and will be found of continual service in questions of astronomy and navigation. We may judge of the immense labour in this undertaking from the number of quarto pages, no less than 670, occupied with numerical figures, with very few exceptions, completely. They contain tables for correcting the observed altitudes of the sun, moon, and stars, and the observed distances of the moon to the sun or a star: togarithmic tables, and tables to convert parts of the circle into time, and vice versâ: tables for computing the latitude by two altitudes of the sun observed at any hour of the day, and by several altitudes near noon: catalogue of right as cension and declination of several stars, amplitudes and variations of amplitudes, lengths of arches on a sphere or spheroid: table of longitude and latitude of places: tables of difference of latitude, and departure for points and quarter-points, and for degrees of meridional parts: tables of proportional parts for the variations which take place in longitude for twelve or twenty-four hours, of great use in computing the sun or moon's place at any point of time from the nautical almanac.

At the end of these tables we find their explanation and use: a part. which we could have wished to have been longer, as the author is so well qualified to give a just account of the instruments used in observations, and by a variety of instances to have made more familiar their use to an observer. The problems which follow the explanation are very good; but here also we could have wished for figures and demonstration. When once the subject is made clear to the mariner by demonstration, he is not likely to forget it, and

the application of rules becomes easy to him; but when he works merely by rule, there is always danger of a mistake, which he, in the conclusion, is not able to correct. The author, however, evidently supposes that they who use his tables have made their way to navigation and astronomy by the proper road, namely, through geometry and trigonometry; a road which many teachers endeavour or pretend to shorten, by substituting their own supposed concise plans for the solid and substantial one laid down by Euclid. We have heard many a mariner complain of this fault in his education in early youth; and they who would understand these tables thoroughly, should recollect that a knowledge of trigonometry is indispensably requisite for every seaman.

The commissioners of the board of longitude, and the East India company, have both contributed to the publication of this work, by which means the expence of it to the public is greatly diminished. But we were sorry to observe that, with this great assistance, too great a sacrifice was required on the part of the author; for, to bring the book within moderate terms, he has given up on his part all the profits of authorship. Every one knows how expensive and how troublesome the publication of tables is, and it is not suited to the generosity of the English nation to receive so great a benefit without a compensation. When we recollect the number of places and pensions conferred, on whose propriety so many doubts may be excited, we should trust that one might be found from which this very excellent author might derive an honourable compen sation for his labours.

THE nature of business respecting money concerns, notes, drafts, &c. is explained in a clear, concise, aud satisfactory manner, and the country trader will here find all the processes developed to him in which he may be concerned in his transactions with London. The greater part of the volume, as must naturally be expected, is taken up with the tables of interest, commission, and discount. Each table of interest contains the interest of 100, 200, 300, and so on, by hundreds to a thousand pounds; and of one, two,

three, and so on, to forty-four pounds inclusive. The interest is calculated to farthings, but the decimals of a farthing are not given, of course we do not see how we can be certain by these tables of the interest of nine hundred and seventy-three thousand six hundred and fifty-one pounds; and the title-page promises more than the book can perform. As far, however, as it goes, and we have tried the tables in several instances, they appear to us to be accurate, and the work will be useful to those for whom it is intended.

THE work contains a great variety of instances in the practice of gauging, whence the practitioner may derive many useful hints. It does not profess to deve lop the theory of this very useful art, a theory which requires more attention than is generally given to the subject. The officers of excise and customs are, we believe, contented to follow the prescribed

rules: they learn one from the other, and it is not expected from them to have demonstrated the propositions on which the art depends. In this work the practice is very well laid down; but we should with greater pleasure have perused it, if it had contained the demonstration of every proposition in such a style, as not to be above the capacity of the common exciseman.

WRITING and accounts are necessary to every merchant, but we doubt much whether the merchant will allow them to be ranked among commercial elements. He must be acquainted with the four rules of arithmetic and the rule of three, with the nature of fractions, and this knowledge he applies to tare and tret, commission, brokerage, and interest, which he learns at school, and to exchanges which are not so generally taught there. This book begins with the application of arithmetic to tare and tret, &c., whence it prooeeds to exchanges; and three hundred and sixty pages are taken up on these calculations. The whole may be compressed, with great ease, into fifty pages, and then perhaps more instances would be given than the case absolutely requires. The rules for tare and tret, commissions, interest, and discount, are well known, and we do not derive any great advantage in this treatise upon these subjects: upon exchanges which depend on the doctrine of proportion or the rule of three, the questions are brought, by an easy and well

known process, into an equation which is reduced into fewer terms, by striking out those which appear on both sides of the equation; and again into terms of less magnitude, by dividing both sides where possible by a common divisor. This process is exemplified in a vast number of instances, taken from the exchanges of a great variety of nations, the tables of whose specie, in coinage or circulation, are given. A few instances would have taught all this as well as a thousand; and, in a merchant's counting-house, practice would very soon make a young man perfect. We have as yet only the first volume: what may appear in the second volume we cannot tell; but we would recommend to the author not to be sparing of his letterpress. We see too many blank spaces in the pages of this work. A complete system of mercantile calculations is, we believe, to be comprised in a short compass, but the observations on speculations in exchange will be found deserving of notice.

THAT mankind has been led away by names, is a truth which all must acknowledge and it would be just as absurd in the present days to ascribe to the names of Copernicus and Newton an absolute au- ́ thority, as it was in former times to place implicit faith in the syllogisms of Aristotle, or the decretals of the see of Rome, But there is a great difference between attributing a certain degree of authority to an eminent character, and discarding entirely the use of our own judgment.

Newton was the last person in this world to require this sacrifice of our reason; and it was with the utmost astonishment that we found him stigmatised with the name of Le Grand Mystificateur, who, of all men in the world, abhorred the attempt to prevent the researches of others by any appearance of mystery. He might err, for who is not liable to error? but he certainly was not one of those who wished to lead mankind into error.

There are two parts in the philosophy

of Newton to be considered. First his abstract mathematical principles: secondly, the application of them to the establishment of the system of Copernicus. In the first part we allow that he has fallen into error even in his very first lemma of the first section of the Principia, for he talks of modifying equality, which is an absurdity; and to say of certain quantities, that they are ultimately equal, as the evanescent chord and tangent of an arc, is absurdity for Euclid has demonstrated that the two last-mentioned quantities can never be equal. But when we define the intended meaning of this term, used by Newton in so improper a manner, all the difficulties cease; and we may allow equality to be the limit to which the evanescent chord and tangent are approaching, Again, the disciples of Newton fall into perpetual errors, and give rise to absurdities, by their expressions of infinitely great and infinitely small quantities, which they pretend to multiply together, and to produce a finite quantity, or by dividing one by the other to produce nothing. Such expectations naturally excite contempt amongst men of sense, and give rise to the term mystificateurs, which may be justly applied to all men who use such nonsensical language.

In algebra also Newton is not free from blame, and his manner of treating it might almost justify the author of this work in saying that algebra is the precipité de la pensée humaine. When men like Mercier hear of quantities less than nothing, and impossible quantities being multiplied together, and equations having numberless imaginary roots, and that these things are justified even by the authority of Newton, it is natural for them, and very properly so too, to hold such a science in contempt; and they may be excused for calling out, Ah! les grands mystificateurs. But we are not obliged to defend Newton or any other person in any error: in sci

ence we depend upon demonstration alone; and if the application of a science to plilosophy is false, we expect that to be made out to us on just principles of reasoning.

But this author is fonder of the argoment called persiflage, than a strict investigation of principles. He bangs forward merely the old arguments against the earth's motion: he would make it fixed to no purpose whatever, and he takeadvantage of the false notions attributed to attraction, instead of examining it upo the plan adopted by sir I. Newton, who considers only the effects produced in nature, for which be cannot use a better word than attraction. Thus the moon approaches to and recedes from the earth; and as this resembles a motion, produced by a man drawing a boat to him, the earth is said to attract the moon, whatever maj be the real cause of the motion.

We would by no means discourage wit. It may be employed on topics of philosophy as well as philosophers; and Swift in his voyage to Laputa has done it to great advantage. But true philosophy smiles only at these efforts; and the third ap! eighth sections of Newton will not be a the least affected by a witticism. We might just as well turn the forty-sevent of Euclid's first book into a joke; and when the wit, like the celebrated epigramwriter of Cambridge, has amused himself with his own fancies, the astronomer a the mariner will nevertheless continue, the one his observations on the heavies, and the other his path in the seas, de pending entirely upon the well-known truth of this proposition. For the young Cantab, however, who is going into the schools, this book will be very useful, z it will afford him many arguments on the questions, which he is called upon to op pose, and he will afterwards smile with us at all mystifications.

IS a bishop to be confined always to his theology? Will not an acquaintance with other sciences tend to soften his manners, and take away from the too high consideration which holy men are apt to set on themselves on their supposed spiritual labours? May not an acquaintance with classical writers and mathematical studies beguile the tedious hours of a father of

the church, and take off from the enti which even episcopacy cannot cure? Is tidious men there are who would confre the bishop to his breviary, and his bible, his articles, and his homilies, and the thers. We are not of that dispositions and have no doubt that a thought now ad then on honey and wheat, and the sto will rather assist than disturb their div

Täygete simul os terris ostendit honestum Pleias, et oceani spretos pede repulit amnes. Aut eadem, sidus fugiens ubi Piscis aquosi Tristior hibernas coelo descendit in undas.”

These two appearances are when they rise heliacally, which the poet expresses by the Pleiad washing away the water of the ocean by her feet, in rising and shewing her face to the earth. This took place in Virgil's time and country soon after the middle of May. The second appearance is when she is running away from the constellation of the Pisces, and sinking into the waves; and this appearance takes place, according to the expositors, in the beginning of November, and is termed the cosmical setting of the Pleiad, or the setting of the star at sunrise. To determine whether this exposition is right, we have nothing else to do but to rectify the globe for the latitude of Rome, find the sun's place in the zodiac for May and November, and examine what is the state of the Pleiads during any day in those two months, and see whether it can be made to correspond with Virgil's verses.

In performing this operation we must remember to make allowance for the precession of the equinoxes; and we may then examine the propriety of the bishop's interpretation. One datum then for gathering the honey is, according to his lordship, the chronical rising of the Pleinds, which happened apparently about the middle of September. The other appearance is derived from the setting of the Fieiads in the evening, when the Fishes, or rather & piscium, rise heliacally in the morning. In that case Virgil's character is supposed to be consistory: namely, that the Pleiad was then running away from the watery fish, and descending into the blustering waves. Now this setting of the Pleiad took place about the 13th of April, styl. Jul.

The conjecture is ingenious, but some difficulties suggest themselves from Fliny's account of the collecting of honey, As

his lordship has condescended to investigate this subject, we could wish, before we resign ourselves completely to this interpretation, to learn the seasons of collecting honey at this time in use in Italy. They differ we dare say very little from the seasons in Virgil's time; and some of his lordship's good friends in that part of the world will, we doubt not, take a pleasure in noticing, not only the times of taking honey, but the appearances of the Pleiads and the fishes; and their communications will be an agreeable confirmation of his lordship's conjecture, as well as point out the difference, if any, in the rising or setting of a star heliacally in those climates, from what takes place in our more ungenial atmosphere.

From the collection of honey we are carried to the sowing of corn; and Virgil is defended against some of the commen tators on the following verses:

"Ante tibi Ear Atlantides abscondantur, Gnossiaque ardentis decedat stella corona, Debita quam sulcis committas semina.”

The question upon these lines is, what is meant by the hiding of the Pleiads, and the departure of the gem in the crown. The hiding may be either from the setting of the star, or its disappearance on the dawn of the solar light. The hiding is interpreted by the bishop to mean the cosmical setting, and the precept then is, wait not only till the cosmical setting of the Pleiads is over, but till the bright star in the crown is setting. The words will evidently bear this meaning, but this pas sage will be set in a clearer light if the time of sowing corn in the present days in Italy is ascertained, and by comparing that time with the appearance of the Pleiads; now we may determine what would be the relation of the season to the appearances of the Pleiads and gemma coronæ in the days of Virgil.

Having interpreted the poet, his lordship enters upon a mathematical problem which is simply this: given the right ascension and declination of a star, to determine its heliacal, cosmical, and achrovical risings and settings. To discover these phænomena, a most laborious aud troublesome projection is used, and two plates are given us with these tables: Sterographia iucidæ Piciadum in plano horizontis urbis Romæ, An. D. O. Par. Jul. 4713. Sterographia Stella Sirii in plano maximotum qui per verticem urbis Meroes

primarii, anno ante epocham ære Domini vulgarem 1344. Per. Jul. 3369. No modern astronomer will give himself the trouble of making such a projection, and few perhaps will even examine with any degree of attention the plates; for any one tolerably versed in the solution of spherical triangles will much sooner solve the problem by a common diagram made with his pen, and the usual calculations, than he can understand this episcopal projection. It discovers indeed a certain degree of ingenuity, but the time is mispent upon it, and the labour unprofitable.

The selection of Sirius, and the latitude of Meroe, as an instance of the projection, was made upon grounds which are highly satisfactory. Meroe has been fixed upon by Mr. Bruce as the seat of the early astronomers. We have no writings from Meroc to determine this point, but antient authors do speak of certain risings of the stars from which we may determine the latitudes of the observers. The year 1344 B. C. was chosen, because in that year the first of Aries rose heliacally at the time the sun passed the vernal equinox. Wri

ters mention Procyon as the precursor of Sirius, and Pliny mentions the time to have been such that if Procyon rose in the morning on one day, Sirius did the same on the next day. Now as this could not take place in Italy or in Egypt, he must have received it from some other writers who lived in former times, and much to the south of him; and as it appears by calculation, that in the year before Christ 1344, the parallel of the simultaneous ris ings of the two stars lay in latitude 11°, 41, 52", the latitude in which Procyon rose only the day before must have been between the 13th and 14th degrees of north latitude, to which latitude we must assign a degree of astronomical observation and culture, very different from what it has possessed for the last two thousand years. This is a very curious subject, and the learned world is much obliged to the bishop for starting it. The history of astronomy will in consequence be better investigated, and we may discover the first authors of our zodiac in a country which we now deem almost unsuited to the existence of rational beings.

THE Evening Amusements for this year are conducted upon the same plan as those for the two last, and cannot fail of communicating the knowledge of astronomy in the easiest manner, to those who have not yet paid any attention to it, as well as of confirming and increasing the knowledge of those who have made some progress in this delightful science. Each month contains three parts; the progress of the moon and planets in the zodiac, by which every star of note is pointed out in its course; the development of a subject, which forms the amusement within as well as without for this year; and statements of the apparent diameters of the sun and moon, with a table for pointing, out the positions of the stars at any hour of the night. The subject for this year is the making of maps, which is shewn from the first and simplest principles, and the learner is properly recommended to map a portion of the heavens by the eye, and then compare it with the map made

by rule. Some instances are given at the end of the book, on which the reader is expected to practise: he is expected to make the map from the rules, and the declination and right ascension of certain stars given, and then to find out by ocular demonstration what part of the heavens he has been mapping. This very useful and ingenious exercise, we hope Mr. Frend will continue in his next year's volume. Twelve positions are given of the stars, which take place within two hours of each other, and these are pointed out by tables at the end of each month, so that whatever remarkable star has been observed at any time of night, the observer may find it by reference to these positions. At the end of the volume tables are given of the magnitudes of the principal stars, and this course of amusements, as it grows upon us, increases in interest. We cannot help observing how much the volume is increased in size without any addition to its price.