458 THEORY OF HEAT. [CHAP. IX. 



they consist solely in the application of known propositions. It 

 was sufficient in this work to give the principle and the result, as 

 we have done in Article 15 of the Memoir cited. From the same 

 condition also the general equation in question is derived by deter 

 mining the whole quantity of heat which each molecule situated 

 at the surface receives and communicates. These very complex 

 calculations make no change in the nature of the proof. 



In the investigation of the differential equation of the move 

 ment of heat, the mass may be supposed to be not homogeneous, 

 and it is very easy to derive the equation from the analytical 

 expression of the flow; it is sufficient to leave the coefficient which 

 measures the conducibility under the sign of differentiation. 



3rd. Newton was the first to consider the law of cooling of 

 bodies in air; that which he has adopted for the case in which the 

 air is carried away with constant velocity accords more closely 

 with observation as the difference of temperatures becomes less; 

 it would exactly hold if that difference were infinitely small. 



Amontons has made a remarkable experiment on the establish 

 ment of heat in a prism whose extremity is submitted to a definite 

 temperature. The logarithmic law of the decrease of the tempera 

 tures in the prism was given for the first time by Lambert, of the 

 Academy of Berlin. Biot and Rumford have confirmed this law 

 by experiment 1 . 



1 Newton, at the end of his Scala graduum caloris et frigoris, Philosophical 

 Transactions, April 1701, or Opuscula ed. Castillioneus, Vol. n. implies that when 

 a plate of iron cools in a current of air flowing uniformly at constant temperature, 

 equal quantities of air come in contact with the metal in equal times and carry 

 off quantities of heat proportional to the excess of the temperature of the iron 

 over that of the air ; whence it may be inferred that the excess temperatures of 

 the iron form a geometrical progression at times which are in arithmetic progres 

 sion, as he has stated. By placing various substances on the heated iron, he 

 obtained their melting points as the metal cooled. 



Amontons, Memoires de VAcademie [1703], Paris, 1705, pp. 205 6, in his 

 Remarques sur la Table de degres de Chaleur extraite des Transactions Philosophi- 

 ques 1701, states that he obtained the melting points of the substances experimented 

 on by Newton by placing them at appropriate points along an iron bar, heated to 

 whiteness at one end ; but he has made an erroneous assumption as to the law 

 of decrease of temperature along the bar. 



Lambert, Pyrometrie, Berlin, 1779, pp. 185 6, combining Newton s calculated 

 temperatures with Amontons measured distances, detected the exponential law 



