.S7A' U'/LLfAM SIEMENS, 



147 



calculated resistances for the higher temperatures by Matthiessen's 



formula : 



Temperature in 

 degrees Cent. 



t - 



100* 



= 800 



= 600 



= 1000" 



= 2000 



Resistance in 

 Units. 



Rt. = I'OOOO 

 = 1-4146 

 = 1-6098 

 = 0-8314 

 = 0-1794 

 = 0-0373 



His formula is indeed inapplicable to temperatures exceeding 

 100 Cent. He adds, it is true, a fourth member to his denomi- 

 nator, containing t s , which has the effect of harmonizing it more 

 completely with the observed values at low temperatures, without, 

 however, producing more reasonable values for high temperatures. 

 This formula, then, is applicable only within the narrow range of 

 the experiments by which it was determined. 



LAW OF INCREASED RESISTANCE. Now if we apply the 

 mechanical laws of work and velocity to the vibratory motions 

 of a body which represent its free heat, we should define this 

 heat as directly proportional to the square of the velocity with 

 which the atoms vibrate. We may further assume that the 

 resistance which a metallic body offers to the passage of an electric 

 impulse from atom to atom is directly proportional to the velocity 

 of the vibrations which represent its heat. In combining these 

 two assumptions, it follows that the resistance of a metallic body 

 increases in the direct ratio of the square root of the free heat 

 communicated to it. 



Algebraically, if (r) represent the resistance of a metallic con- 

 ductor at the temperature T, reckoning from the absolute zero, and 

 a an experimental co-efficient of increase peculiar to the particular 

 metal under consideration, we should have the expression r = aT J . 



This purely parabolical expression would make no allowance for 

 the probable increase of resistance, due to the increasing distance 

 between adjoining particles with increase of heat, which would 

 depend upon the co-efficient of expansion, and may be expressed 

 by /3T, which would have to be added to the former expression. 

 To these factors a third would have to be added, expressing 

 an ultimate constant resistance of the material itself at the 



