366 Dr. Karl Heumann's Contributions to 



out, taxed the vast analytic power of Euler himself. In two 

 different memoirs * it is a subject of inquiry with him ; and in 

 one place f he says that he had spent much labour upon it, but 

 that the harder it seemed the more advantage did he hope to 

 draw from the solution. And yet Wallis's theorem is, as we 

 have seen, one of the simplest cases of the general result here 

 established with comparative ease. 

 Glasgow, February 6, 1877. 



L. Contributions to the Theory of Luminous Flames. 

 By Dr. Karl HeumannJ. 



[Plate II.] 

 [Concluded from p. 107.] 



IN a former part of these papers I have declared my belief in 

 the view which regards the separation of solid carbon as 

 the cause of the luminosity of the flame produced by burning 

 hydrocarbonaceous bodies. I have now to prove experimen- 

 tally the justice of this belief, and to demonstrate the existence 

 of free carbon in such flames. 



The increase in the " light-effect " of a gas-flame occasioned 

 by heating the burner-tube has been already traced to the in- 

 crease in the intensity of light of the flame-mantle, and to the 

 simultaneous enlargement of the flame itself. The increase in 

 intensity of the light may be itself traced either to the higher 

 temperature to which the carbon particles are raised, or to the 

 production of a greater number of such particles in a given 

 volume of the flame-mantle. In either case more light will 

 be emitted by any special portion of the flame. Whether both 

 causes are at work when the burner-tube is heated must re- 

 main meanwhile undecided. The increase in size of the flame- 

 mantle, noticed when the burner-tube is heated, has been re- 

 ferred to an earlier separation of carbon in the flame, this 

 separation becoming possible by reason of the high tempera- 

 ture to which the gas has been raised. 



If this explanation be the true one, it is manifest that any 

 agent, other than heat, capable of producing a separation of 

 carbon in the comparatively cold lower portions of the flame, 

 should also be capable of producing an increase in the size of 

 the flame-mantle. Chlorine and bromine are known to be 



* " De Fractionibus Continuis Observationes," Comment. Acad. Petro- 

 sal, vol. xi. 1739, pp. 32-81 ; " De Fractionibus Continuis "Wallisii," 

 Memoires de VAcad. de St. Tetersbourg, vol. v. 1815, pp. 24-44. 



t Comment. Acad. Petropol. 1739, p. 41. 



X Tianslated, and somewhat condensed, from Liebigs Annalen, vol. 

 clxxxiv. pp. 206-254, by M. M. Pattison Muir. 



