machinery has been for four months past, three cords of wood has been found sufficient to raise steam enough to carry the whole machinery 24 hours.

"6th. The quantity of water evaporated per hour, as near as I could ascertain, when in full operation, has been about 60 gallons.

"7th. The engine was first started about the beginning of Sept. 1835, and continued to work the pump and four mills only, until March, 1836, at which time the whole machinery was attached, making altogether nearly 10 months.

"8th. The cost of repairs has been very trifling, the whole expense of repairs, that could properly be said to belong to the engine during the whole time, will not exceed ten dollars.

"9th. With careful attention it is not liable to get out of order.

"10th. The cost compared with a piston engine of equal power will not, I presume, much exceed one-half that of the piston engine.

66 11th. If I was in want of another engine of about 20-horse power, I would certainly prefer the rotary to the piston engine.

"In conclusion, sir, after answering your several questions, permit me to state, that in my opinion the rotary is preferable in many respects to the piston engine. It can be attended by persons of less skill, is less expensive in transportation, and less expensive in erection than engines generally of the piston kind."

In all the foregoing testimonials with respect to Avery's engine, there is great want of that particular evidence, which is required in England, to establish the superiority of one kind of engine over another; it is all too vague and general -all calculation upon established rules and good data has been avoided. We acknowledge, that in America (for which, indeed, it is intended) the evidence given will have, perhaps, more effect than any founded upon calculation-engineers being there but little accustomed to look beyond the surface of matters. But here, instances must first be shown to be founded on general principles, before they will be received. Work must be shown to tally with calculation, and calculation with work. We would recoinmend the American patentees to put up an engine of their best manufacture, as a sample machine, and submit it to some such trials as Austen's steam-engine underwent (see our 643rd Number). When we hear the results of such a trial, we shall be better able to give an opinion.

VOL. XXV.

417

THE NEWTONIAN THEORY OF THE

TIDES.

Sir,-My old acquaintance, Ursa Major, tells us that he is "sufficiently read in mathematical science to discern that where there are half a dozen different demonstrations contradicting each other, they cannot be all true." I do not know what meaning Ursa Major attaches to the word demonstration. I always thought that a demonstration was meant to prove the truth of a proposition, so as to render it a matter of certainty; in that sense to speak of demonstrations contradicting one another, would be repugnant to common sense. But are you sure, friend Ursa Major, that your knowledge in mathematical and physical science is such, that when you read two authors on the same mathematical or physical subject, and find them to disagree, you can determine which of them is right (supposing one of them to be so); or supposing one of them partly right and partly wrong, could you separate the chaff from the corn? I am afraid you could not; or if you could, you surely never read with attention that passage you have quoted in your last letter in the Mechanics' Magazine from the writings of Dr. Wilkinson, which you seem to imagine will set the matter in dispute in a fair point of view. Newton is to be compared with Dr. Wilkinson! What next? Sir Henry Halford, I suppose, with Dr. Eady. But

let us see what sense we can extract from this selected passage that is to set the matter in dispute in a fair point of view.

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So

Supposing (says Dr. Wilkinson) the mean distance of the moon from the earth to be sixty times the radius of the earth; and if the law of gravitation be assumed, according to Newton, as diminishing as the square of the distance increases, it will be evident that 60 multiplied by 60 being equal to 3600, will express this proportion, viz. that 3600lbs. on the surface of the earth removed to the moon's surface would only weigh 1lb. (!)” says the learned Dr. Wilkinson, and so believes his enlightened constellate, Ursa Major. But in opposition to such mighty authority, I (Kinclaven) assert, that Newton never maintained nor ever dreamed of such a thing. Newton has demonstrated, that if a body is placed at any distance above the surface of the earth, the gravity or weight of this body diminishes in the inverse ratio of the 2 E

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1 224

will only raise the sea part of an

inch! It is true, the Doctor contrives to make the height of the tide 6 feet; but let it be remembered, the Doctor assumes that the moon exerts one-half the force of gravity at the earth's surface to what she does at her own surface!! Whereas I have supposed (taking Newton for my guide) that the gravitation of the moon follows the same law as that of the earth, namely, the inverse ratio of the squares of the distances. But enough of this part of the Doctor's nonsense.

The Doctor then proceeds to find the centre of gravity between the earth and moon, assuming the distance between their centres 60 semi-diameters of the earth, the moon's diameter 2161 miles, their mass in the ratio of 49-22 to 1, and the density of the moon to the density of

the earth as 11 to 9. Here the Doctor, forgetting his former statement, now makes the density of the moon (comparing equal bulks) greater than that of the earth! He calculates the ratio of the distances of the centre of gravity from the centres of the bodies to be as 39.788 to 1; and that the centre of gravity is 5880 miles from the centre of the earth. But the data is far from being correct, and the answers from that data are wrong; so that the Doctor's knowledge in the simple rules of arithmetic seems to be on a par with his physical attainments.

Ursa Major says he asked me for an explanation of the paradox of the tides, &c. I have already told him that there is no paradox in the matter, and that hundreds of explanations and demonstrations have been given of it-from the humble explanation of Ferguson to the profound researches of La Place. So that it would be an act of supererogation to give an explanation or demonstration of that (unless I could do it in a simpler way) which has already been given by so many. if he is unable to follow their demonstrations, it is his own fault; he might just as well ask me to give him a demonstration of the 47th proposition of the 1st book of Euclid, because he could not understand that given by Euclid, and for this reason, too, that he could not be troubled to read the whole of the propositions upon which the proof of the 47th depends. We should have lots of profound mathematicians, too, if it was not for that great bore of learning, the multiplication-table. Indeed, Ursa Major, from your last letter it appears you ought to take a spell for some time at the "Tutor's Assistant," and let physical science alone until you are better prepared to enter upon the study of it. I am, Sir, yours, &c.

KINCLAVEN.

OBSERVATIONS ON MR. EXLEY'S NEW THEORY OF PHYSICS.

Sir, The following paper, containing observations on Mr. Exley's new Theory of Physics," was written soon after that gentleman's reply to some former strictures of mine on the same subject, but has been delayed in consequence of my wish to append to it an examination of the validity of the distinction between the primary and secondary qualities of mat

ter. An arduous profession allows me little leisure for such pursuits, and the subject is difficult. So much time therefore elapsed, that though I continued the investigation, having another object in view, yet thinking all interest in Mr. Exley's theory must have ceased, I long since gave up the intention of sending you even any portion of my paper. Mr. Exley, however, having again brought his theory before the public, through the medium of the British Association during its late sittings at Bristol, I am induced to revise my opinion respecting the propriety of resuming the discussion, for though this communication is out of date, in a controversial point of view, yet the general subject is of no fugitive character; and the theory itself is likely to have a permanent interest attached to it, by the very favourable manner in which it was received by Doctors Dalton and Thomson. I shall not, however, enter on the abstruse inquiry alluded to above, but merely subjoin my view of some metaphysical consequences which must result from Mr. Exley's physical doctrines.

It is announced that Mr. Exley has brought forward in favour of his hypothesis some fresh facts in relation to the specific gravity of the gases. If these instances of verification do not rest on principles, data, and results, which run. in a circle, and acquire merely a mutual, self-derived support-if they are upheld by collateral and independent proofs, and by a course of reasoning untainted by subsidiary hypothesis-I shall receive great satisfaction from the circumstance, for my prepossessions are entirely in favour of Mr. Exley's theory; and I shall be eager to congratulate him on his having verified it, though but in part, after that more satisfactory and unexceptionable manner, the necessity of which is pointed out in the following paper.

I am, Sir, yours truly,
BENJAMIN CHEVERTON.

Sir, In the review which I took of "Mr. Exley's new theory of physics," I was sincerely desirous of forming an impartial estimate of its merits; and I cannot think I failed, because I felt called upon to moderate in some degree the expectations of its author. I wished, also, to embrace the opportunity of making some general observations on that, or any other theory of physics, which, like it,

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should aspire to explain all the pheno mena of inorganic nature, by deriving them from a supposed original constitution of the laws and qualities of matter. I thought it would be useful to notice the difficulties which in the present state of knowledge such an attempt has to encounter, and to examine the degree of evidence which, in the nature of things, such a theory is capable of receiving. I am sorry, therefore, that the observations in the reply with which Mr. Exley has favoured you should not have led directly to such an enlarged and philosophic dis cussion; that he should not have willingly engaged in throwing as much light as possible on these most interesting and important topics, with an especial reference, though it may be, to the corroboration of his own theory; that he should have thought it more advisable, or at least quite sufficient, in defence of that theory, to indulge merely in a running comment on what appeared to him objectionable points in my communication; and that the general tone of his remarks should imply, that I had not touched upon the more useful investigation alluded to, and had not applied the considerations which arose in the inquiry, as well for as against his theory, but that I had merely strung together a series of adverse observations or captious objections.

The most interesting point, as also the pivot on which the controversy turus, is the inquiry concerning the probability of Mr. Exley's theory being the true system of nature. If, without any doubt, the principles on which it is founded were what he asserts they are-certain ultimate facts or truths-still there would be room for a reasonable degree of scepticism, grounded on the possibility of some unknown principles affording, conjointly with the others, a more satisfactory explanation of phenomena. But those principles, wanting the character of axioms, and being avowedly advanced as postulates, he is not in a position to challenge so confidently the attention of seientific men to his theory as he otherwise would be entitled to do; and I fear that even as an hypothesis-plausible, ingenious, and elaborate as it inust be allowed to be-it has not met with that reception which, from its extensive applicability, and the numerous accordances therewith of observations and experiments, it justly deserves. For it must be

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in allusion to this theory, that Sir John Herschel observes, in his "Discourse on the Study of Natural Philosophy :""Molecular attraction has been attempted to be confounded by some with the general attraction of gravity, which all matter exerts on all other matter; but this idea is refuted by the plainest facts."*

In order to strengthen his position, that the first principles of his theory are undeniable physical truths, Mr. Exley observes, that "these principles are not arbitrarily assumed, but are themselves analytical deductions; and although named postulates, they are such only in a certain sense." It is also, I presume, only in a certain sense he would have us understand that they are "analytical deductions." Undoubtedly, it was from a review of the various phenomena of matter, that he was led in a general manner, analytically and inductively, and not arbitrarily, to fix on these principles as being of themselves sufficient on which to erect his system; but will he affirm, that he has entered on so pointed and definite an analytical investigation of any phenomena, as should make an inference of these principles therefrom, a necessary indubitable consequence. If so, let him publish it, by all means, and it shall have more weight towards the establishment of these principles, than any proof derived from the agreement of experiments or observations with deductions from them. Can he, for instance, bring forward any analysis which shall unequivocally indi-, cate that the law of attraction between the atoms, to say nothing of the law of repulsion, is in the inverse ratio of the square of the distance. He will refer us, probably, to the heavenly bodies, asserting that "the voice of all their actions makes it appear that gravitation belongs to every atom of matter." This may be, but it is begging the question, if he would thence infer, that the law of molecular attraction is proved by the law of gravitation, for he must first assume that these forces are the same. He further observes, Analysis carries us upward to

This hypothesis, however, cannot be so very absurd, or Sir John Herschel would not have bestowed any notice on it; he surely, therefore, might have referred us to a few of those facts which so plainly refute it. The truth is, that the assumption of knowledge on subjects of this kind, in so very confident a tone, whether it be in the way of affirmation or denial, is equally to be deprecated, as unphilosophical, and as unfavourable to the progress of discovery.

the extended heavens, and downward to the unextended centres of atoms." Here, again, it is taken for granted, that because gravity attaches to the ultimate particles of matter, that it must extend to the centres of the atoms, pervading or constituting their very nature. Besides, independently of the law, the quantities of the forces in action between atoms and between masses may be different, for aught that any thing in the present state of knowledge can be brought to prove the contrary; and although this is not enough to affect the validity or the sufficiency of the fundamental principles of Mr. Exley's theory, it is sufficient to show that their existence cannot with any certainty be deduced from the universal existence of gravity. They may be inferred from various analogical and philosophical considerations; and that is the ground on which he should be content, for the present, to rest them, corroborated as they are by the evidence derived from the numerous accordances already referred to. It is quite in vain that he takes the high ground of insisting, that they are ultimate natural truths and facts, and it must be in vain, until the laws of atomic action have been more fully investigated by experimental research. He has made an effort to anticipate the natural progress of knowledge, and he must be satisfied accordingly with the position he has taken, and with having his system regarded as a not improbable hypothesis, to be kept in view in the future progress of science, for the purpose of having its principles established or refuted; and he should perceive, that in the mean time he is not entitled to claim attention to it as an undoubted and unquestionable theory. If it were such-if this distinction were conferred on it, as he contends it is, by my definition of a theory, namely, that it is "a system whose first principles are ultimate natural facts or truths, whether self-evident or analytically traced through a course of observations or experiments"how is it that Mr. Exley's principles, if facts or truths, can admit of any doubt in any one's mind? How is it that only their fitness to explain phenomena is brought forward to justify our belief of their existence ?

Then as to the law of repulsion-have we even as good a warrant for it as for the law of attraction? Do the experi

ments on compressibility countenance it? -but this discrepancy, it may be said, can be explained away on the hypothesis, however be it remembered, of the escape of ethereal matter. In order to avoid in some measure the too manifest appearance of the gratuitous character of this law, Mr. Exley would lead us to conceive of repulsion as being an inverted kind of attraction, and that therefore the law must needs be the same; "Gravitation," he says, "extends to the centre of atoms, while near the centre its direction is reversed." Besides unnecessarily complicating the hypothesis, in expression at least, how can we imagine that antagonist forces, although the law may be the same, can be identical.

It would be wrong to limit the progress of science, but it is not unreasonable to doubt whether discovery will ever reach to the primary laws of atomic action, in any very direct and satisfactory manner. Supposing Mr. Exley's conjecture to be true, that molecular and universal attraction is the same force, what an almost infinite distance apart on the scale of intensity must our inquiries be conducted, and how are we to connect them together, so as to acquire proof of the identity of the qualities investigated? What can we apply as a common measure to such wide extremes? A mountain is required to produce the slightest deflection of the plummet, and yet what an immensity of force do the phenomena of cohesion exhibit? Doubtless the atoms of matter, as every thing teaches us, are almost infinitely small; and this consideration presents us with a solution of the difficulty as a matter of fact, but at the same time it immeasurably adds to the difficulty as a matter of investigation and proof.

But let us admit that the first principles of Mr. Exley's system are unquestionable-let it pass for a moment as a genuine theory, we shall next have to ascertain whether it be a true theory, that is, whether there be a sufficiency in the principles, and a right mechanism in the process, from which and by which we are to work out all the results of nature. We are to ascertain whether this world of our concocting belongs to reality or to pure imagination. Every thing may be made out very plausibly, but are we certain that the phenomena can be explained in no other and no better manner? Are we assured that no other principles can

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possibly be implicated therein, than those which we have adopted, or that our rationale of nature's procedure is her true modus operandi? We want, as I said in my former article, the "Instantiæ crucis," of which Bacon speaks, to decide the question by rejecting all the causes but one;" and I must again repeat, that "Mr. Exley has precluded himself from that more satisfactory analytical proof, by an exclusive adoption of the strict synthetical form." To which he replies, "this is said unadvisedly; a little thought would show that these principles are not adopted arbitrarily, but are themselves analytical deductions-they are the demands of nature herself-the very results of that more satisfactory analytical proof." No, no, I have not spoken unadvisedly, but with a perfect knowledge both of what I meant and of what I said. The truth is, Mr. Exley has not given sufficient consideration to the tenor of my observations, nor weighed sufficiently the import of my words. I did not then. allude to nor speak of his principles as wanting the character of analytical deductions, though, as I have now shown, they, strictly speaking, are really not entitled to it; but I said that the system viewed as a whole-and not then questioning the principles on which it is founded-was in want of that more satisfactory proof which Bacon had described, and which I quoted; or, at least, that Mr. Exley had not advanced such, proof in support of it. Admitting his first principles to be true-admitting they are what they are not--a legitimate analytical induction from phenomena-still, in reference to the system founded on them, proof is required that they alone are quite sufficient, and that they only are adequate to explain the processes of nature; and this proof is afforded, when, on an examination of all possible modes of accounting for things, the whole of them are rejected save one. This is the analytical proof (that was my word) of, the validity of a system, and by implication of the fitness and adequacy of its principles. Now this proof is of course brought forward subsequently to the system being framed, but Mr. Exley has confounded it with the prior analytical induction of the fundamental principles, which equally, of course, must be advanced before the system can be framed; and because he has not distinguished be

A