78 Major W. T. David on the Calculation of 



Rate of Emission of Radiation during Cooling. 



(a) Cylindrical Explosion Vessel 30 cm. diameter and 

 30 cm. long. Gaseous Mixtures at Atmospheric Density. 



15. It is not possible to build up an accurate formula for 

 R at any temperature under wide conditions of mixture 

 strength, density, and volume until much further experi- 

 mental work is accomplished. The whole question is 

 complicated greatly by the fact that the transparency of 

 the gaseous mixture varies with the time after ignition, and 

 also (to a much less extent) because the vibratory energy of 

 the molecules is dependent upon other factors as well as 

 temperature*. It is important, however, from the point of 

 view of gas-engine calculations to be able to estimate the 

 radiation loss at various points during the expansion stroke, 

 ;and it is believed that an empirical formula sufficiently 

 accurate for this purpose can be established. 



16. It has been previously shown that the radiation from 

 the gaseous mixture when corrected for absorption varies 

 with the temperature approximately in accordance with 

 Planck's formula for a wave-length of 3'6/jl f (which at high 

 temperatures varies very nearly as the square of the absolute 

 temperature). It so happens, however, that when uncorrected 

 for absorption R in a vessel of the dimensions used in the 

 •experiments is approximately proportional to i , and it is 

 considered that a formula based upon this law w r ill give gas- 

 engine designers fairly reliable information as to radiation 

 loss when applied to cylinders within the limits of dimensions 

 15 cm. x 15 cm. to 60 cm. X 60 cm. J 



* See Phil. Mag. Feb. 1913, p. 267. 



t Phil. Trans. A. vol. ccxi. p. 402. 



X See Phil. Trans, p. 386, fig. 9. The 4 curve there was made to 

 coincide with K at comparatively low gas temperatures when the radia- 

 tion is small. By increasing the scale a close agreement mav be obtained 

 at the high temperatures (2400° C. abs. to 1600° C. abs.), which is the 

 important part of the curve from the point of view of the gas-engine. 

 The agreement between the 8 i curve and li in the neighbourhood of the 

 maximum temperature in the 9*8 per cent, mixture is not so good, but a 

 fairly correct value for 11 in this epoch, for weak mixtures may be obtained 

 by calculating the mean of E, given by the 6 l formula (equation (9) § 17) 

 and It max. a s determined by the equation in the preceding sections. 



The statement made in the paper referred to (footnote p. 402) to the 

 effect that the # l law would not hold in the case of a cylinder of widely 

 different dimensions from those of the vessel used in the experiments 

 requires some modification. There seems little doubt that this statement 



