620 Prof. W. M. Thornton on the 



depends only upon H. From Table I., and still better from 



a graph of the figures given there, it is seen that k, the ratio 



of b to a, is as a first approximation constant. 



Thus 



7 V7rHcr 7rH , 7 7rH 



ka = - — , ^=-77^, and 0— -r T . 



Since b, Table II., is found experimentally to be a constant 

 ratio for any given wire, H is constant. Ignition of all gases 

 but hydrogen and carbon monoxide occurs at the same rate 

 of generation of heat in unit length of wire. This clearly 

 points to ignition starting by thermionic emission under the 

 same electron pressure in each case. 



7. Influence of Convection. 



Since a steady state is reached, at least in the smaller 

 wires, at the moment of ignition, it may be concluded that 

 the heat generated by the current which first starts surface 

 combustion is removed in a manner that does not depend 

 upon the diameter or surface of the wire. In support of 

 this Kennedy's observations may be quoted, that the cooling 

 of a wire bv convection is approximately the same for unit 

 length of all small diameters. 



8. Surface Combustion. 



In a wire heated both by current and surface combustion 

 there is a temperature of equilibrium between the heat dissi- 

 pated by radiation and convection and that generated. 



Let H c be the heat of combustion of one gramme of gas, 

 not the mixture, and m the mass of gas burnt per second. 

 The heat removed by convection is proportional to the first 

 power of the temperature *. So that in calories 



mR c + -24 ri 2 = K(0*- 6> 4 ) + -24(-0004 + '0064 d)(0— O ). 



Here K is Stefan's coefficient 5*3 . 10~ 12 watt per sq. cm. 

 per second per degree, r is the resistance of a length of 

 wire of unit area. 



In the case of hydrogen ignited by 0*1 mm. platinum the 

 length of wire with unit surface is 32 centimetres, giving 

 4*4 ohms resistance. The igniting current of hydrogen is 

 1*2 amperes, for which W 2 = 6*33 watts. The mass of 

 hydrogen which must be burnt per second to give equilibrium 



* " The Convection of Heat from Small Copper Wires." By A. E. 

 Kennelly, C. A. Wright, and J. S. van Bvlevelt. Trans. Amer. Inst. 

 Elec. Eng. 1909, p. 719. 



