tion of the planetary motions, must be aware that we never faw one inftance, either of reft, or of uniform rectilineal motion. With refpect to reft there is no difficulty, all mankind admitting that a body at reft muft continue for ever at reft, unless put into motion by fome mechanical force; but motion, fay fome, is a continued effect, and therefore requiring a continuation of the caufe. Dr. R. fhows that this is contrary to experience, and then adds,

"It is equally contrary to our notions of a moving force. By its inftantaneous action, fuch a force produces motion, that is, a fucceffive change of place, otherwife it produces nothing. Or if in any inftant of its action it do not produce a continuing motion, it cannot produce it by continuing to act. Continuation of motion is implied in our very idea of motion. In any inftant the body does not move over any space, but it is in a certain condition (however imperfectly understood by us) or has a certain determination, which we call velocity, by which, if not hindered, a certain length of path is paffed over in a fecond. This must be effected by the inftantaneous action of the moving caufe, otherwise it is not a caufe of motion. In fhort, motion is a state or condition, into which a body may be put, by various caufes, but by no means a thing which can be infufed into a body or taken out of it."

P. 102.

From this expreffion the reader will perceive that Dr. R. is no advocate for the doctrine of a vis infita corpori moto, of which fo much ufe has been made by fome philofphers. He is not; and what he says againft it, as commonly understood, is at once profound, and, as we think, conclufive.

In his commentary on the fecond law of motion, he ftre. nuously oppofes the measure propofed by Leibnitz of mechanical action or force, and reclaims to our countryman Dr. Hooke the difcovery of the facts on which the hypothefis of Leibnitz was founded. The British and French philofophers have generally held that the force of a body in motion is in proportion to its velocity; the Germans, with Leibnitz at their head, that it is in proportion to the fquare of its ve locity; and both parties have urged facts in fupport of their refpective opinions. Dr. R. proves, at fome length, that in the Leibnitzian measure many things are gratuitoully affumed, many contradictions are incurred, and, finally, that it is only becaufe forces are affumed as proportional to the velocities which they generate, that the facts obferved by Hooke, and employed by Leibnitz, come to be proportional to the fquares of the fame velecities. In the courfe of his difquifitions on this fubject the Profeffor gives us a beautiful demonftration of the law of the

changes

changes of motion; for which, however, we must refer to the work itself.

Of Newton's third law of motion this author has not the fame opinion as of the two former. That the actions of bodies upon one another are always mutual, equal, and in contrary directions, he admits to be a fact obferved in all cafes which we can examine with accuracy; but that this equality of action and reaction is an axiom deduced from the relations of ideas feems, he fays, to be doubtful.

"Because a magnet caufes the iron to approach towards it, it does not appear that we neceffarily fuppofe that the iron alfo attracts the magnet. The fact is, that although many obfervations are to be found in the writings of the antients concerning the attractive power of the magnet, not one of them has mentioned the attractive power of the iron. It is a modern discovery, and Dr. Gilbert is, I think, the earliest writer, in whofe works we meet with it. He affirms that this mutual attraction is obferved between the magnet and iron, and between all electrical fubftances and the light bodies attracted by them." P. 124.

This reafoning is plaufible, but we think not conclufive, if it be poffible to conceive in the magnet any power of operating like attraction on the iron at a diftance. If a magnet of an ounce weight can be fuppofed capable of drawing towards itfelf an ounce of iron, it feems to follow, from the very notion of drawing, that these two bodies must meet in the middle of the fpace between them, and that fuch a magnet would rush to a piece of iron of two ounces weight, the iron remaining all the time at reft. It is not indeed a law of human thought, but a matter of mere observation, that the magnet is endowed with what is called power to act on iron at a distance, or vice verfa, that iron has power so to act on the magnet; but if it be granted that either of thefe bodies has power to attract or repel the other, it feems to follow neceffarily that the attraction or repulfion must be mutual. What the Profeffor fays, however, in fupport of his opinion is well worth the attention of every reflecting reader; and it is perhaps fufficient for all the purpofes of ufeful fcience to know that, with refpect to all bodies on which we can make experiment or obfervation, reaction is always equal and contrary to action.

"As it is an univerfal law, we cannot rid ourfelves of the perfuafion that it depends on fome general principle, which influences all the matter in the univerfe. It powerfully induces us to believe that the ultimate atoms of matter are all perfectly alike-that a certain collection of properties belong (belongs) in

fome

fome degree to every atom-and that all the fenfible differences of fubftances which we observe arise from a different combination of primary atoms in the formation of a particle of thofe fubftances. A very flight confideration may fhew us that this is perfectly poffible. Now, if fuch be the conftitution of every primary atom, there can be no action of any kind of particle, or collection of particles, on matter, which will not be accompanied by an equal motion in an oppofite direction. Nothing can be clearer than this. This therefore is, in all probability, the origin of this third law of motion." P. 125.

With all poffible refpect for the memory of Profeffor Robifon, we cannot help thinking that in this paragraph, if we thoroughly understand it, he reafons, as the logicians exprefs it, in a circle. He firft obferves, that the admiffion of this third law of motion powerfully induces us to believe that the ultimate atoms of matter are all perfectly alike; and then from this conclufion he infers the truth of the third law of motion. He has thought perhaps the lefs, and reasoned the more loafely on this third law, that he considers it as comparatively of little importance.

"The three axioms, and, indeed, the two firft, feem to include the whole principles of dynamics, and enable us, without other help, to accomplish every purpofe of the fcience. Some authors of eminence have thought that there were (are) other principles, which influenced (influence) every natural operation, and that these operations could not (cannot) be fully understood, nor an explanation properly deduced, without employing thefe principles. Of this kind is the principle of ECONOMY OF ACTION, OF SMALLEST ACTION, affirmed by M. Maupertius to be purfued in all the operations of nature. This philofopher fays, that the perfect wifdom of Deity muft caufe him to accomplish every change by the fmalleft poffible expenditure of power of every kind; and he gives a theorem, which he fays expreffes this economy in all cafes of mechanical action. He then afferts, that, in order to fhew in what manner fuch and fuch bodies, fo and fo fituated, fhall change each other's condition, we muft find what change in each will agree with this value of the fmallest action. He applies this to the folution of many problems, fome of which are intricate, and gives folutions perfectly agreeable to the phenomena. But the fact is, that the theorem was fuggefted by the phenomena, and is only an induction of particulars. It is a law, of a certain extent, but by no means a first principle; for the law is comprehended in, and is fubordinate, by many degrees, to the three laws of motion now established. It is no juft expreffion of a minimum of action; and he has obtained folutions, by means of problems, in which its elements are altogether fuppofititious, which is proof fufficient of its nullity and impropriety. "M. D'Alembert

"M. D'Alembert and M. De la Grange have alfo given ge neral theorems, which they call firft principles, and which they think highly neceffary in dynamical difquifitions. Thefe, too, are nothing but general, but very fubordinate laws, moft ingenioufly employed by their authors in the folution of intricate problems, where they are really of immense service. But ftill they are not principles; and a perfon may understand the mechanique analytique of De la Grange, by ftudying it with care, and yet be very ignorant of the real natural principles of mechanifm. All these theorems are only ingenious combinations of the second and third Newtonian laws of motion." P. 129.

Our author next employs the three laws of motion, or rather the two firft, to difcover thofe mechanical powers of natural fubftances which fit them for being parts of a permanent universe, and to explain those mechanical powers of bodies which occafionally accelerate, retard, and deflect the motions of other bodies. Under this laft head he treats mathematically, but with great perfpicuity, of Accelerating and retarding forces; of Deflecting forces in general; and of Central forces. We can give no abftract of this part of the work, which would be intelligible without diagrams; but we can recommend it with confidence to the reflecting reader as exhibiting perhaps the most complete view, that he will readily find, of Dynamics; or, in other words, of the abstract and metaphyfical doctrines of Mechanical Philofophy.

(To be concluded in our next.)

ART. II. The Harmonic Preceptor; A Didactic Poem, in Three Parts. Written by Mr. Dibdin. Price 18s. large 4to. 149 pp. with engraved mufical Plates. Publifhed by the Author, Leicester Place. Prefton, &c. &c.

1804.

THE author of a didactic poem is not obliged to attempt wit, but he ought to poffefs a competent thare of judgment and learning. His wit, if he does undertake to employ it, fhould be fomething more than a continual effort to excite rifibility by verbal puns; his judgment fhould teach him that a trifing jingle, (an humble imitation of Anftey's Bath Guide) is not exactly appropriate to convey important inftruction; and his learning ought at leaft to be shown in the true ortho graphy of fuch scientific terms as he defigns to notice. In

short

fhort, whatever may be this author's claims to wit (such as it is) fmall indeed are the evidences of his poffeffing either of the two other valuable qualities. There is, however, to be feen, in the advertisement, a fufficient stock of vanity, felf-conceit, and egotifm, which, as a friendly beacon to the youthful and unexperienced, we fhall here fully display.

"It has been imagined, perhaps, that I have indulged a ca. pricious and vain expectation in an endeavour to teach a science through the medium of a poem. This undertaking never appeared to me in any fuch light. I was aware of all I had to encounter; but I knew my own refources, and I was affured of the public fuffrage in favour of that zeal, which has fo long, and fo fuccefsfully, marked my character. I must confefs, that I had fome apprehenfion of finding my tafk difficult, in proportion as I should be under the neceffity of carrying mufic into complication; but, upon trial, this very part of it confirmed both the practicability and propriety of my labour; for, having proceeded gradually myfelf, and kept pace exactly with the fort of study that I recommend to my pupils, I found I had nothing more to do, than add together thofe precepts which I had before taught fingly; and, therefore, I met with lefs trouble, and re. ceived more pleasure as I advanced, and from this I augured the moft reputable fuccefs. I therefore pronounce, that I have given to the world a production of general utility; all thofe, who perufe the work with earnestnefs and care, will join me in this opinion. Under this conviction, I leave it with the public, who, I know, from long experience, will judge of it with candour and indulgence.

"My lectures, which I intend to commence on the day that this poem will be published, are meant to enlarge on all its precepts, and teach a complete fyftem of rational mufic.

"I cannot close this addrefs, without a fincere acknowledge. ment to my kind and folicitous friend, Mr. Ballantyne, who has given this publication all the correctnefs, beauty, and embellishment, that it could receive from printing. I would fay much more, but that I know he will not permit his eulogium to iffue from his prefs." P. P. 5.

The compliment to Mr. Ballantyne is nothing more than is deferved, for the book is certainly brought out in the beit typographical manner, and the meadow of margin is no doubt left uncultivated for the accommodation of fuch ftudents as chofe to decorate it with obfervation and memorandums.

Before we prefume to analyze this curious production, we fhall prefent the reader with Mr. D.'s own profpectus of

each book.