SECT. IV.] LAW OF THE FLOW OF HEAT. 459 



To discover the differential equations of the variable movement 

 of heat, even in the most elementary case, as that of a cylindrical 

 prism of very small radius, it was necessary to know the mathe 

 matical expression of the quantity of heat which traverses an 

 extremely short part of the prism. This quantity is not simply 

 proportional to the difference of the temperatures of the two 

 sections which bound the layer. It is proved in the most rigorous 

 manner that it is also in the inverse ratio of the thickness of the 

 layer, that is to say, that if tivo layers of the same prism were un 

 equally thick, and if in the first the difference of the temperatures of 

 the two bases was the same as in the second, the quantities of heat 

 traversing the layers during the same instant would be in the inverse 

 ratio of the thicknesses. The preceding lemma applies not only to 

 layers whose thickness is infinitely small; it applies to prisms of 

 any length. This notion of the flow is fundamental ; in so far as 

 we have not acquired it, we cannot form an exact idea of the 

 phenomenon and of the equation which expresses it. 



It is evident that the instantaneous increase of the tempera- 



of temperatures in a long bar heated at one end. Lambert s work contains a 

 most complete account of the progress of thermal measurement up to that time. 



Biot, Journal des Mines, Paris, 1804, xvn. pp. 203 224. Eumford, Jlemoires 

 de VInstitut, Sciences Math, et Phys. Tome vi. Paris, 1805, pp. 106 122. 



Ericsson, Nature, Vol. vi. pp. 106 8, describes some experiments on cooling 

 in vacuo which for a limited range of excess temperature, 10 to 100 Fah. shew 

 a very close approach to Newton s law of cooling in a current of air. These 

 experiments are insufficient to discredit the law of cooling in vacuo derived by 

 M. M. Dulong and Petit (Journal Poll/technique, Tome xi. or Ann. de Ch. et 

 de Ph. 1817, Tome vn.) from their carefully devised and more extensive range 

 of experiments. But other experiments made by Ericsson with an ingeniously 

 contrived calorimeter (Nature, Vol. v. pp. 505 7) on the emissive power of molten 

 iron, seem to shew that the law of Dulong and Petit, for cooling in vacuo, is 

 very far from being applicable to masses at exceedingly high temperatures giving 

 off heat in free air, though their law for such conditions is reducible to the former 

 law. 



Fourier has published some remarks on Newton s law of cooling in his 

 Questions sur la theorie physique de la Chaleur rayonnante, Ann. de Chimie et de 

 Physique, 1817, Tome vi. p. 298. He distinguishes between the surface conduction 

 and radiation to free air. 



Newton s original statement in the Scala graduum is &quot; Calor quern ferrum 

 calefactum corporibus frigidis sibi contiguis dato tempore communicat, hoc est 

 Calor, quern ferrum dato tempore amittit, est ut Calor totus fern.&quot; This supposes 

 the iron to be perfectly conducible, and the surrounding masses to be at zero 

 temperature. It can only be interpreted by his subsequent explanation, as above. 



[A. F.] 



