428 RECENT PROGRESS IN PHYSICS. 



paribus, inversely proportional to the section of the wire ; or expressed 

 algebraically, 



a. q^ 



10 = ——, 



j,.2 g 



in whicli ^^ is substituted for n in the equation, and a represents a 



constant factor. 



Hence, if a wire twice or thrice as thick be placed in the air ther- 

 mometer, the temperature of the air in the globe will be four or nine 

 times less than before the change. 



The rise of temperature of the air in the globe is evidently propor- 

 tional to the quantity of heat evolved in the wire ; hence, having de- 

 termined the temperature of the air, we learn the quantity of heat 

 set free. 



A wire twice, or three or four times as thick, has, for the same 

 length,, a mass four, nine or sixteen times as great; now if in the 

 thick wires there is as much heat set free as in the thinner ones, the 

 same quantity of heat has a greater mass to spread over, the elevation 

 of the temperature is inversely as the mass, or, the square of the 

 diameter, or algebraically, 



in which y is a constant factor, and T indicates the temperature of the 

 wire. From this follows the equation, 



Tr2 



y ; 



if this value of iv be substituted in the above equation, we have 



y r^ s, 



hence 



T =^ i— ^ f 



the interpretation of which is : The elevation of the temperature of a 

 wire, cceteris paribus, is inversely j^^oportional to the fourth poiver of 

 its diameter. Hence, a wire two or three times as thick will occasion 

 a rise of temperature sixteen or eighty-one times less, when perfectly 

 equal charges of the same density are discharged through it, pro- 

 vided that the length of the wire is unchanged. 



These relations hold good, of course, only when wires of the same 

 substance are compared with each other, and as each substance has a 

 different specific heat, for each one a different proportion will be found 

 between the quantity of heat and the elevation of temperature. 



In the experiments of Itiess just described, platinum wires were 

 used in the thermometer. 



The last exceedingly fine wire did not accord with the law, which 

 Biess explained by assuming, that the law is valid only for equal 

 times of discharge, which may be considered equal as long as the 

 diameter does not fall below a certain limit, biffc when this is the case. 



