ON THE CONDUCTION OF HEAT. 21 



(10.) A rod composed of a mixture of tin and bismuth in equal portions, 

 which melts at the temperature of boiling water, was plunged at one extre- 

 mity into a basin of mercurj'. The mercury was kept successively for a long 

 time at different constant temperatures, by means of a lamp placed below it. 

 A thermometer was adjusted to the other extremity of the rod, in a little cap- 

 sule filled with mercury. Observations of the temperature indicated by this 

 thermometer, corresponding Avith each stated temperature of the mercury in 

 the basin, were made, when the state had become stationary. Tlie following 

 table exhibits the corresponding excesses of temperature of the mercury and 

 of the thermometer above that of the air. The latter was 20°. 



Excess of temp, at heated end 

 Corresp. excess at other extr^. 



10-25 19-75 29-25 49 69-75 80 

 3 5-5 8 10-5 11-75 12-5 



Before we compare this table with theory, it is right that we express our 

 belief that there has been some mistake in the obsei-vations. We think this 

 will be made out when it is seen that the following is the order of elevations 

 of the upper thermometer, due to elevations of temperature of the heated end. 



For the first 10°-25 the thermometer rose 3°; 



For the second 9°-5 the thermometer rose 2°-5 ; 



For the third 9°"5 the thermometer rose 2°-5 ; 

 in which the rise of the thermometer is nearly, but not quite, proportionate 

 to that of the mercury ; but 



For the fourth 19°-5 the thermometer rose only 2°-5. 

 This we think very unlikely. We should expect to find the proportion of the 

 increase of temperature of the thermometer to that of the mercury continually 

 diminish as the absolute temperature increases. The following are, however, 

 the ratios as given by the above table : 



1 J_ J_ J_ _L I 



3-146' 3-8' 3-8' 7-9' 16-6' 13-66' 

 If this be correct, the law is discontinuous. 



Calculations. 

 M. Biot gives the following results as calculated by an empirical formula : 

 12 3 4 5 



3-7 6-18 8 10-37 11-75 



I. From formula \0,v=^Cu. 



12 3 4 5 6 



3 5-78 8-56 14-34 20-41 23*41 



II. and III. On Libri's or Foisson's hypothesis we have approximately 

 (from 12 and \S)v = Cu — 'D u'^. 



If we apply experiments (3.) and (5.) to obtain the constants C and D, 

 there results 



1 2 3 4 5 6 



4-06 5-86 8 10-03 11-75 12 



IV. 1 2 3 4 5 6 



2-9 4-61 6-66 10-5 14 15-68 



It must be observed here, that we have only one constant to be determined 

 by experiment. We must not expect, therefore, to find so close an agree- 

 ment as when we have two. 



We are not ignorant that there are a vast number of experiments on radia- 

 tion and conduction to which we have not referred. Our reason for omit- 

 ting the mention of some of the most valuable is, that we desire to confine 

 our attention strictly to the matter in hand — the examination of theoretical 

 formulaj by experiments calculated to test their accuracy. 



