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engaged the attention of several eminent mathematicians; and it is more difficult than the determination of the true distance of the moon from a star. M. Mendoza's rule is founded on the direct solution: but mariners have hitherto adopted an approximate method; employing, as an element of calculation, the latitude by account. An approximate method called Douwe's method, is given in the Requisite Tables: but it is sometimes tedious, requiring a repetition of the operation, and, when repeated, not always leading to right conclusions. On this account, Mr. Brinkley, an astronomer at Dublin, inverted a supplementary process of computation; by which the latitude, once found by Douwe's method, might be conveniently corrected; and this process, with its demonstration and tables, was published in the year 1793, when the Nautical Almanac for 1797 appeared. Mr. Brinkley, we apprehend, was the author of this method; for, although a memoir on the same subject, containing the same formula from which the rules are deduced, was published as early as the year 1791 in the Connoissance des Temps for 1793, (page 289) by M. Mendoza, yet, from a passage in that memoir, the priority of invention seems in some degree awarded to the Dublin Astronomer *. At this distance of time, however, the circumstance is involved in some perplexity. If Mr. Brinkley merely calculated

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published the method as his own in the Nautical Almanac. On the other hand, if a copy of the method was in M. Mendoza's possession before the publication of the Connoissance des Temps, then is Mr. B. in fact the author of the method, and 'M. Mendoza has not acted fairly in rendering him so slight, and, which is worse, so ambiguous an homage.

The two methods for correcting Douwe's rule are in fact the same. If L be the true and the computed latitude, then, according to Mr. Brinkley +,

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* The passage is this: " L'expression ci dessus est assez commode; mais pour en faciliter l'usage, on pourra substituer deux tables qui donnent 1 et de tan. d cotan. 1. M. Brinkley, Astronome de l'Université de Dublin, les ayant calculées, a eu la bonté de m'en donner une copie, et c'est avec plaisir que je lui rends cet hommage."

cos. M

+ We have observed two errors in the Nautical Almanac; p. 14. merid. Altitude is put for Zenith distance, and p. 15. 1. 9. cos. L. is put for sin. L.

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Tbeing the time nearest to noon and M the middle time. According to M. Mendoza, (p. 294, Connoissance des Temps, pour l'Année 1793.)

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consequently

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2 -I= tan. M sin. T-vers. T cos. M

The two expressions, then, are precisely the same; since, in this latter case, dL answers to in the former, and dl to L' Mr. Brinkley and M. Mendoza have both resclved the problem of Douwe by means of the orthographic projection of the circle but this is by no means necessary; and in fact, all' things considered, the resolution is not so simple as by the ordinary and obvious processes of spherical trigonometry, The simplification of problems, by the adventitious aid of new' principles and new branches of science, is generally delusive.

M Kraft, who, as we have already mentioned, solved the problem of clearing the moon's distance from the effects of parallax and refraction, has also given in the Petersburgh Acts for 1795, p. 353. a short memoir on the determination of the latitude from two altitudes and the elapsed time: but his solution of the problem appears to us to have no advantages over the common and direct solution.

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In our account of this volume, we have hitherto dwelt only on the two principal problems of Nautical Astronomy; and indeed the other problems which are here solved by rule, and for which tables are constructed, are of inferior concern. page 26, problem 3, which proposes to determine the Azimuth, appears to us that versed sine is printed instead of suversed: for if a be the Azimuth, the polar distance, λ the latitude, and a the altitude, then

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Table 31. is constructed for the purpose of finding the amplitude: but we doubt whether much time is gained by the formation of this table: because in using it we are obliged to make two multiplications, and in finding the amplitude by the common logarithmic tables, we have only to add the logarithmic sine of the declination to the logarithmic secant of the latitude, and to take out the angle corresponding to the L sine of the sum.-An error also appears to us to be made in the example given for the illustration of this table, p. 14. where the sun's declination is put 6o 17: from which the amplitude does not result from the common method, 7° 18′: the true declination ought, it seems to us, to be 6o 47′: the error is nothing in itself, but it tends to raise suspicion in the mind of the calculator who makes use of the tables.

Table 43. of proportional parts, is very useful and commo. dious; and the author has fully explained its use.

We believe that the present volume contains all the tables which are requisite in Nautical Astronomy: that is, the tables here given suffice for the solution of all nautical problems: but the analytical solution of such problems must be accommodated to the tables. Solutions, for instance, that involve natural sines. or cosines, must be rejected, or altered; and solutions also, which are expressed in terms of tangents or cotangents, are not adapted to the present tables, which contain no logarithmic tangents. We rather wish that the tangents had been inserted; for the present publication is much more sizeable than Taylor's quarto, and it is desirable to use it in cases for which the author has not given solutions, which solutions may be expressed by means of tangents. For instance, we had occasion to compute, from the lunar tables, the distance of the moon from a certain fixed star; and we found ourselves obliged, when we had gone half way in the computation, to put aside the present tables, and to seek in those of Taylor for a logarithmic tangent which we wanted: thus, if D and d be the declinations of the moon and a star, and r the difference of their right ascensions, then D and d being opposite declinations, vers. (dist.): vers. (D+d). (sec. 0)"

where is such that

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suvers. (dist.) suvers. . suvers. (D+d)

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It is to be remarked that neither of these forms is applicable in all instances.

Other cases might be adduced, into which tangents enter; and time is expended in adapting the solutions to these tables, or in seeking for others. It may be argued, indeed, that we are neither obliged to look for other tables, nor to alter our solutions; because, if we take out the logarithmic sine and logarithmic secant, and add them together, we shall have the logarithmic tangent:-but then this is an operation; and if we admit such, we really want only a table of sines and cosines. That the present tables, however, will cause any unnecessary expenditure of time in computation, is the last reproach that ought to be made against them. From our own experience in the use of them, which is not altogether inconsiderable, and from our discernment of their plan and construction, we can boldly say that they facilitate and expedite computation much beyond any former tables. Almost every thing is done for the mariner, that, without extravagance of expectation, can be expected. If he can use his sextant, understand a plain statement, and add figures together, he may not despair of ascer taining the latitude and longitude of his vessel.

The ingenious author has received some pecuniary assistance from the Board of Longitude, and some from the East India Company: but he is eminently, in our opinion, intitled to pub lic encouragement. From navigators he must derive his recompense; and we hope that familiarity with previous tables will not prevent them from making trial of the present. By their testimony, also, must the proof of the accuracy of these tables be obtained; a point on which it would be unreasonable to expect that we should speak.

ART. III. Familiar Letters from Italy, to a Friend in England. By Peter Beckford, Esq. 2 Vols. Svo. 195. Boards. Hatchard, &c. 1805.

TH

HE character of a book of travels usually receives its colouring from some natural or acquired propensity of the author, and relates chiefly to antiquities, connoisseurship, topography, minerals, vegetables, animals, or the state of society, according to the reigning sentiments and dispositions of the tourist. There are individuals, however, of more capacious

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minds, who take a wider range of observation, and consign to their journals every description and reflection which the occur. rences of their progress suggest. Mr. Beckford belongs to this class of writers: but, as inany of his letters were written before the year 1787, and most of them before the invasion of Italy by the French, the reader is honestly cautioned in the outset against perusing them with the view of obtaining recent intelligence. The multitude of publications, in which Italy is described, may also be presumed to diminish the expectations with which we open another on the same subject. Much has, doubtless, been anticipated, and much gratuitously repeated; yet the present writer very properly reminds us that different individuals contemplate the same objects in different lights, and describe them in different humours. We could have wished, therefore, that he had borrowed with more reserve from Lalande and others, and that he had not needlessly reechoed what has been already so often said, merely because it happens to accord with his own observation and sentiments. A few references to the original authorities might have reduced these two volumes to one: but the author probably shrunk from the task of formal consultation; since we find him manifesting a marked dislike to the accurate indication even of those passages which he introduces in the way of illustration. If I should mention Dionysius,' says he, Polybius, or any other Greek author, as probably I may, do not fancy that I read Greek. I have contented myself with an English translation, and advise you to do the same. As I have read more for amusement than improvement, I have trusted too much to memory. Favourite passages that I have transcribed from books, are not only incorrect, but unaccompanied often with the names of the authors, and sometimes even with the references to them. All this may be very amusing to Mr. Beckford: but is it either amusing or respectful to the public?

On Florence, Pisa, Siena, Rome, and Naples, we have very extensive annotations, much of the historical and descriptive portions of which might have been spared; and an epitome of Roman history, however well executed, is surely misplaced in a rambling account of modern Rome. Some of the anecdotes, too, though not destitute of point, are rather aukwardly squeezed into the narrative; repetition has deprived others of their poignancy; and a' regard to delicacy should have precluded the insertion of some. These remarks apply also to other parts of the performance. The style, though perspicuous and forcible, is occasionally too familar, and rather affectedly interlarded with foreign expressions. Commercio libero is substituted for free trade, theriaque de Venise for Venice treacle, and Coro for choir, though

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