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ganeral equations which express the Uw uf the distribution f heat in 

 solids tny l derived from the internal radiation of the jwrticK-* which 

 compose them. Whichever uf these two view iuy be adopted, we 

 an led U> important physical distinction* between different hoiu, . 

 substances, vix. their conducting power* internally and externally. If 

 we Uke two substances, M a piece of metal and of wuod, at the some 

 temperature M indicated by the thermometer, when held in the warm 

 hand the metal will feel colder than the wood, the heat of the hand 

 being more rapidly absorbed by the metal, a* being the better cuitdnclur 

 of heat. Or if we ]Jace the extrcmitiee of a rod of copper and of 

 glass in a fire, and hold with the hand* the other extremities, the heat 

 will be found to ascend rapidly through the metal and very slowly 

 through the glass rod. Though such plain observation* are sufficient 

 to give a general idea that bodies conduct heat differently, yet, to 

 obtain exact measurement* of conducting powers, it will be necessary 

 to have a more precise idea, since such power is a constant coefficient 

 belonging to every body in particular, and without the knowledge of 

 which it would be impossible to compare the result of theory with 

 olservatiuu. 



Newton remarked that, when two substances of unequal tempera- 

 tures were placed in contact, the colder received from the other in a 

 given small time a quantity of heat proportional to the difference of 

 uicir temperatures. This simple law has been found to be not strictly 

 correct, but is sufficiently so when the difference of temperatures a 

 inconsiderable. If ( t' represent the temperatures of two bodies of 

 the same physical nature placed in contact, and if we leave out of 

 consideration the heat escaping by radiation from their surfaces, the 

 quantity of heat communicated may, by Newton's law, be represented 

 by k (t (') ; where the coefficient A is a constant peculiar to the given 

 substance, and is proportional to the interior conductibility. 



If now we conceive the surface of the body to be of a uniform 

 temperature, and subject to a current of air also of a uniform but 

 inferior temperature T, the loes of heat by a unit of surface in a unit of 

 time indefinitely small will, by the some law, be represented by ft 

 (t T), where tic coefficient 11 is proportional to the exterior con- 

 ductibility under such circumstances. 



The exterior couduotibility may be very different in the same body 

 by slight alterations in the smoothness or even colour of the M 

 it is by this antagonist principle. that heat acquires a permanent state 

 corresponding to the different positions of the parts of bodies relative 

 to the sources of heat and the dispersing surfaces. 



The mathematical theory of the distribution of heat to founded mi 

 the principle that when a body has arrived at a permanent state of 

 it literature the quantity of beat given out by any particle to the 

 adjacent colder region must be equal to that received from the warmer 

 particles near it, and conversely. For example, suppose a solid body 

 to be contained by two parallel planes of indefinite extent , the lower 

 plane being preserved by any means at a uniform temperature repre- 

 sented by o, and the upper likewise preserved at a uniform temperature. 

 In this case it is easily seen that the temperature would lie uniform in 

 any section of the body parallel to its bases, but would increase from 

 the lower plane in an arithmetical progression to the upper, for with 

 this Uw the temperature of any point of the body taken in the 

 transverse direction will differ by equal quantities from the temperatures 

 of any two points which are at equal distances, the one above and tlie 

 other below it ; hence the flux of heat from the wai-nn T region to this 

 point is equal to that from thin point to the colder. Though there is 

 therefore a constant flux of heat from the upper to the lower plane, 

 the distribution of heat has then acquired a permanency. 



In the above instance we have had no regard to the external con- 

 dueliliility through the sides by supposing the planes of indi finite 

 extent. A Dimple instance will now be adduced in which we can show 

 the manner in which thu consideration may be introduced into the 

 calculus. 



Suppose a thin cylindrical rod to be placed in a medium of which 

 the temperature is constantly zero, while its extremities are maintained 

 at constant but different temperatures. In thU ease the distribution of 

 beat will follow, at equal distances along the rod, a geometrical 

 progression, increasing from the colder extremity to the hotter ; for on 

 this supposition the heat which would be retained by any section in 

 consequence of the unequal differences of iU temperature with those 

 of sections similarly placed above and below it, if there were no 

 radiation, will be exactly lost by the external means of conduction, for 

 it is a property of the terms of a geometrical progression that the 

 second differences are pro|>ortional to the terms themselves ; the heat 

 which would be retained is proportional to this second difference, and 

 the heat externally emitted is proportional to the temperature itself. 

 Thus this law, which renders the internal gain of heat equal to its loss 

 externally, represent* the law of its permanent distribution. Those 

 who are acquainted with the calculus of partial differences may find 

 these principles applied, not only to the permanent distribution of 

 heat, but to the laws of cooling in bodies wanned from any sources, 

 and bounded by any surfaces, in the excellent work of Kurier 

 (Tkiorit <U Ckaltvr), and in the memoirs of Pouson, Libri, and others. 



The propagation of heat in liquids depends very little on any com- 

 munication by contact. If we place a heated plate on the surface of 

 water in a vessel, but so as not to touch the edges, a thermometer 

 pUood in the water will indicate little or no alteration of tempera- 



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*ure; liquids ore therefore heated by the tnm-p --lti"n of their 

 part*, or by oimtrtuM as it is called. Thu>, if with a Uowpi|>c we 

 apply best to the bottom of a vet- ug water, in which are 



floating some small particles of diut, a current will be perceived of the 

 warmed liquid rising fi .1... h hurt hits been applied, 



and another descending current of the colder parts, which being heated 

 in turn rise also ; in this manner the heat is d 1.1 > .di the 



whole liquid, for as the beat expands the particles of liquid which it 

 first meet*, they become specifically lighter than the adjacent fluid, 

 and they must therefore ascend by the laws of hydrostatics, while the 

 heavier take their places. 



The experiment* which have been made to determine whether 

 liquids ore conductors of heat, consist in introducing into a cylindrical 

 vessel half filled with the fluid whose conducting power was to lie 

 examined, a quantity of heated fluid of Jess specific gravity, all due 

 precautions being used to prevent the particles of the two fluid 

 intermixing ; and it was constantly found that thermometers placed at 

 dillcient depths in the former indicated a gradual descent of caloric 

 from thu upper to the lower surface. By such experiment* Thomson, 

 Daltou, and others, have found that, with equul volumes of the fluids, 

 the conducting power of Unseed oil is rather greater than that of w atcr, 

 and the conducting power of mercury about twice as great. 



Little as is the conducting power of liquids, that of gases is probably 

 much less, if any ; but there would be great difficulty in establishing 

 this experimentally. The effect of heat on gases is to increase pro- 

 portionally their elasticity, and this disturbing force produces . 

 motions in their parts, so that the whole shortly acquires a tn 

 temperature, when other forces, such as gravity, are not taki: 

 consideration, and when the bounding surfaces are not essentially sub- 

 jected to constant unequal temperatures. 



These three modes of the propagation of heat exist in our globe, 

 and are the cause of important phenomena in the distribution of 

 climate. 



the great mass of the earth, considered in reference to its solid 

 parts, has an external source of heat in radiation principally from the 

 sun. The maximum quantity of this heat is bestowed on the < 

 between the tropics, while the poles ore at a temperature which, but 

 for the action of the sea and atmosphere, would probably be that of 

 space ; the internal heat of the earth would in a homogeneous sphere 

 be distributed symmetrically relative to its centre, diminishing towards 

 the surface, which would lose heat by external radiation: but the 

 external source of heat alluded to, by producing a flux from the equator 

 to the poles, forms a permanent compensation for this radiation. 



If wo suppose the moss of the earth to have been at any remote 

 period at a very high temperature, of which, besides its general 

 there ore many striking geological proofs, i the radiation of 



its heat through the colder surrounding sjiace would be to cool first 

 the siqierficial strata, and successively, though in a less degr> 

 internal strata, until a permanent state was reached, when the dimi- 

 nished, ladiation would be exactly compensated from external sources. 

 Hence, on descending below that comparatively shallow envelope affected 

 with diurnal or annual variations of temperature, we ought to find a 

 continually increasing temperature towards thu centre, a result which 

 has been verified in the mines in several countries in I'.uiope. 1'oisson 

 deems these experiments inconclusive, in con t the small 



depth which we are enabled to pcnetrat" ; for without assuming any 

 increase of heat towards the centre, the same supertici d phcti. .- 

 would occur on the .-uppo-itioii that the whole solar system had 

 transferred into a region of space possessing a different temperature 

 I'rom that in which it formerly moved; but this view, which is purely 

 speculative, cannot be verified by facts. 



The propagation of heat by motion in fluids has a .necessary ten- 

 dency to equalise tho temperatures of different latitude,, and the un- 

 equal depths of different places in tho bed of the sea would, from the 

 same cause, produce currents wanner than the adjacent water. The 

 elasticity acquired by portions of the air in contact with the warmer 

 regions of the globe destroys the equilibrium of that fluid, and gene- 

 rates winds of which the heat is communicated to the districts 

 traversed, while tho counter-currents, or cold winds, rush forward to 

 occupy the abandoned spaces. The earth having always had a rota- 

 tion, a limiting surface necessarily existed beyond which the centrifugal 

 I ; hence if the surface of the earth has ever had a tem- 

 perature of 212 Fnlir., the waters now occupying the bed of the sea, 

 being in a state of vapour, could have filled no more than the space 

 between that limiting surface and the surface of the earth; but tin 

 greater cold would necessarily convert the vapour in the up 

 into water, which, descending in rain, would be again vaporised, and 

 this reciprocal action going on during the process of cooling, would 

 be ca|iable of producing immense alterations on the earth's surface. 

 It has been suggested by Mr. liabbage, that a cause of a similar nature 

 may have led to the rings and belts of the superior planets. 



Most of the instruments constructed to measure heat are founded 

 on its general tendency to produce expansion, but a few of them ou 

 other properties of heat. Besides the various thermometers, we may 

 notice the calorimeter of Lavoisier and Laplace, in which an internal 

 chamber of a box is preserved at the temperature of melting ice, being 

 constantly surrounded with that substance, guarded against the contact 

 of the air: in a division of this chamber, a cell furnished with a 



