Lagging of Pipes and Wires. 515 



Deviations from simple theory. 



Where the difference o£ temperature is so considerable it 

 is of course not sufficient to consider the various data as 

 independent of the temperature. In this experiment the 

 same current passes through both portions of the wire, and 

 therefore, owing to the change of specific resistance with 

 temperature, the rate of generation of heat in equal portions 

 is not the same. Tf a is the coefficient of increase of re- 

 sistance with temperature, p the specific resistance at 

 atmospheric temperature, and C the current, the equation 

 becomes 



o A f i u i \ 



or 



The critical radius is still b = kje, but # a /(l + a# a ), sa y ®> 

 takes the place of 6 a . Hence for the given wire and coat 

 we have; 



®uncoated/® coated = 5 nearly ; 



and if a be taken as *004 this gives a temperature of about 

 50° C. for the coated portion when the uncoated is at 1600° (J. 

 The increase in the resistance with temperature has thus a 

 very large intensifying action. The value of (1 + "004 0a) 

 may be called the " intensifying ratio " due to the resistance 

 change. Its value for different values of 6 a is given in 

 Table III. 



Table III. 



9a. 



1 + -004 Ba. 







1 



100 



1-4 



500 



30 



1000 



5-0 



2000 



90 



That is to say, a current which would maintain a wire at 

 200° excess with a given coat if the resistance remained 

 constant (as it would do approximately in the case of an 

 alloy) will heat it to 1000° C. in the case of a metal for 

 which a = '004 (as it approximately is for pure metals). 



2M2 



