ON GASEOUS EXPLOSIONS. 



223 



amount of heat absorbed rather uncertain. Since, however, the curves of 

 temperature-rise in the two cases (blackened and polished) are very 

 nearly similar, differing only as regards temperature scale, the propor- 

 tion of heat lost will be the same in the two cases, and the ratio of heat 

 absorption by the blackened and polished surfaces will be nearly equal 

 to the ratio of the temperatures. The ratio of the temperatures shown 

 in fig. 5 is 0'75 at the end of 0"2-5 sees, from ignition, which agrees as 

 well as might be expected with the ratio of the rates of cooling deduced 

 from the pressure records with blackened and reflecting walls, having 

 regard to the great effect of small differences in polish upon the rate of 

 cooling. The ratio of the bolometer temperatures increases a little as 

 the gas temperature falls, which again agrees with the gradual approxi- 

 mation as regards rate of cooling disclosed by the pressure records. 



Some estimate of the heat lost to the backing can be made as 

 follows : If the temperature of the surface of a solid be caused to vary 

 in a given manner, then the quantity of heat which has passed into it 



Fig. 5. 



at any time can be calculated by means of the Fourier analysis, provided 

 that the product of the thermal conductivity k and the thermal capacity 

 c of the solid is known, being for a given temperature variation pro- 

 portional to the square root of this product. In the present case the 

 solid is the linoleum backing, and the surface temperature is that of the 

 silver in contact with it, and is given by the bolometer record. The 

 total heat absorbed by the bolometer per square centimetre at any instant 

 can therefore be estimated from the bolometer record, subject only to a 

 knowledge of s/ k c which occurs as a multiplier, and thence, assuming 

 that the average heat loss over the whole surface is the same as that 

 absorbed by the bolometer, the whole heat given by the gas can be calcu- 

 lated. This heat loss can be obtained also from the pressure record by 

 deducting from the whole heat of combustion the quantity of heat 

 remaining in the gas, whose energy at a temperature of, say, 1000° C. 

 may be considered as known sufficiently nearly for this purpose. The 

 value of the factor >J k c is then chosen as to make the heat obtained 

 from the bolometer equal to that deduced from the pressure record. 

 Table I., page 224, showing the absolute heat losses has been obtained 

 in this way. 



Q 2 



