326 Heat-loss by Conduction in Explosions of Coal-gas. 



At temperatures above 2000° C. abs. the rate at which 

 conduction-loss proceeds in the 15 per cent, mixture is 

 roughly proportional to the fourth power o£ the difference in 

 temperature between the gaseous mixture and the vessel- 

 walls, while at temperatures below 2000° C. abs. the rate of 

 loss is more nearly proportional to the third power of the 

 temperature difference. That this is so will be seen from 

 the dotted curve which, above 2000° C. abs., is proportional 

 to the fourth power of the temperature difference and, below 

 2000° C. abs., is proportional to the third power of this 

 difference. 



The equation to the dotted curve is 



= 4 xlO- 13 (0-0 u )* 

 for temperatures above 2000° C. abs., and 



= 7 xlO- lo (0-0 w ) 3 



lor temperatures below 2000° C. abs. Where 



= rate of loss by conduction in calories per sq. cm. of 



wall-surface per sec, 

 = mean absolute temperature of the gaseous mixture, 

 and 6o = absolute temperature of the walls of the explosion 

 vessel which in these experiments has been taken 

 to be 300°. 



The equations given above are sufficiently accurate for 

 rough calculation, but on closer examination the law of: 

 cooling by conduction would appear to be more complicated. 

 In the neighbourhood of 2400° 0. abs. (when convection 

 currents are probably somewhat vigorous) the rate of loss is 

 proportional to the fifth power of the temperature difference, 

 whereas in the neighbourhood of 1600° 0. abs. it approaches 

 proportionality to the square of the temperature difference. . 

 An inspection of the curve indicates that is proportional 

 to (0 — W )5 in the neighbourhood of 2400° C. abs., 

 {e-6u>f „ „ „ 2100° 0. abs., 



(0-0u>y „ „ „ 1800° C. abs., 



and (0-0u>) 2 „ „ „ 1500° Cabs. 



At still lower temperatures it is probable that C would 

 become proportional to the temperature difference simply. 



The experiments described in this paper were made in the 

 Engineering Laboratory at Cambridge in the years before 

 the war. The Laboratory was then under the control of the 

 late Prof. Bertram Hopkinson, and I desire to place on 

 record an expression of my indebtedness to him for the 

 valuable advice and assistance he so readily gave me. 



