point of sail.