Form of Temperature Wave spreading by Conduction. 367 



that Q= r,™*g, 

 6 



( r-x)* -{r +x)2. 



AcaW 2 



The temperatures given in Table IV. are calculated from 

 equation (6) with a = 005 cm. and Q = 0'001 calorie. The 

 initial temperature of the source is 13640° C. 



Table IV. 





r cm. 



t sec. 



















•05 



•1 



•125 



•15 







13640 



13640 



o 











•001 



7207 



3388 



284 



38 



2-5 



•002 



3530 



2174 



498 



160 



40 



| -003 



2162 



1518 



526 



236 



88 



•004 



1493 



1130 



494 



264 



124 



•005 



1105 



879 



447 



268 



143 



Comparison of this table with Table I. shows that, at the 

 times given in the tables, the temperature at short distances 

 from the centre, due to the spherical volume source, is lower, 

 and at great distances is higher, than that due to the instan- 

 taneous point source. The greatest volume raised to or 

 above 700° by the spherical volume source is nearly the 

 same as that raised by the instantaneous point source — 

 namely, the volume of a sphere 091 cm. in radius. With 

 the spherical volume source this is effected after a time 

 t = 0*002 sec. The form of the temperature wave at this 

 time is shown in fig. 1, curve D. 



It appears, therefore, for the particular values assumed in 



