492 Major W. T. David on the Origin of 



If tanh a or v 7 l — a 2 \(? is a rational number, say —p\qi 

 where p and q are integers with no common factor, the curve 

 is algebraic. It has 2p cusps and is re-entrant after q — p 

 revolutions about the pole. 



(3) In the intermediate case c = a, the integral is 



= cot-i<£, 



where = 0, = 180° initially. If = 0, <£ = initially, W 

 is at the pole A and remains there. There is therefore only 

 the outer branch remaining. It is a spiral tending to the 

 pole, and having a cusp at a distance 2a. 



In each case the C-locus, or evolute of the slip-curve, has 

 asymptotes touching the circle r = c and cutting the slip- 

 curve orthogonally at the points of inflexion. 



Victoria Univ. Coll., 



Wellington, N.Z. " 

 Sept. 25th, 1918. 



XL VIII. The Origin of Radiation in a Gaseous Explosion. 

 By Major W. T. David, M.A., M.Sc* 



1. VT is now well known that inflammable gaseous mixtures 

 J_ emit radiation strongly both during explosion and 

 subsequent cooling. In some experiments made in 1909 

 and 1910 the radiation emitted by exploded coal-gas and air 

 mixtures was found to amount to as much as 25 per cent, of 

 the total heat of combustion of the coal-gas present in the 

 explosion-vessel |. 



2. The British Association Committee on Gaseous Ex- 

 plosions were much interested in these results, and for a 

 time their discussions mainly centred round the question as 

 to the probable origin of the radiation. The chemists on the 

 Committee were of the opinion that the radiation was wholly 

 due to chemical causes. They believed that gases which are 

 capable of emitting radiation can only do so when under- 

 going chemical or quasi-chemical reaction. This opinion 

 was not generally held. Many of the members held the 

 view that the chemical activities which may be proceeding 

 during the cooling of the exploded mixture were not sufficient 



* Communicated by the Author. 



t Hopkinson, Roy. Soc. Proc. A. vol. Ixxxiv. p. loo. David, Phil. 

 Trans. A. vol. ccxi. p. 375. 



