20 LECTURES TO SCIENCE TEACHERS. 



applicable to different conditions, such as straight bars, 

 rings of metal, spheres which had been uniformly heated 

 and were then left to cool, and various other particular 

 cases which he examined theoretically. Some of these 

 have been tested by experiment, and some of the most 

 celebrated experiments of this kind are those of the French 

 physicist, Despretz. Despretz employed the metal bars 

 which you see here ; there is one of iron and two of copper. 

 Holes were bored in them to be filled with mercury, and 

 thermometers were allowed to rest in each of these holes 

 a number of finely graduated and tested thermometers 

 which are used for such experiments ; then one end of the 

 bar is heated in a crucible, and the other end is left to cool 

 in the air. The temperature of the different parts of the 

 bar is read off when it has arrived at the permanent 

 condition of temperature. Applying these observations 

 to Fourier's theory, Despretz arrived at certain values of 

 this constant K, which was supposed to be the conductivity 

 of the different metals he was observing. These were very 

 carefully made experiments, and acquired a great reputation, 

 and are still quoted as amongst the most important deter- 

 minations that we have. 



But in the first place, I must point out to you that 

 Fourier made two assumptions in getting at his formula, 

 which were, of course, also made by Despretz in his 

 calculations. One of these was, that when a hot body is 

 cooling in the air by radiation and convection the amount 

 of heat which escapes in a unit of time is proportional to 

 the difference in temperature between the cooling body and 

 the atmosphere around it. This is what is called Newton's 

 law of cooling, but from the experiments of Messrs. Dulong 

 and Petit we know perfectly well that it is not quite correct ; 

 but they had not discovered their law before Fourier 

 published his theory, and fortunately so perhaps, because 

 otherwise it is doubtful whether Fourier would have 

 ventured to have undertaken such a frightful calculation 

 as the theory would have required, without his own book to 

 start with, the book founded on this simple law. He also 

 assumed that this law maintains in the interior of these 

 bars, that the flux of heat is directly proportional to the 

 difference in temperature at unit distances along the bar. 

 This is what we assume in stating this formula of Fourier, 



