Form of Temperature Wave spreading by Conduction. 365 



medium. Again, assuming an inflammable mixture with an 

 ignition temperature o£ 700° to be substituted for the air, 

 this temperature is approximately the maximum temperature 

 attained at a distance r= 0*0855 cm., and it is reached after 

 an interval of time t = 0*006 sec. The temperature wave at 

 this time is shown in fig. 1, curve B. Thus the greatest 

 volume which is raised to at least 700° (by conduction alone) 

 is that of a sphere of radius 0*0855 cm., or 2'62 mm. 3 This 

 volume accordingly represents the incendivity of the con- 

 tinued point source of heat. The incendivity of a point 

 source of total heat 0*001 calorie, uniformly in action over 

 0*005 sec, is thus about 17 per cent, less than that of an 

 instantaneous point source of the same total heat. 



Similar calculations for other values of the time of heat 

 supply T showed that as T is increased, the surface repre- 

 senting the 700° limit continues to shrink, and that as T is 

 diminished, the temperature distribution continually ap- 

 proaches that given by an instantaneous point source (T = 0) 

 of the same total heat. The incendivity of a source of small 

 rate of heat supply may therefore be very much less than 

 that of an instantaneous source of the same total heat. 



The general conclusions to be drawn from a comparison 

 of Tables I. and II. are: (1) if an inflammable mixture is to 

 be ignited by a given quantity of heat supplied at a point, 

 the more quickly it is supplied the better ; and (2) the total 

 quantity of heat supplied by a given source is no criterion 

 as to its incendivity unless the rate of supply also is specified. 



III. Instantaneous Spherical Surface Source. 



The distribution of temperature when the heat is supplied 

 instantaneously and uniformly over a spherical surface has 

 been stated by Lord Kelvin *. In this instance, if a is the 

 radius of the spherical surface source, the temperature at 

 any point distance r from the centre is given by 



-(r-g)2 -(r+g)2 



ikt _ 4kt 



e=Q6 8cW 2 (V ' • V * (5) 



Some values of 6 calculated from equation (5) with a 

 taken as 0*1 cm. and q as 0*001 calorie, are given in 

 Table III. 



* Eric. Brit. 9th ed. Art. " Heat," Appendix. Tlie expression given 

 by Kelvin should, however, be divided by it. 



