be made for the water value of the calorimeter, thermometer, and stirrer. This method of measuring specific heats is found only to work satisfactorily in the case of liquids, since it is only with these that the contents of the calorimeter can be kept at a uniform temperature throughout during the cooling, this condition being obtained by continuous stirring.

The further consideration of radiant heat will be deferred till the chapters dealing with the emission, absorption, &c., of light, since there is no sharp physical line of demarcation between what we recognise by one set of senses as radiant heat, and what we recognise by our sense of sight as light.

CHAPTER VI

THE MECHANICAL THEORY OF HEAT

249. Theories as to the Nature of Heat.-Up to the end of the eighteenth century there existed two rival theories as to the nature of heat. According to one of these theories, known as the caloric theory, heat was supposed to be a subtle, elastic, imponderable fluid called caloric, which permeated all kinds of matter existing in the interstices between the molecules. According to the other theory, which was only held by very few, heat was supposed to be due to the rapid motion of the molecules of matter.

It was well known that heat could be produced by friction or percussion, and the supporters of the caloric theory explained these facts by supposing that in the case of percussion the caloric was squeezed out of the body, and hence flowed into a neighbouring body such as a thermometer, and, in the case of friction, that during the friction some of the body was rubbed off, and that the capacity of matter for caloric was less in the form of a powder than in the form of a solid block. That this explanation of the production of heat by friction was untenable was first shown by Count Rumford in 1798.

Being struck by the large amount of heat developed when cannon were being bored at the arsenal at Munich, Rumford performed an experiment in which a blunt steel borer was rotated while kept pressed against the bottom of a hole in a large mass of gun-metal. The borer was rotated nearly a thousand times, and the heat developed was sufficient to raise the temperature of the whole block, which weighed 113 lbs., about 70° F., while the amount of metal rubbed off from the bottom of the hole was only 837 grains troy. Rumford, in the account of his experiments, draws attention to the fact that the supply of heat obtained in this way from a given lump of metal seems quite inexhaustible, and hence cannot be a material substance, but must be "motion."

The supporters of the caloric theory for some time maintained that the source of heat was the abraded metal, although this explanation was completely refuted by an experiment performed by Davy. He rubbed together two blocks of ice at a temperature below o° C., and found that heat was developed and the ice melted. Since it was allowed by the calorists that water contained more caloric than ice, if we can produce water by the friction of ice, the heat developed must be due to some other cause than the extrusion of caloric.

We have seen, when dealing with radiant heat, that a hot body is continually radiating heat into surrounding space; and when we come to the consideration of the subject of light, we shall see that there is conclusive evidence that radiant heat, after it leaves the hot body, exists as a wave-motion in some medium surrounding the body. Now in order to set up waves in a medium, we must have a body which is itself in motion in the medium. Thus, since a hot body can set up such waves, we infer that it must be in a state of motion. Also, since the highest-power microscope is quite unable to detect any motion in a hot body, we infer that this motion must be a motion of the molecules as a whole, or of the parts of a molecule, or both combined.

We are hence reduced to the theory that heat is a "mode of motion." 250. Dynamical Equivalent of Heat-First Law of ThermoDynamics. In Rumford's experiments, the heat produced in the cannon was indirectly due to the work done by the horse which turned the boring tool, and it is obviously of interest to see what connection there is between the work done by the horse and the amount of heat produced. We shall see in later sections, that whenever mechanical work is converted into heat, or mechanical work performed at the expense of heat, there exists a constant relation between the work done and the heat produced or lost. The quantity of work which must be done in order that, when all the work is converted into heat, the unit quantity of heat energy may be produced is called the mechanical or dynamical equivalent of heat. If is the value of the mechanical equivalent, then the relation between the work I converted into heat and the quantity of heat H produced is given by the equation

W=JH.

This equation, which we shall justify subsequently, expresses symbolically what is known as the first law of thermo-dynamics, which may be stated as follows:- Whenever mechanical energy is converted into heat, or heat into mechanical energy, the ratio of the mechanical energy to the heat is constant.

251. The Determination of the Mechanical Equivalent of Heat. The first to experimentally show that the first law of thermodynamics is true, and determine the value of the mechanical equivalent of heat, was Joule, who between 1843 and 1878 carried on a classic series of experiments on this subject, in which he showed that the value for the mechanical equivalent was always the same, although the methods employed for converting the mechanical energy into heat differed greatly.

One of the first methods employed by Joule consisted in measuring the heat developed when a known amount of work was done in stirring water. The apparatus used consisted of a copper vessel B (Fig. 201), inside which a brass paddle-wheel worked. A system of partitions were fixed

within the vessel, so that the vanes of the paddle could just pass, the object of these partitions being to prevent the water as a whole assuming a motion of rotation. The paddle was rotated by means of two weights E and F, which were attached to strings wound round the axle A of the paddle, which was so arranged that the weights could be wound up without turning the paddle. The rise in temperature of the calorimeter and its contents caused by allowing the weights to fall twenty times was obtained, and knowing the water value of the calorimeter and contents, the number of heat units produced could be calculated. The work done is the product of the sum of the weights of E and F into the total height through which they fall. Corrections have, however, to be applied for the fact that when the weights reach the floor they are moving with a finite velocity v, and that their kinetic energy is destroyed in the impact.

The height through which a body, falling freely, would acquire a velocity 7 has therefore to be deducted from the actual fall. Another correction has to be applied, to allow for the effect of the elasticity of the strings on which the weights are hung, for this causes the paddle to rotate a little after the weights have reached the ground. The weights themselves have in addition to be reduced by the weight, which, when the two strings are detached from the axle A and joined together, added to E or F, will just cause the weights to move uniformly. This weight represents the allowance to be made on account of the friction of the pulleys D and C and the rigidity of the string. Lastly, a correction was made for the fact that some of the mechanical energy was spent in the production of sound, and the magnitude of this correction was roughly obtained by noting the work which had to be done to make the string of a violoncello produce a sound that could be heard at the same distance as was that produced by the instrument during the fall of the weights.

In addition, Joule made a series of experiments in which the water was replaced by mercury, and also one using the friction of one iron ring against another, both being immersed in mercury.

The numbers obtained for the value of the mechanical equivalent were practically the same in all cases. Joule expressed his results in terms of the mercury-in-glass thermometer, but they have been reduced to the air thermometer by Rowland, and give the value of the energy which must be converted into heat to raise the temperature of one gram of water from 14°.5 to 15°.5 as

4.182 × 197 ergs.

Rowland has made some very careful measurements of the mechanical equivalent of heat by the method of stirring water, and has employed a method of measuring the mechanical work done, which was also used by Joule in his later experiments. Since this method has considerable advantages over that described above, it is worth while describing it. A diagrammatic plan of the arrangement is shown in Fig. 202. The calorimeter, like

D

ded by means of

a fine wire, so that it was free to rotate about a vertical axis coinciding with that about which the paddle-wheel turned.

Owing to the viscosity of the water, the calorimeter tends to rotate in the same direction as the paddle, and to prevent this, two strings, DP, D'P', were attached to the circumference of a disc which was itself fixed to the calorimeter, and these strings were pulled with a force just sufficient to keep the calorimeter from rotating when the paddle was turning at a uniform speed. If the radius of the disc is R, the couple acting along DP and D'P' is

due to the two parallel forces

2Rp.

Now as action and reaction are equal and opposite, and as the couple