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



Table III. 



t sec. 



r cm. 



















•05 



•1 



•125 



•15 















00 











•0005 



1-8 



166 



1015 



435 



55 



•001 



97 



411 



718 



420 



137 



•002 



416 



540 



507 



347 



181 



•003 



522 



527 



414 



299 



182 



•004 



514 



482 



356 



265 



175 



As might be expected, the temperature in the neighbour- 

 hood of the source falls to small values much more rapidly 

 with the spherical surface source of heat than with the 

 instantaneous point source (Table 1.). Thus with the spherical 

 source the temperature, after an interval of time £ = 0*002 

 sec, is at no point in the medium as high as 700° C. It 

 can be shown that at a time £ = 0*0005 sec, the volume of 

 the spherical shell bounded by the surfaces ?• = 0*075 cm. 

 and t — 0*115 cm. is at or above 700° C. (see fig. 1, curve C). 

 This volume is 4*605 mm. 3 -, which is considerably greater 

 than the greatest volume raised simultaneously to or above 

 700° by the instantaneous point source, and is 1*76 times 

 as great as the maximum obtained with the continued point 

 source (Table II.). Arguing solely on the distribution of 

 heat by conduction, it is therefore to be expected that the 

 effectiveness of a source of ignition will be improved by 

 spreading it over a surface rather than by concentrating it 

 into a small space. It is also a fair conclusion that a number 

 of simultaneous sparks arranged close together in parallel 

 would be more effective than a single spark of the same 

 length and the same total heat content. 



IV. Instantaneous Spherical Volume Source. 



We arrive at the solution for this case by integration from 

 equation (5). Thus, if q is the heat generated instanta- 

 neously per unit volume of a spherical source of radius a, so 



