218 REPORTS ON THE STATE OF SCIENCE. 



effect on the radiation. Several series of measurements were taken 

 with one to six burners lighted in different orders, for two distinct states 

 of the flame which were easily reproducible, namely (1) with full air- 

 supply and (2) with the inner cones 2"5 cm. high. In the latter case 

 the flames all touched each other, and the layer of flame was 21"6 cm. 

 thick and was sensibly homogeneous. 



Summary of Observations. 



1. Full Air-Supply, Mean thickness per flame, 2-8 cm. 



Number of Flames ... 1 2 3 



Radiation Observed . . . 68 124 171 

 Radiation Calculated ... 66 124 173 



Formula R = 473 (l—e-ossT*) 



Limit B,/x when a- = o, = 473x0-0537 = 25-4 per cm. thickness x. 



Limit of R when x = infinity, R = 473. 



2. Cones 2-5 cm. high. Mean thickness per flame, 3-6 cm. 



Number of Flames ... 1 2 3 4 5 6 



Radiation Observed ... 72 122 165 197 232 261 

 Radiation Calculated ... 66 120 166 201 232 257 



Formula R = 373 (1-e - 05 "*). 



Limit R/z when x — o, = 373x0-0541 = 20-2 per cm. thickness. 



Limit of R when x = infinity, R = 373. 



The observed and calculated values agree as closely as could be 

 expected with the exponential law of absorption, which is fairly appro- 

 priate in this case, since the radiation emitted is necessarily of the 

 same quality as that absorbed and the flame is nearly homogeneous. 

 An apparent confirmation of the formula is that the coefficient of absorp- 

 tion is practically the same, namely 0'054 for the two flames. The limit 

 of E/x, when ,t = 0, which gives the intrinsic radiance per cm. of 

 flame corrected for absorption, is higher for the case of complete com- 

 bustion because the temperature of the flame is higher. The limit of 

 radiance for an infinite thickness of flame is higher in the same propor- 

 tion. The radiation observed for a single flame in case (2) is rather 

 larger than that calculated, because the thickness of a single flame was 

 slightly greater than the mean of several flames in contact. It will 

 be observed that the flame is surprisingly transparent to its own radia- 

 tion. It is very commonly assumed that, because a flame absorbs 

 precisely those radiations which it emits, and absorbs them in the same 

 proportion as it emits them, the flame would, therefore, be practically 

 opaque to its own radiation, so that the radiation proceeding from the 

 interior of a mass of homogeneous flame might be neglected, and the 

 total radiation assumed proportional to the surface. The above observa- 

 tions show that this is very far from being the case, owing to the 

 relatively wide separation of the radiating and absorbing molecules. 



Effect of Temperature and Pressure. 



The effect of temperature and pressure on the intrinsic radiance of 

 a flame of this kind can be theoretically predicted with a reasonable 

 degree of probability, but it would be difficult to determine either experi- 

 mentally. Within moderate limits of pressure, the radiating and 

 absorbing powers of a flame per unit thickness at a given temperature 



