the momentum of either one before the stroke." That bodies act with a force equal to their momentum, is a maxim which D. has repeatedly and triumphantly quoted, and momentum is the quantity of motion in a given direction. It is also quite clear that neither of the balls can themselves act in a direction opposite to that in which they are moving. The utmost intensity of force, therefore, with which either of the balls can act, is its own momentum; and that only in the direction towards which it moves. The acting force is necessarily the same at the time of the collision as before; and consequently at the instant of collision each ball acts with a force equal to its own momentum in the direction towards which it moves; and as both balls are moving in opposite directions, they each act with a force equal to their own momentum in a direction opposite to the direction of the other ball. The intensity of the collision, therefore, is the sum of the momenta of the two, but the force in each direction is the momentum of each one; and consequently "the intensity of the stroke as felt by each body in a direction opposite to that in which it was moving," is equal to the momentum of one ball, and not the momenta of two; for if they acted in each direction with a force equal to the momenta of two balls, it is evident the whole force would be doubled by the collision, which is impos-sible. D. professes to demonstrate the proposition from the principles admitted in the whole theory, and he commences by stating. truly, that "By the old theory, if a hard body A, having the velocity of a, strike another hard equal body A' at rest, the motion communicated to A' by the impulse is 4 A = A a A a " This he properly treats as the intensity of the stroke, and uses it as such in his reasoning. But in the same argument in which he uses this as correct, he states, and assumes that he has proved, that "when one of the bodies is at rest," "the intensity of the stroke on each is equal to the momentum of the moving body." I have already shown that the latter statement is not true; but if it were, the former could not be so; and the reasoning can little deserve the term of strict mathematical induction, which assumes in its support as true two propositions quite inconsistent with each other; namely, that the intensity of the stroke is equal to, or half the momentum of A, and also equal to the momentum of the moving body, or the whole momentum of A. It is, however, worthy of the corollory which he founds upon it, but which has already been sufficiently refuted. "Hence," he says, "the two equal bodies after the impulse recede towards the parts whence they came with the same momenta they had before they met." A "In the theory of motion rightly understood," says Maclaurin, in his Account of Newton's Philosophical Discoveries, p. 130, "the same laws that serve for comparing, compounding, or resolving motions, are likewise observed by pressures; that is, the powers that generate motion or tend to produce it; and it adds no small beauty to this theory of motion that both observe the same laws." Accordingly many of the laws of collision of bodies are afterwards exhibited by Maclaurin from the effects of pressure. In formerly observing, therefore, upon Mr. H.'s theory, I exhibited the incorrect consequences which were deducible from his reasoning on the laws of motion' in a sentence similar to the corallary just quoted, by an instance of its effect in a case of pressure. Thus if a man push with all his strength against a wall, say with a force as 10, action and reaction being equal, the wall resists with a force as 10, exactly in a similar manner to the fixed plane in Mr. H.'s proposition. If instead of the wall there be an opposing active force, another person, for instance, pushing against the first with an exactly equal force, the effect to the first will be just the same as the wall, and neither person will be able to move the other. But by Mr. Herapath's reasoning, each person would be acted on in a direction opposite to that towards which he pushed, by a force equal to twice the force of either one; that is, with a force as 20; and consequently both must be pushed backwards; a conclusion notoriously contrary to fact. And yet this is the reasoning by which are to be overturned, in one short page, the doctrines of Newton, Maclaurin, Hutton, Playfair, and innumerable other mathematicians, in relation to the collision of hard bodies; the first principles of which too are as nearly as possible self-evident." Upon this, D. observes, "These sentences, as far as I understand them, distinctly charge Mr. H. with confounding pressure with impulse." Certainly no understanding can be worse than one which chooses to misunderstand, and no other could derive such a charge from those sentences. He adds afterwards, "C. tells us that the pushing case I have just quoted which (with how much truth the reader may judge from the counter quotations), he informs the orld, is Mr. Herapath's, is that, by which it is intended by Mr. H. that the doctrines of Newton," &c. " are to be overturned, in relation to the collision of hard bodies." I will only observe upon this, that the extract is all that I ever said on the subject; and it may be thence ascertained whether, when D. said that I charged Mr. H. "with confounding pressure with impulse," that I informed the world that "the pushing case," as he calls it, was Mr. Herapath's, and that I told them it was by that by which it was intended by Mr. H. that the doctrines of Newton, &c. were to be overturned, his assertion was not absolutely untrue. motive in the assertion may be gathered from his insinuation that what I said was not accordant with truth. I have now, I believe, examined all that is offered in the form of reasoning in D.'s papers. Had it indeed been reasoning, however able or severe it might have been, and however difficult to have been answered, that examination would have given me much pleasure. The mental effort required to meet a powerful argument, though great, is invigorating to the mind, and healthful; and gives it that tone and elastic energy which is no inconsiderable enjoyment; but the toil of dissecting and exposing a vast mass of misstatement and misrepresentation, though less difficult to accomplish, is merely laborious, fatiguing, and disgusting; and I fear the exposition will be found so by your readers. There still, however, remain one or two topics which D. has used for declamation, which will claim a few observations. The first which I would notice is the boast that Mr. H. has compared his theory with so many experiments, and has predicted the phenomena of so many new and untried cases. Probably the credit which is claimed for Mr. H. in his prophetic character may not be readily granted, as long as the cases remain new and untried. It is, however, by no means extraordinary, that he should be able by his theory plausibly to explain many phenomena. Seriously to publish any hypothesis which was evidently incompetent to account for any of the phenomena of nature, would prove the writer not foolish, but insane; it is, therefore, to be expected, that every theory should afford an explanation of some class of experiments or observations. But that which may properly be demanded of it is, that it should besides be consistent with all the phenomena of nature; for if its truth be clearly contradicted by any one fact, that is sufficient to prove its incorrectness. In my former paper, I pointed out many cases in which facts were inconsistent with the theory; and in this, I have endeavoured to show that they still remain unexplained. But Mr. H. himself admits that his theory opposes conclusions drawn by other writers, though the observations on which they are founded are exceedingly numerous. Thus he does not hesitate to conclude, that if two in volume of hydrogen unite with one in volume of oxygen to form water, the atoms of oxygen will be double in number those of hydrogen. (Annals, June, 1821, p. 403.) Yet that conclusion is opposed by almost all the ablest chemical writers. The manner in which the coincidence between the theory and those experiments with which it accords is produced is so singular, that it will deserve a few moments' examination. "On the supposition," says Mr. H. "that mercury and water are homogeneous fluids, I have found from the best experiments I can procure, that the ratio of the numeratoms of mercury and water is about equal to that of 1 to 2; and the ratio of the magnitudes of the particles equal to about that of 27 to 1; and, therefore, the ratio of their diameters, supposing them similar, about that of 3 ito 1. This greater numeratom of the water is indicated by the mean temperature of the mixture of equal parts of mercury and water always being in favour of the temperature of the water, and the excess of magnitude in the particles of mercury by its less disposition to be affected in volume by changes of temperature." Thus it appears that Mr. H. pretends to ascertain the proportionate number of atoms by the mean temperature of the bodies on their mixture, as determined by experiment; and it having been so determined that if a given volume of mercury at the temperature of 100° Fahr. be mixed with an equal volume of water at the temperature of 40°, the temperature of the mixture is about 60°, and consequently that the effect of the water upon the temperature in proportion to that of mercury is as 2 to 1 nearly, that is assumed by Mr. H. to be the proportionate number of atoms. Mr. H. then proceeds, "Taking these numbers for correct, I find that if a given volume of mercury at the temperature of 100° Fahr. be mixed with an equal volume of water at the temperature of 40°, the temperature of the mixture should be 5910; by Dr. Henry, it is 60°. And if the same temperatures be taken, but the water be put at the higher, and the mercury at the lower temperature, the mixture should be at 79: Dr. Henry says it is nearly 80°." Thus it is first assumed that if upon the mixture of equal quantities of mercury at 100°, and water at 40°, the resulting temperature is 60°, the numeratom, as Mr. H. calls it; that is, the proportionate number of atoms in the water in comparison with those in the mercury shall be as 2 to 1. And the comparison of Mr. H.'s theory with experiment consists in reasoning back again, that if the numeratom be as 2 to 1, then if a given quantity of mercury at 100° be mixed with an equal quantity of water at 40°, the resulting temperature ought to be nearly 60°. That is, if it be true that if the resulting temperature be as 60°, the numeratom must be as 2 to 1, then if the numeratom be as 2 to 1, the resulting temperature shall be as 60°. So that if you will tell Mr. H. what will be the resulting temperature of a mixture of two fluids having certain previous temperatures, he will by his theory again tell you the very same, and will also calculate what will be the temperature of a mixture of the same fluids mingled at other temperatures. This mode of reasoning will doubtless give results very accurately coinciding with experiments, but as it is merely reasoning in a circle, it can tend very little to prove the truth of the theory, however long a list may be furnished of such facts. Another topic to which D. frequently refers, with much apparent self gratulation, is the opinions of other philosophers, and chiefly that of Sir I. Newton. To him he refers more than a dozen times, but only once for the purpose of making a quotation in confirmation of the theory, and that once he draws an inference which the next sentence would have shown was incorrect, and which is directly contradicted by other parts of his works. With what justice he claims the support of several other philosophical writers to whom he has referred, the extracts which I have already given will sufficiently show. With respect to Sir I. Newton's opinions also, I have already proved by extracts from his works, that on the laws of collision, they directly, both in words and meaning, contradict Mr. Herapath's. Even, therefore, if Newton had positively stated it as his opinion that there did exist such a gravific medium as Mr. H. speaks of, and that he really considered it to be proved that heat was only motion, yet as Mr. H.'s laws of collision of hard bodies is at the very basis of his theory, there would still exist a difference in relation to all that is peculiar to Mr. Herapath's philosophy. The manner, however, in which Newton suggests these peculiar thoughts on heat and gravity is so striking an illustration of the distinction which should be made in the statement of hypotheses and facts, and offers so singular an instance of the modesty of his exalted mind, that I cannot refuse myself the pleasure of making some extracts. But," says Maclaurin, speaking of Sir I. Newton, in his Account of his Philosophical Discoveries, p. 9, "while he was thus demonstrating a great number of truths, he could not but meet with hints of many other things that his sagacity and diligent observation suggested to him, which he was not able to establish with equal certainty, and as these were not to be neglected but to be separated with care from the others, he, therefore, collected them together, and proposed them under the modest title of queries." It is in those queries, and in what he calls " Cogitationes varia," that are contained those speculations of Newton on the causes and nature of heat and gravity, to which D. refers. But the manner in which he suggests them affords no pretence to consider them his opinions. Thus in the advertisement to that part of his works, in which the "Question" relating to gravity is published (Newt. Opera, vol. iv), he says, "And to show that I do not take gravity for an essential property of bodies, I have added one question concerning its cause, choosing to propose it by way of a question, because I am not yet satisfied about it for want of experiments.' And in the question itseif, speaking of the objections made to his opinion of gravity, because he cannot account for the causes, he says, "Later philosophers banish the consideration of such things out of natural philosophy, feigning hypotheses for explaining all things mechanically, and referring other causes to metaphysics; whereas the main business of natural philosophy is to argue from phenomena without feigning hypotheses, and to deduce causes from effects till we come to the very first cause, which certainly is not mechanical." In his letter to the Hon. Mr. Boyle (Ibid. p. 385), he says, "The truth is, my notions about things of this kind are so indigested, that I am not well satisfied myself about them; and what I am not satisfied in, I can scarce esteem fit to be communicated to others, especially in natural philosophy, where there is no end of |