Conductivity of Metals with Temperature. 



209 



function of 0, will represent the observed rate of cooling of a 

 body in a vacuum. 



A.nd first I will take the experiments of Narr* (see Wiillner, 

 vol. iii. p. 254). The following Table contains the result of 

 his experiments in a vacuum. The first column is the observed 

 rate of cooling at the Centigrade temperature shown in the 

 second column, the enclosure being at zero Centigrade. The 

 third column contains the product of excess of temperature t 

 and absolute temperature v, divided by the rate of cooling, to 

 show how far this ratio is constant. These numbers are ob- 

 served to decrease regularly, though slowly, and in a manner 

 which has an obvious relation to the corresponding number in 

 the preceding column ; so that if twenty times that number 

 be subtracted from each, the result will be very constant, as is 

 shown in the last column. 



t. 



t. 



(274+0 1- 



v 4-tit 



t 



3-26 



o 



115 



13720 



11420 



3-11 



110 



13580 



11380 



2-80 



100 



13360 



11360 



2-49 



90 



13160 



11360 



2-18 



80 



12990 



11390 



1-88 



70 



12810 



11410 



1-73 



65 



12740 



11440 



Hence 



~-20t= const =11400. 

 t 



We may write this, 



m=m±-. t . 



or, approximately, 



570 + * 



(80 



t± 



11400 



(274+0(1-5*5), 



which is of the form of equation (7), namely the excess of 

 temperature t multiplied by a quadratic factor. The nume- 

 rical value of the constants do not, indeed, agree well with those 

 of Dulong, especially in the fact of the sign of the coefficient 

 of t 2 being negative ; but this is hardly to be expected, as 

 Narr seems to have undertaken his experiments with the object 

 of upsetting Dulong's results. Narr's experiments, moreover, 

 do not extend over any thing like the range of temperature 

 that Dulong and Petit' s did. 



* Pogg. Ann. vol. cxlii. 



