This is a fufficient proof that the Pythagoreans had, at that early time, embraced this opinion; but as this was near two centuries after the time of Pythagoras, and as Plato, the mafter of Ariftotle, makes Timeus, who was a Pythagorean, place the earth in the centre of the univerfe, there feems fufficient reafon for fuppofing that this fyftem was not taught by Pythagoras, nor his immediate fucceffors. The time of the invention, therefore, and the real inventor, feem entirely loft in obfcurity. Numa's Temple of Vefta, where a continual central fire was kept up, which, as fir Ifaac Newton obferves (De Mundi Syftemate), favours much of the Egyptian myfteries, certainly affords an argument for the high antiquity of this difcovery.

Though the era of this invention is unknown; and though the time in which Ariftarchus flourished is indeterminable; yet, as Archimedes is the oldest writer who has mentioned Ariftarchus, we cannot but be inclined to concur in the general opinion, that the true fyftem of the world must have been known in Italy long before his time. Indeed it appears to us extremely probable that he was a very eminent defender of this fyftem, about the time of Archimedes, as Voffius places him; and this probably was the reason of that celebrated mathematician making him (as Libertus Fromondus expreffes it) the chief of that opinion (Hujus paradoxi principem fecit Archimedes.)

The remainder of the preface contains an account of the different editions made ufe of by the tranflator, and their feveral merits; one of which is not a little extraordinary, as it differs confiderably from all the other Greek editions; and though complete, has neither date, editor's name, nor place of printing.-We have made fome enquiries concerning this work, but have been equally unfuccefsful with Mr. Anderfon.

The tranflation appears free and correct, as far as we have had any opportunity of judging; the tranflator having in general followed Dr. Wallis's edition. A confiderable number of notes are added, at the end of the work, which contain fome criticisms on the Greek text, and, on the folution of the problems, tending to elucidate the more obfcure parts of this performance. But as we have already dwelt longer than ufual upon this article, our limits will not permit us to enter into a difcuffion of their merits. We fhall therefore prefent our readers with Archimedes' account of the fyftem of Aristarchus, and conclude, with wifhing that this little performance may meet with fuch encouragement from the public as will induce

the

the tranflator to undertake the whole of this author's writings.

'According to the hypothefis of Ariftarchus, neither the fixed ftars, nor the fun, are fubject to any motion; but the earth annually revolves round the fun, in the circumference of a circle, in the centre of which the fun remains fixed; and the. fphere of the fixed stars, whofe centre he fuppofes to coincide with the fun's, is of fuch immenfe magnitude, that the circle, in whofe periphery the earth is fuppofed to revolve round the fun, bears no greater proportion to the distance of the fixed ftars, than the centre of a sphere does to its fuperficies.'

To this is added, a tranflation of a differtation by Christopher Clavius, on the same subject; which, being expressed by cyphers, tends in fome degree to illuftrate Archimedes' doctrine.Before we leave this fubject we cannot help remarking to what an extent Archimedes has carried the powers of numeration, having invented terms to exprefs numbers which would require 80,000,000,000,000,000 cyphers, with an unit annexed to denote them.-If the extent of calculation be, as fome have afferted, a criterion to judge of the improvement of a country in the fine arts, Greece muft, at that time, have arrived at the highest fummit of knowledge.

A Treatise on the Art of Mufic; in which the Elements of Har mony and Air are practically confidered, and illuftrated by an Hundred and Fifty Examples in Notes; many of them taken from the beft Authors. The whole being intended as a Courfe of Lectures, preparatory to the Practice of Thorough-Bass, and Mufical Compofition. By Mr. Jones. Fol. l. 15. Longman and Broderip.

MUfic is a fcience which had been treated either obfcurely

or fuperficially by many authors; fome parts of it had scarcely been confidered at all, though neceffary to be known by all compofers who wish to rife above the fervility of imitation, and would work upon fuch principles as can alone give value to originality of fentiment in mufical compofition. A way was therefore open for a mufical author to methodize the art, and lay down its laws more clearly, for the benefit of mufical students. This is the defign of Mr. Jones's work, aş he has explained it in his Introduction; where he tells us, his work, short and imperfect as it is, contains much of that information which, as a ftudent in mufic, he often wished to find, but never could.' Yet it does not interfere with the profeffion of mafters who teach the performance of mufic; be ing rather intended to improve thofe in fcience and judgment VOL. LIX. June, 1785.

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who

who are already proficients: and the author wishes every reader of his work to be able to touch all the examples, as they occur, upon fome keyed inftrument.

In the order of his work Mr. Jones begins, where the art itself muft, with laying down the octave as a system of degrees; and he delivers the old fcheme of fol-fa-ing, to fhew the difpofition of tones and femi-tones in the major and minor keys.

A rule is here given, which fimplifies the practice of hitting the intervals with the voice; and the author recommends it to practitioners to learn finging by the fol-fa rather than by an inftrument; because this keeps them ignorant of the true principle of finging by notes, and renders their improvement much more flow and uncertain. It is a practice too common in fome cathedrals to learn boys to follow the organ by ear rather than to take the intervals by rule; in confequence of which they ftill remain ignorant beginners at every new piece .of mufic. Whoever tries the fol-fa properly, will foon be fenfible of its wonderful effect in producing rapid improve

ment.

In a fecond chapter Mr. Jones treats of concords or confonant intervals, and fhews particularly how many different relations one fingle note is capable of, when referred to other notes above and below it.

In his third chapter he treats of the octave as a system of harmony; fhews how the whole natural harmony of the octave is comprehended in the chord of the key itself, the chord of its fifth, and the chord of its fourth: whence the key and its fifth and its fourth are the three fundamental notes of the octave. This leads to the harmonic accompaniments of the degrees in an octave; all of which is illuftrated by examples in notes, for which we muft refer to the work itself.

The fourth chapter treats of the inverfion of concords, for the purpose of producing variety without departing from the key; and here a new and curious doctrine of what the author calls internal confonance, is advanced; and it is fhewn how the fame chord, when inverted, changes from minor into major, and affumes a form more agreeable to the ear; which may lead to many improvements.

The fifth chapter delivers the doctrine of discords, and fhews how they become allowable by means of a confonant relation to fome, concord; which rule alfo fhews why fome difcords have a natural preference to others. The generation

of difcords out of one another, and their respective refolutions, are shewn at large, and illuftrated by examples; and a rule, more extensive and universal than that of Rameau, is laid

down

down for finding fundamental baffes. But that which carries the scholar more deep into the myfteries of mufic, is the doctrine of modulation, in the fixth chapter, which comprehends the rules for paffing from one key to another. To keep this

art of modulation within its true bounds, the author derives it from its true principle; by the application of which, it is confined to thofe keys only which have a natural relation to the original key, as primaries or fecondaries.

The feventh chapter lays down feveral periods of harmony, fome of which arife from the foregoing rules, and fome are borrowed from the greatest compofers. The ufe of these is to form a fort of common-place, out of which the voluntary player or compofer may enlarge his ftock of matter and im. prove his judgment. Here it is alfo fhewn how a fugue or canon may be conftructed, by comparing with one another a series of concords in an harmonic period: of this the author gives an example, from one of the periods in his work. A piece for the organ is formed on the harmonic accompaniment of that period, which confifts of the eight degrees of the fifth of the key; this is fubjoined in the thirty-eighth plate of the mufical examples. Some remarks are added on the excellence of a refponfive correfpondence in the feveral parts of a compofition, and the endless variety which the compofer may invent in this species of mufic. The several kinds of cadences, perfect, imperfect, and ad libitum, are defcribed and, in plate nineteen, example eighty-fix, a piece of mufic is given, in which fourteen different cadences are introduced; which piece might be performed as a voluntary upon the organ with good effect.

To this chapter is added a theory of the chromatic system, where the chromatic octave, or octave of half notes, is de-, duced from its proper original, and the limitations of chromatic melody are afcertained by examples from the greatest mafters. The harmonic accompaniments of chromatic basses afcending and defcending, are fhewn in feveral periods of harmony; and fome obfervations are added on the ufe of chromatic harmony in vocal mufic, which are illustrated by examples from Purcell and Pergolefi. In the foregoing periods (fays the author) I have endeavoured to exhibit the moft confiderable parts of what may be called the materia mųfica, which experience and fancy are to compound and apply in different ways. I might have multiplied thefe examples; but when the learner has ftudied what is here given, he will be able to do this and much more for himself. Out of these periods he will conftruct others, by compounding them together, at pleasure, when ufe has made it easy to apply the

rules of inverfion and modulation. And when the fancy is furnished with fome variety of air and measure, the scholar becomes an extempore performer, who will find his ftores inexhaustible, if he has laid in a proper foundation of harmony.'

The eighth chapter treats of the analyfis of mufical air, and the conduct of fubject. The author proceeds upon an analogy betwixt poetry, rhetoric, and music, and infers the neceffity of measure in mufical air, and a divifion of it into claufes and fentences; without which, mufic has no more sense in it than poetry or oratory would have under the like disadvantages. He fhews how air is measured, by decompofing some of the pieces of our beft mafters and here he takes occafion to cenfure the want of meaning and method, with that barren tautology, which are too frequently found in the prevailing style of mufic. Some mafters have ventured to predict, that this ftyle will foon be out of fashion, but that (fays the author, page 43), is more than I can forefee; light people will always be pleafed with light mufic, and little minds will give the preference to little things.' In treating of air, he endeavours to prove, by examples, that the effect of melody upon the ear is very much heightened by an harmonic confecution in the notes of the melody. Of this we fhall not undertake to decide, but leave it, as a nice point, to the experience of the mufical reader.

For the management of a mufical fubject, and its improvement, feveral rules are laid down and confirmed by examples. The firft rule for this purpofe is to diverfify the fubject by breaking it into parts, and taking them up alternately. A fecond is, to apply the measure of the fubject to a different order of tones and femi-tones; taking care that, if chromatic melody is introduced for variety, the chromatic femi-tones fhould, at proper places, fall into the diatonic degrees, and belong to fome certain key. A third rule for improving a subject without departing from it, is to augment or diminish the time or value of its notes, of which fome remarkable examples are given. A fourth is to run divifions upon its harmony; and of this a large example is given.

This chapter is concluded with fome obfervations on expreffion and contrast, both of which, as the author obferves, are of great importance to compofers and performers.

In a ninth chapter, all the foregoing rules are fummed up: and when the mufical ftudent has been directed how to apply them for his improvement, Mr. Jones concludes his work in the following words: If the best authors are ftudied and examined by thefe rules, I am perfuaded there will be more true tafte and judgment amongst the lovers of music, better voluntaries