332 ELEMENTARY LESSONS ON [CHAP. vn. 



short thin wire of small mass, it will get very hot, whereas 

 in the latter case it will perhaps only warm to an imper- 

 ceptible degree the mass of the long thick wire. If the 

 wire weigh w grammes, and have a specific capacity for 

 heat Sj then H = swO, where 9 is the rise of tempera- 

 ture in degrees (Centigrade). Hence 



/, C 2 R/ 



6 = 0-24 x 



sw 



Since the resistance of metals increases as they rise in 

 temperature, a thin wire heated by the current will resist 

 more, and grow hotter and hotter until its rate of loss of 

 heat by conduction and radiation into the surrounding 

 air equals the rate at which heat is supplied by the 

 current. 



The following pretty experiment illustrates the laws of 

 heating. The current from a few cells is sent through a 

 chain made of alternate links of silver and platinum 

 wires. The platinum links glow red-hot while the silver 

 links remain comparatively cool. The explanation is 

 that the specific resistance of platinum is about six times 

 that of silver, and its capacity for heat about half as 

 great ; hence the rise of temperature in wires of equal 

 thickness traversed by the same current is roughly twelve 

 times as great for platinum as for silver. 



Thin wires heat much more rapidly than thick, the 

 rise of temperature in different parts of the same wire 

 (carrying the same current), being, for different thick- 

 nesses, inversely proportional to the fourth power of the 

 diameters. 



Thus, suppose a wire at any point to become reduced to half 

 its diameter, the cross-section will have an area J as great as in 

 the thicker part. The resistance here will be 4 times as great, 

 and the number of heat units developed will be 4 times as great 

 as in an equal length of the thicker wire. But 4 times the 

 amount of heat spent on the amount of metal will warm it to 

 a degree 16 times as great, and 16 = 2 4 . 



For surgical purposes a thin platinum wire, heated 

 white-hot by a current, is sometimes used instead of a 



