1830.] 
and the Communication of Heat. 
313 
l>\ direct expel iment on the cooling of masses of liquids. These experiments, sub- 
sequently repeated by other enquirers, prove, in fact, that for differences of tempera- 
ture, which do not exceed 40 or 50 degrees, the law of a geometrical progression re- 
presents pretty accurately the rate of cooling of any body. 
Martin * had in a dissertation but little known, but published in 1740, being several 
years before Kraft and Richmann h«d made known the result of their researches, 
shown the incorrectness of the preceding law, and had endeavoured to investigate 
one which should give a more rapidly converging series of decrements. 
Erxleben * had also proved, by very accurate experiments, that the errors of the hy- 
pothetical law increased with the difference of temperature ; and deduced the conclu- 
sion, that it could not be safely applied to differences of temperature, ranch exceed- 
ing those at which it had been verified. This well founded remark of Erxleben does 
not appear to have been much attended to by philosophers ; for in every subsequent 
enquiry the law of Newton is always assumed, not as an approximation, hut ns a 
real and demonstrated truth. 
In this way Mr. Leslie, 5 in his ingenious researches on heat, has founded sereral 
of his determinations on this law, which are, for that reason alone, objectionable, 
as we shall prove in the sequel. 
Some time after the publication of Mr. Leslie’s work, M. Dalton made known, in 
his T realist on Chemical Philosophy, a series of experiments made on the cooling of 
bodies heated to very high temperatures. The result of these experiments wenttoshow 
conclusively, that Richmann’s law is only approximately true in low temperatures, 
and becomes very inaccurate, as the temperature increases. Mr. Dalton, instead of 
endeavouring to investigate a law that should represent his own observations, endea- 
vours to reconcile them with that of Richmann, by substituting for the ordinary thcr- 
mometrFc scale, that which be had founded on the considerations we linve discussed 
in the first part ot this memoir But even admitting the soundness of the principles 
on which he has founded this new scale, it would still be not the less true, that 
the decrements of temperature are nut proportional to the excess of the temperature 
of the body over that of the circumambient air, or in other words, that the esta- 
blishment of his scale does not necessarily infer the law of Richmann ; lor in this 
case it would follow, that the law of cooling must be the same for every body, where- 
as our experiments have clearly proved the contrary to he the case. 
The most recent labours on this subject are those of Laroche, inserted in his 
treatise On Radiating Heat ; amongst other conclusions, lie establishes the follow- 
ing.— that the heat which a body yields in a given time, through the means of ra- 
diation to a colder body, situated at a distance, follows (all else being equal) a 
progression more rapid than that which represents the excess of temperature of 
the one body over those of the other. ( , 
This proposition, it may be seen, is much the same as Mr. Dalton’s, substituting 
merely the heat lost by radiation, for the total heat lost by a body immersed in air. 
Laroche, however, only gives particular results, and does not attempt the investi- 
gation of the law on which they depend. We shall see in what follows, that these 
results include the effects of some particular causes which tend to render the en- 
quiry more complicated ; and that it is necessary to separate these last to obtain 
even the law of cooling in a vacuum, which, it is to be noted again, is not the same 
as the law of radiation. , . . .. , 
The labours then of philosopher? have, as far as regards the laws of cooling, een 
hitherto confined to proving that Newton’s law is sufficiently exact, when the ques- 
tion only concerns small excesses of temperature, but that it becomes ^^erro- 
neous as^ the differences of temperature increase. If in this cursory vnw of what 
has bee, done n this enquiry, we have omitted to mention the mathematical inves- 
So n " on the distrffiution of heat by M. Fourier, it is because his enquiry pro- 
ceeds upon the basis of Newton’s law, assumed as au undoubted truth, whereas our 
experinfents have had ftrttdr « 
'preserve all their ^ in th™ in which 
the law of Newton is found sufficiently exact, and L . • . we are now 
he sufficient to modify them conformably with the new laws which we 
about to establish. 
» Dissertation sur la Cbaleur, p. 72. et. seq. 
4 Novi Comment. Soc. Gottmg. t v in. p-^ 
6 An Inquiry into the Nature of Heu , p. - 
