with a puff into the beam of light, while I kept my attention fixed upon the screen. As soon as the hair-powder reached the beam of light the screen was suddenly covered with the most beautiful arrangement of concentric circles displaying all the brilliant colours of the rainbow. A great variety in the size of the rings was obtained by making the assistant strew the powder into the beam at a greater distance from the mirror; for the rings contract by an increase of the distance and dilate on a nearer approach of the powder.

This experiment is so simple, and points out the general causes of the rings which are here produced in so plain a manner, that we may confidently say they arise from the flection of the rays of light on the particles of the floating powder, modified by the curvature of the reflecting surface of the mirror.

Here we have no interposed plate of glass of a given thickness between one surface and another, that might produce the colours by reflecting some rays of light and transmitting others; and if we were inclined to look upon the distance of the particles of the floating powder from the mirror as plates of air, it would not be possible to assign any certain thickness to them, since these particles may be spread in the beam of light over a considerable space, and perhaps none of them will be exactly at the same distance from the mirror.

I shall not enter into a further analysis of this experi ment, as the only purpose for which it is given in this place is to show that the principle of thin or thick plates, either of air or glass, on which the rays might alternately exert their fits of easy reflection and easy transmission, must be given up, and that the fits themselves of course cannot be shown to have any exisistence.

XXXIV. Conclusion.

It will hardly be necessary to say, that all the theory relating to the size of the parts of natural bodies and their interstices, which Sir I. Newton has founded upon the exis tence of fits of easy reflection and easy transmission, exerted differently, according to the different thickness of the thin plates of which he supposes the parts of natural bodies to

consist

consist, will remain unsupported; for if the above-mentioned fits have no existence, the whole foundation on which the theory of the size of such parts is placed, will be taken away, and we shall consequently have to look out for a more firm basis on which a similar edifice may be placed. That there is such a one we cannot doubt, and what I have already said will lead us to look for it in the modifying power which the two surfaces, that have been proved to be essential to the formation of rings, exert upon the rays of light. The second part of this paper, therefore, will enter into an examination of the various modifications that light receives in its approach to, entrance into, or passage by, differently disposed surfaces or bodies; in order to discover, if possible, which of them may be the immediate cause of the coloured rings that are formed between glasses.

XLIII. Essay upon Machines in General. By M. Carnot, Member of the French Institute, &c. &c.

[Continued from p. 158.]

X. THE science of machines in general is therefore reduced to the following question:

"Being acquainted with the virtual movement of any system of bodies (that is to say, that movement which each of these bodies would take if it were free), find the real movement which will take place the instant following, on account of the reciprocal action of bodies, by considering them such as they exist in nature, i. e. as endowed with all the inertness common to all the particles of matter."

XI. Now, as this question evidently contains the whole of mechanics, we must, in order to proceed with precision, go back to the first laws which nature observes in the communication of movements. We may reduce them in general to two, which are the following:

FUNDAMENTAL LAWS OF EQUILIBRIUM, AND MOTION. FIRST LAW-Action and Reaction are always equal and contrary.

This

.

This law consists in this, that every body which changes its state of repose or uniform and rectilinear motion, never does so except by the influence or action of some other body, upon which it impresses, at the same time, a quantity of motion equal and directly opposite to that which it receives from it; that is to say, that the velocity it assumes the instant afterwards is the force resulting from that which this other body impresses upon it, and from that which it would have had without this last, force. Every body therefore resists its change of state; and this resistance, which is called vis inertiæ, is always equal and directly opposite to the quantity of motion it receives, i. e. to the quantity of motion which combined with that which it had immediately before the change, produces, as the result, the quantity of motion which it should really have immediately afterwards. This is also expressed by saying, that in the reciprocal action of bodies, the quantity of motion lost by the one is always gained by the others, in the same time and in the same ratio.

SECOND LAW.IVhen two hard bodies act upon each other, by shock or pressure, i. e. in virtue of their inpenetrability, their relative velocity, immediately after the reci procal action, is always mull.

In fact, we constantly observe, that if two hard bodies give a shock to each other, their velocities, immediately after the shock, estimated perpendicularly to their common surface at the point of contact, are equal, in the same way as if they were drawn by inèxtensible wires, or pushed by incompressible rods; their velocities, estimated in the ratio of this wire or rod, would necessarily be equal: whence it follows that their relative velocity, i. e. that by which they approach or recede from each other, is in every case mull at the first instant."

From these two principles it is easy to draw the laws of the shock of hard bodies, and consequently to conchide the two other secondary principles, the use of which is continual in mechanics, viz.

1. That the intensity of the shock, or of the action which

is exercised between two bodies which meet, does not de-' pend upon their absolute movements, but solely upon their relative movements. 2. That the force or quantity of movement which they exercise upon each other, by the shock, is always directed perpendicularly to their common surface at the point of contact.

7

XII. Of the two fundamental laws, the first generally agrees with all the bodies of nature, as well as the two secondary laws which we have seen; and the second solely regards hard bodies; but as those which are not hard have different degrees of elasticity, we generally refer the laws of their movement to those of the hard bodies, which we take for a term of comparison, i. e. we regard the elastic bodies as composed of an infinity of hard corpuscles separated by small compressible rods, to which we attribute all the1 elastic virtue of these bodies; so that, properly speaking, we do not consider in nature any other than bodies endowed with different moving forces. We shall follow this method as the simplest: we shall therefore reduce the question to the investigation of the laws observed by hard bodies, and shall afterwards make some applications of them to cases in which bodies are endowed with different degrees of elasticity.

XIII. This essay upon machines not being a treatise upon mechanics, my object is not to explain in detail, nor to prove the fundamental laws I have related; these are truths which all the world knows, as to which they are generally agreed, and which are most strongly manifested in all the phænomena of nature. This is sufficient for my object, which is merely to draw from these laws a simple and exact method for finding the state of rest or of movement which results from them in any given system of bodies, i. e. to present the same laws under a form which may facilitate their application to each particular case.

XIV. Let us suppose therefore any system of hard bodies, the virtual given movement of which is changed by their reciprocal action into another which we wish to find; and in order to embrace the question in all its extent, let us suppose that the movement may either change suddenly, or Vol. 30. No. 119. April 1808.

vary

vary by insensible degrees: finally, as fixed points or some obstacles may be met with, let us consider them as they really are in fact, that is to say, as ordinary bodies of themselves, making part of the system proposed, but firmly arrested in the spot where they are placed.

XV. In order to attain the solution of this problem, let us first observe, that, all the parts of the system being supposed, perfectly hard, i. e. incompressible and inextensible, we may visibly, whatever it may be, regard it as composed of an infinity of hard corpuscles, separated from each other either by small incompressible rods, or by small inextensible wires; for when two bodies strike, push, or tend in general to approach each other without being able to do it, on account of their impenetrability, we can conceive between the two a small incompressible rod, and suppose that the movement is transmitted from the one to the other according to this rod and in the same way, if two bodies tend to separate, we may conceive that the one is attached to the other by a small inextensible wire, according to which the movement is propagated: this being done, let us consider successively the action of each of these small corpuscles upon all those which are adjacent to it, i. e. let us examine two by two all these small corpuscles separated from each other by a small incompressible rod, or by a small inextensible wire, and we shall see what ought to result in the general system of all these corpuscles. Let us name for this purpose,

m' and m" The masses of the adjacent corpuscles.

V' and V" The velocities they ought to have the following instant.

F' The action of m" upon m', that is to say, the force or quantity of movement which the first of these corpuscles impresses upon the other.

F" The reaction of m' upon m".

qand q" The angles formed by the directions of V' and F' and by those of V” and F”.

This being done, the real velocity of m′ being V', this velocity estimated in the direction of F will be V' cosine q'; in the same manner the velocity of m" estimated in the direction of F will be V" cosine q". Therefore, since by

the