362 Prof. Taylor Jones, Mr. Morgan, and Prof. Wheeler on 



The following numerical values, appropriate to air as the 

 medium, will be assumed throughout: k = 0'b, c — 0*00014, 

 both in c.g.s. units. The total heat supplied, Q, will be 

 taken as O'OOl calorie, and the original temperature of the 

 medium will be assumed to be 0° C. 



I. Instantaneous Point Source. 



The solution of equation (1) for this case was given by 

 Fourier * in the form 



0=^—^ (2) 



Sc(7rktf 2 ' 



Values of #, the temperature in degrees centigrade for 

 various values of r and t, calculated from equation (2), are 

 given in Table I. 



Table I. 



t sec. 







Temperature at 























•05 



•075 -1 



•15 



•2 cm. 







00 























•001 



14350 



4111 



862 



97 



•2 







•002 



5074 



2716 



1244 



416 



20 



•2 



•003 



2762 



1820 



1081 



521 



65 



35 



•004 



1794 



1313 



888 



514 



- 108 



12 



005 



1283 



999 



731 



472 



135 



23 



•006 



j 



976 



793 



611 



424 



150 



35 



At any distance, r, from the origin the temperature of the 

 air reaches the highest value it can attain there after an 

 interval of time, t = r 2 /6k. 



Thus, at a distance of 0*05 em. the maximum temperature 

 is reached after 0'00083 sec, and at a distance of 0*1 cm. 

 it is reached after 0*00333 sec. ; at this latter distance the 

 temperature of the air never rises higher than about 526°. 



If an inflammable mixture of the same thermal properties 

 is assumed to be substituted for the air, and the ignition 

 temperature of this mixture is assumed to be 700°, then the 

 greatest volume of the mixture that can be simultaneously 

 raised (by conduction of heat only) to a temperature not less 

 than this ignition temperature, is approximately that of a 



* M. Fourier, Theorie de la Chaleur, § 385. 



