Bearing in mind Carnot's notion of a cycle, we see that the amount by which the piston is to be depressed while the whole stands on the condenser, is to be determined by the condition that when the whole is finally placed on the impervious stand, and the piston pressed home, the temperature of the contents shall be raised to S, the temperature of the boiler. [This complete rectification of Carnot's cycle was given by James Thomson in 1849.] If this be effected, we can transfer the cylinder to the body A, and everything is in the condition from which we started, so that the operation may be repeated as often as we please.

LECTURE V.

TRANSFORMATION OF HEAT INTO WORK.

Carnot's Cycle-continued. Watt's Diagram of Energy. The Impossibility of the Perpetual Motion is an experimental truth. Conditions of Reversibility. Absolute definition of Temperature. Second Law of Thermodynamics. Absolute zero of temperature, or temperature of a body devoid of heat. Efficiency of the best steam-engine. Effect of pressure on the freezing point of water. Mechanism of Glacier motion.

You will remember that at the close of my last lecture I had just given a sketch of the first part of the reasoning of Carnot—the most important reasoning that has ever been introduced into the treatment of any part of the dynamical theory of heat. I may briefly recapitulate (but in a somewhat improved form) what I then said, in order that there may be no break of continuity.

The nature of the hypothetical operation which Carnot introduced for the purpose of reasoning on this subject, and only for that purpose, is of this kind. He said-Let us have a hot body which is constantly maintained at a certain temperature. Let us have a cold body which is also constantly maintained at a definite temperature lower than the first. Then let us suppose that in addition to these we have a body which, as regards other bodies, is neither cold nor hot, for the simple reason that it is incapable of absorbing heat or of giving it out,-a body which is a non-conductor of heat. Then commence your series of operations, not as I did (after Carnot) in my last lecture, but with the

non-conductor. Suppose your cylinder and your piston to be non-conductors, but the bottom of the cylinder a perfect conductor. If you have a quantity of water and steam in the cylinder, both at the temperature of the cold body, and expend work in pressing down the piston, the contents will become warmer, and some steam will be liquefied.1 Continue this process till the temperature rises to that of the hot body-then transfer the cylinder to it. Now allow the piston to rise, the contents remaining at the temperature of the hot body, fresh steam is generated, and work is done. Arrest this process at any stage and transfer the cylinder to the non-conducting body. If we now allow the contents further to expand, more work is done, but the temperature gradually sinks. Continue this till the temperature falls to that of the cold body, to which, therefore, without loss or gain of heat, it may now be transferred. Next apply work to compress it at the constant temperature of the cold body till (by condensation) the contents have become exactly as they were at starting. The cylinder may now be transferred to the non-conducting stand, and everything is as it was at first—save that some heat was taken from the hot body in the second operation, and heat was given to the cold body during the fourth. Also it is evident that more work has been done during the second and third operations than was spent in the first and fourth, for the temperature, and therefore the pressure, of the contents were

1 [Note to Third Edition. This statement requires limitation, in order to avoid complications not alluded to in the text. If there be too small a quantity of water, as compared with the steam, pressure will vaporise some of the water, instead of, as is assumed in the text, condensing some of the steam. See Tait's HEAT, § 391.]

greater during the expansion than during the compression. Of course you can go over this operation as many times as you please.

Notice particularly what the peculiarity of the operation is. You must always have the steam or expanding substance, whatever it is, for air or anything else would do equally well,-in contact with bodies at its own temperature, or else with non-conducting bodies. If it were in contact with a body which was not at its own temperature, there would be a waste of heat. Heat would pass by conduction from the cylinder to external bodies, and would of course be wasted as regards work. The same would happen if we were to take it from, let us say, the non-conducting body and place it upon the cold body, before we had let it expand far enough to cool down to the temperature of the cold body:-we should have some heat conducted away at once without having any good from it. So, throughout the whole of Carnot's operation, it is essential that there should be no direct transfer of heat at all except while heat is being taken in from the hot body or given out to the cold body: the temperature of the contents of the cylinder being in each of these cases the same as that of the body with which they are at the time in contact.

A remark of great importance must now be made, though it involves somewhat of a digression. You must have noticed how much more easily we managed in to-day's than in yesterday's lecture to lay down the limits for the range of volume of the working substance during each of the four operations included in Carnot's cycle. Yet the only difference in our proceedings consisted in the fact that yesterday, following Carnot himself, we began with expansion at the higher temperature

-while to-day we have preferred to commence with compression on the non-conducting stand. With the help of a device due to Watt it may be possible to make this point much more easily intelligible. The device I allude to is called the Indicator Diagram, and is even now constantly employed for the purpose of ascertaining the work actually done by an engine, especially that of a steam-ship.

It is not my business to enter into purely mechanical details, and therefore I shall only say that this diagram is traced out by a pencil attached to the piston-rod of the engine, and therefore sharing its to-and-fro motion; while it has also a motion in a direction perpendicular to the piston-rod, such that the displacement at any instant is proportional to the pressure in the cylinder at that instant. To fix the ideas, suppose the cylinder to be horizontal, and the just-mentioned transverse motion vertical. Then any re-entrant line whatever (lying wholly