of the researches which we have just mentioned, says7, "When I undertook these experiments, it never once came into my thoughts that they could conduct me with any probability to a table of real degrees of heat. But hope grows with success, and desire with hope.' Accordingly he pursued this inquiry for a long course of years.

What are the principles by which we are to be guided to the true measure of heat? Here, as in all the sciences of this class, we have the general principle, that the secondary quality, Heat, must be supposed to be perceived in some way by a material Medium or Fluid. If we take that which is, perhaps, the simplest form of this hypothesis, that the heat depends upon the quantity of this fluid, or Caloric, which is present, we shall find that we are led to propositions which may serve as a foundation for a natural measure of heat. The Method of Mixtures is one example of such a result. If we mix together two pints of water, one hot and one cold, is it not manifest that the temperature of the mixture must be midway between the two? Each of the two portions brings with it its own heat. The whole heat, or caloric, of the mixture is the sum of the two; and the heat of each half must be the half of this sum, and therefore its temperature must be intermediate between the temperatures of the equal portions which were mixed. Deluc made experiments founded upon this principle, and was led by them to conclude that the dilatations of mercury follow an accelerated march for successive equal augmentations of heat.'

But there are various circumstances which prevent this method of mixtures from being so satisfactory as at first sight it seems to promise to be. The different capacities for heat of different substances, and even of the same substance at different temperatures, introduce much difficulty into the experiments; and this path of inquiry has not yet led to a satisfactory result.

7 Modif. de l'Atmosph. 1782, p. 303.

6. Another mode of inquiring into the natural sure of heat is to seek it by researches on the law ooling of hot bodies. If we assume that the proof cooling of hot bodies consists in a certain maal heat flying off, we may, by means of certain bable hypotheses, determine mathematically the law ording to which the temperature decreases as time on; and we may assume that to be the true meaof temperature which gives to the experimental of cooling the most simple and probable form. = appears evident from the most obvious conceps which we can form of the manner in which a - parts with its superabundant heat, that the hotter dy is, the faster it cools; though it is not clear out experiment, by what law the rate of cooling depend upon the heat of the body. Newton for granted the most simple and seemingly natuaw of this dependence: he supposed the rate of ng to be proportional to the temperature, and this supposition he could deduce the temperature ot iron, calculating from the original temperature the time during which it had been cooling. By lation founded on such a basis, he graduated his

But a little further consideration showed that ate of cooling of a hot body depended upon the erature of the surrounding bodies, as well as upon n temperature. Prevost's Theory of Exchanges ropounded with a view of explaining this dependand was generally accepted. According to this 7, all bodies radiate heat to one another, and are onstantly giving and receiving heat; and a body is hotter than surrounding bodies, cools itself, arms the surrounding bodies, by an exchange of or heat, in which they are the gainers. Hence if he temperature of the bodies, or of the space, by the hot body is surrounded, and + t the tempeof the hot body, the rate of cooling will depend

echerches sur la Chaleur, 1791. Hist. Ind. Sc. b. x. c. i. sect. 2.

upon the excess of the radiation for a temperature ✪ +t, above the radiation for a temperature 0.

Accordingly, in the admirable researches of MM. Dulong and Petit upon the cooling of bodies, it was assumed that the rate of cooling of the hot body was represented by the excess of F (0+t) above F(0); where F represented some mathematical function, that is, some expression obtained by arithmetical operations from the temperatures + t and 0; although what these operations are to be, was left undecided, and was in fact determined by the experiments. And the result of their investigations was, that the function is of this kind: when the temperature increases by equal intervals, the function increases in a continued geometric proportion. This was, in fact, the same law which had been assumed by Newton and others, with this difference, that they had neglected the term which depends upon the temperature of the surrounding space.

18. This law falls in so well with the best conceptions we can form of the mechanism of cooling upon the supposition of a radiant fluid caloric, that it gives great probability to the scale of temperature on which. the simplicity of the result depends. Now the temperatures in the formulæ just referred to were expressed by means of the air thermometer. Hence MM. Du

long and Petit justly state, that while all different substances employed as thermometers give different laws of thermotical phenomena, their own success in obtaining simple and general laws by means of the air thermometer, is a strong recommendation of that as the natural scale of heat. They add1o, 'The well-known uniformity of the principal physical properties of all gases, and especially the perfect identity of their laws of dilatation by heat, [a very important discovery of

10

9 The formula for the rate of cool

ing is ma 0+t-ma, where the quan

tity m depends upon the nature of

the body, the state of its surface, and other circumstances.-Ann. Chim. vii. 150.

10 Annales de Chimie, vii. 153.

lton and Gay Lussac",] make it very probable that this class of bodies the disturbing causes have not same influence as in solids and liquids; and conseently that the changes of bulk produced by the on of heat are here in a more immediate depende on the force which produces them.'

9. Still we cannot consider this point as settled we obtain a more complete theoretical insight into nature of heat itself. If it be true that heat conin the vibrations of a fluid, then, although, as père has shown 12, the laws of radiation will, on hematical grounds, be the same as they are on the othesis of emission, we cannot consider the natural e of heat as determined, till we have discovered e means of measuring the caloriferous vibrations e measure luminiferous vibrations. We shall only w what the quantity of heat is when we know heat itself is;-when we have obtained a theory h satisfactorily explains the manner in which the ance or medium of heat produces its effects. When ee how radiation and conduction, dilatation and faction, are all produced by mechanical changes of ame fluid, we shall then see what the nature of change is which dilatation really measures, and relation it bears to any more proper standard of

e may add, that while our thermotical theory is o imperfect as it is, all attempts to divine the ature of the relation between light and heat are ture, and must be in the highest degree insecure sionary. Speculations in which, from the general ption of a caloriferous and luminiferous medium, om a few facts arbitrarily selected and loosely ed, a general theory of light and heat is asare entirely foreign to the course of inductive and cannot lead to any stable and substantial

354 PHILOSOPHY OF THE MECHANICAL SCIENCES.

instruments of which the object is to measure, not sensible qualities, but some effect or modification of the cause by which such qualities are produced: such, for instance, are the Calorimeter, employed by Lavoisier and Laplace, in order to compare the Specific Heat of different substances; and the Actinometer, invented by Sir John Herschel, in order to determine the effect of the Sun's Rays by means of the heat which they communicate in a given time; which effect is, as may readily be supposed, very different under different circumstances of atmosphere and position. The laws of such effects may be valuable contributions to our knowledge of heat, but the interpretation of them must depend on a previous knowledge of the relations which temperature bears to heat, according to the views just explained.

SECT. VI.-Scales of other Qualities.

21. BEFORE quitting the subject of the measures of sensible qualities, we may observe that there are several other such qualities for which it would be necessary to have scales and means of measuring, in order to make any approach to science on such subjects. This is true, for instance, of Tastes and Smells. Indeed some attempts have been made towards a classification of the Tastes of sapid substances, but these have not yet assumed any satisfactory or systematic character; and I am not aware that any instrument has been suggested for measuring either the Flavour or the Odour of bodies which possess such qualities.

22. Quality of Sounds.—The same is true of that kind of difference in sounds which is peculiarly termed their Quality; that character by which, for instance, the sound of a flute differs from that of a hautbois, when the note is the same; or a woman's voice from a boy's.

23. Articulate Sounds.-There is also in sounds another difference, of which the nature is still obscure, but in reducing which to rule, and consequently to measure, some progress has nevertheless been made.