Thermal Conductivity with Temperature, 



515 



order that C may be negative, it is necessary not only that m 

 shall be negative, but also that it shall be numerically greater 



than n + A © + - ; hence this is the condition which will allow 



C a 



- to be positive when k is negative. 



34. It may be useful to calculate the numerical value of 

 these constants for such metals as we at present possess any 

 experimental data for. We will assume the temperature of 

 the enclosure to be 0° C. (so that m = b and n = (3, see § 30), 

 and the highest observed point of temperature © on the rod 

 to be 100° C. : then the following Table contains the values 

 of the constants A, B, and C for iron and copper, together 

 with certain ratios which will be used later. The row of num- 

 bers deduced from the experiments of Forbes, confirmed by 

 Tait, are probably nearly accurate ; the others are subject to 

 discount. 



Metal. 



Value of 

 /3 or n 

 accord- 

 ing to 

 Bede and 

 Fizeau. 



Value of 



accord- 

 ing to 



b or m 



A. 



B. 



C. 



Iron ... 

 Copper. . 



760 1 

 2200 1 



Forbes ... 



o 



Angstrom 



o 



Angstrom 

 Tait 



- 700 



- 640 



- 940 

 + 2000 



- 578,000 



- 504,600 

 -1,964,000 

 +4,912,200 



- 1,360 



- 1,200 



- 5,063 

 + 15,166 



+ -577 

 + -746 

 + 3-4 

 + 12 3 



2A 



2C 

 B= S - 



4AC 



+850 

 + 841 

 +7757 

 +647-8 



-•00085 

 -00124 

 -00134 

 + 00162 



- 7225 

 -10428 



- 10394 

 + 1 0494 



35. The integral of equation [13] may be written down 

 without difficulty ; and it constitutes the equation to the per- 

 manent curve of temperature down a long thin uniform cy- 

 lindrical metal rod with a blackened surface heated at one end 



in vacuo. 



log 



{t + b + 8 'M£ + S+ c )} 



s/^s 



{2Ct? + B + 2vC v '(A + B0+C0 i! )^ 



= v / (R<™>z.[14] 



