From the fubject of these pretended letters, our author takes occafion alfo to make a fhrewd 1emark on literary impofitions, and the truth of printed anecdotes in general. "It is true, Sir, that there is no great harm in afcribing letters to Pope Ganganelli and Queen Chrftina of Sweden, which neither the one nor the other did write. It is a long time fince quacks began to deceive the world for money. The world fhould be pretty well acquainted with it, fince that grave hiftorian, Flavius Jofephus, hath certified, that a beautiful writing of the son of Seth, who was the grandfon of Adam, upon aftrology, was to be feen in his time: that one part of the book was engraved upon a pillar of stone, to refift water when the human race were to be destroyed by a deluge; and another part upon a pillar of brick, to refift fire, when the general conflagration fhould destroy the world. No writing can give an earlier date to falfities. I think it was the Abbé Tilladet who faid, As foon as any thing is printed, tho' you have not read it, lay a wager it is not true; I will go your halves, and it will make my fortune. Philofophical Tranfactions, of the Royal Society of London. Vol. LXVI. For the Year 1776. Part II. 4to. Price 7s. 6d. Davis. This part of the volume of Philofophical Tranfactions for the last year, contains Art. XVIII, an abridged state of the weather, at London, for one year, commencing with the month of March 1775, collected from the Meteorological Journal of the Royal Society. By Dr. Horfley.-On the table, refpecting the quantity of rain which fell in the course of the year, the Doctor infinuates that the common notion of the moon's influence in this cafe is by no means fupported by experience, although he admits that the trial turns out more in favour of the moon this year, than it did the last. The expofition of vulgar errors is certainly a proper employment for philofophers; it is as requifite, however, for their own credit, that they should pay equal attention to certain vulgar truths: in which cafe, they would not fo often expose their ignorance of circumftances, familiar even to the multitude. We drop this hint on account of the formal declaration of the worthy prefident, in his fpeech on the diftribution of the last year's medal, concerning Capt. Cook's discovery of the tranfmutation of falt water into fresh, by freezing. This phænomenon is nothing new nor furprizing; being well known to every Dutch or Danifh boor on the northern coafts; the ice of falt-water being in fome places tranfported many a mile in that form, and ufed, when diffolved, by way of preference to common fresh water. A Prefident of the Royal Society fhould not have been ignorant of fo well-known a fact. "XIX. Extract of a Meteorological Journal for the year 1775, kept at Bristol, by Samuel Farr, M. D. "XX. Extract of a Register of the Barometer, Thermometer, and Rain, at Lyndon, in Rutland, 1775. By Thomas Barker, Efquire. Communicated by Sir John Pringle, Bart. P. R. S. "XXI. An Account of the Meteorological Inftruments used at the Royal Society's Houfe. By the Hon. Henry Cavendish, F.R.S. "XXII. Method taken for preferving the Health of the Crew of His Majefty's Ship the Refolution during her late Voyage round the World. By Captain James Cook, F.R.S. Addreffed to Sir John Pringle, Bart. P.R.S. "XXIII. Extraordinary Electricity of the Atmosphere observed at Iflington on the Month of October, 1775. By Mr. Tiberius Cavallo. Communicated by William Watfon, M.D.V.P.R.S. "XXIV. Propofals for the Recovery of People apparently drowned. By John Hunter, Efq. F. R S. The Proposals contained in this article, appear to be very judicious and fenfible, and are well worthy the attention of the faculty, and of all fuch as would be inftrumental in the recovery of perfons, affected by a fufpenfion of the action of life from any cause whatever. "XXV. An extraordinary Cure of wounded Intestines. By Charles Nourse, Surgeon, at Oxford. "*XXV. Extract of a Letter from Mr. Alexander Small, Surgeon to the Train of Artillery at Minorca, to Sir John Pringle, Bart. P.R.S. Dated St. Philip's, Aug. 8, 1775. "XXVI. Of the Tides in the Sout Scas. By Captain James Cook, F.R.S. "XXVII. An Experimental Examination of the Quantity and Proportion of Mechanic Power neceffary to be employed in giving different Degrees of Velocity to Heavy Bodies from a State of Reft. By Mr. John Smeaton, F.R.S. We have here a very curious paper on a fubject perhaps the most important, in the prefent ftate of mechanical fcience, of any other whatever. We are glad, therefore, to find fo expert and excellent a practical mechanician, as Mr. Smeaton, has turned his thoughts to the fubject; a subject that has been fo long neglected, as to be almost entirely exploded, as being beneath, or beyond, inveftigation. This is the means of eltimating the momentum or force of bodies in motion; which made fo much noife in the philofophical world at the latter end of the laft, and in the beginning of the prefent, century; and about which the mathematicians have been divided in their fentiments ever fince. Mr. Smeaton, indeed, has here given another turn to its expreffion, by calling fuch force `mechanic power, and confining it to its effect of giving motion to heavy bodies at reft: but the ancient axiom ftill holds good, notwithstanding the partiality of the prefent experiments; P 2 re requiring juft as much and no more force, or mechanical power, to ftop a body in motion, as it does to put the fame body into motion. Nor can any good reafon be given, why the measure of force fhould be rather that which puts bodies in motion, than that which ftops or puts them to reft.-We will give, however, Mr. Smeaton's own ftate of the cafe. "About the year 1686 Sir Ifaac Newton first published his Principia, and, conformably to the language of mathematicians of thofe times, defined, that "the quantity of motion is the measure of the "fame, arifing from the velocity and quantity of matter conjointly." Very foon after this publication, the truth or propriety of this de finition was difputed by certain philofophers, who contended, that the measure of the quantity of motion fhould be eftimated by taking the quantity of matter and the fquare of the velocity conjointly. There is nothing more certain, than that from equal impelling powers, acting for equal intervals of time, equal increafes of velocity are acquired by given bodies, when unrefifted by a medium; thus gravity caufes a body, in obeying its impulfe during one fecond of time, to acquire a velocity which would carry it uniformly forward, without any additional impulfe, at the rate of 32 ft. 2 in. per fecond; and if gravity is fuffered to act upon it for two feconds, it will have, in that time, acquired a velocity that would carry it, at an uniform rate, juft double of the former; that is, at the rate of 64 ft. 4 in. per fecond. Now, if in confequence of this equal increase of velocity, in an equal increase of time, by the continuance of the fame impelling power, we define that to be a double quantity of motion, which is generated in a given quantity of matter, by the action of the fame impelling power for a double time; this will be co-incident with Sir Ifaac Newton's definition abovementioned; whereas, in trying experiments upon the total effects of bodies in motion, it appears, that when a body is put in motion, by whatever caufe, the impreffion it will make upon an uniformly refifting medium, or upon uniformly yielding fubflances, will be as the mafs of matter of the moving body, multiplied by the fquare of its velocity: the queftion, therefore, properly is, whether thofe terms, the quantity of motion, the momenta of bodies in motion, or forces of bodies in motion, which have generally been etteemed fynonymous, are with the most propriety of language to be eteemed equal, double, or triple, when they have been generated by an equitable impulfe, acting for an equal, double, or triple time; or that it fhould be meafured by the effects being equal, double, er triple, in overcoming refiflances before a body in motion can be stopped? For, according as thote terms are understood in this or that way, it will neceffarily follow, that the momenta of equal bodies will be as the velocities, or as the fquares of the velocities, refpectively; it being certain, that, whichever we take for the proper definition of the term quantity of motion, by paying a proper regard to the collateral circumstances that attend the application of it, the fame conclufion, in point of computation, will refult. It is true, that it is " according as the above terms are un"derftood" that, ex hypothefe, we may allow the momenta of moving moving bodies to be eftimated; but if we are to adhere either to "propriety of language" or precifion of idea, we must not make the measure of a partial effed, the measure of a general caufe. In all experiments, made with unyielding, or unelaftic bodies, the measure both of cause and effect is the fame; viz. according to Sir Ifaac Newton, the momentum or force is, fimply, as the velocity multiplied by the weight. In experiments with yielding media, and bodies highly elastic, the measure of cause and effect differ widely: that of the former being fimply as the velocity, that of the latter as the Square of the velocity. It is no wonder, therefore, that practical mechanics, not attending to that, difference, fhould, as Mr. Smeaton obferves, fall into egregious errors *. It is, of courfe, with great juftice, that Mr. Smeaton reprehends and expofes their blunders. We are not of opinion, however, that he has properly corrected their theoretical mistakes. "Finding thefe matters, fays he, as well as others, to come out in the experiments, fo very different from the opinions and calculations of authors of the first reputation, who, reafoning according to the Newtonian definition, must have been led into these errors from a want of attending to the proper collateral circumstances; I thought it very material, efpecially for the practical artift, that he should make use of a kind of reafoning in which he fhould not be fo liable to mistakes; in order, therefore, to make this matter perfectly clear to myself, and poffibly fo to others, I refolved to try a fet of experiments from whence it might be inferred, what proportion or quantity of mechanical power is expended in giving the fane body different degrees of velocity. The reader, who understands the subject, and attends to propriety of language, will here hefitate, with us, at the word expended. Even as money may be spent and laid out to wafle, fo may power. It is not to be denied, that, in the or dinary method of experiment on the percuffion of bodies, there is ufually much more force expended in giving velocity to bodies at reft, than is poffeffed by the percutient bodies giving fuch velocity of motion. But it does not thence follow that all the force of fuch percutient bodies is fairly expended, that is, communicated to the bodies at reft, put in motion by them: neither does it follow, that, becaufe the ordinary methods are infufficient to communicate the whole force of a body in motion, to another unequal body at reft, fuch com Efpecially as their theoretical mafters run into fome still more egregious, than any pratical mecha ic can be fufpected to fall into; thus Mr. Smeaton obferves, that, between Belidor and Defaguliers, in calculating the proportion of work to be done by a Corn-mill, there is no lefs a difference in the proportion, than that of fixty to one. A difference fo opprobrious to pretenders to fcience that it is almoft incredible! munication munication is either impoffible or impracticable. In the disputes on this fubject between Leibtnitz, Poleni, and others, the grand difficulty was started, and in fome measure difcuffed: viz. that of communicating the whole force of a heavy body in motion, to a lighter one at reft. In the Acta Eruditorum of Leipzig (if we mistake not, for the year 1695) methods of fuch communication are pointed out: thefe, we muft frankly own, we have tried, and found infufficient. There are yet other methods, which will answer the fame end, or produce the effect required, from the fame caufe: fo that, without impeaching either Sir Ifaac Newton's theory, or the truth of the experiments, on which the contrary notion is founded, the apparently-contrary effects may be fhewn to be perfectly confiftent and conformable to the general and univerfally-admitted laws of motion. If Mr. Smeaton's fet of experiments was performed merely to afcertain that the effect, of an unyielding or unclaftic body in motion, acting against a pervious medium, a yielding or elaftic fubftance, is in proportion to the fquare of the velocity of the moving body, as it appears, he might have faved himself the trouble; because the elder Bernoulli, s'Gravefande, and many others, made fuch experiments, and, with as good an apparatus, upwards of fifty years ago. The refult of their experiments was uncontrovertible: it proved that the refiftance of yielding substances, pervious media, and even of fteel fprings, is in proportion to the fquare of the velocity of the unyielding body, ftriking againft, compreffing, or endeavouring to pass through them. But the meature of the force of the refifting medium; or body at reft, is not the measure of the force of the percutient body in motion. A heavy body thrown up perpendicularly will rife to a height proportional to the fquare of the velocity with which it is fo thrown up; but this space is the measure of the resistance it meets with from the action of gravity during the time it is rifing; and not of the force with which it is thrown up.-It is the fame with the refiftance of any fubftance whofe tenacity will admit of its perforation; and even with that of elaftic fprings of any fubftance whatever. Let us bend a steel fpring, for inftance, to fuch a degree, that in unbending itfelf against a body weighing four pounds, it will throw fuch body off with a velocity, which we will call four degrees. It is well known that if fuch fpring, so bent, were to discharge itself againft a body of one pound only, it would give it but two degrees of velocity, and not four, as it See'sGravefande's Mathematical Elements, Book I. Part I. fhould |