18 Prof. W. M. Thornton on the 



If £ be the radius of the circle chosen % can be expressed 

 in terms of a, f , and r. Differentiation with respect to (• and 

 division by 27r£ give, to the degree of approximation adopted 

 in this investigation, for the axial velocity 



cor 



€•«?+«> 



where h = a — %. If h — r, so that the circle chosen is the 

 smallest, parallel to the circular axis, that can be taken on 

 the anchor-ring, this becomes 



: log [-cor. 



vrra r 



From this result the same equation (17) as before for the 

 velocity of the circular axis of the vortex ring can be obtained. 



Innellan, April, 1914. 



III. The Lost Pressure in Gaseous Explosions. By Prof. 

 W. M. Thornton, D.Sc, D.Eng., Armstrong College, 

 Newcastle-on-Tyne *. 



(1) The " suppression of heat " caused by the forces of 

 cohesion in molecular formation. 



WHEN a quantity of heat Q is given to unit mass of a 

 gaseous mixture by slow external heating at con- 

 stant volume, the rise of pressure is proportional to the 

 increase in the absolute temperature and can therefore be 

 calculated when the appropriate specific heat (J v is known. 

 If, however, the heat is derived from the explosion of the 

 mixture the maximum pressure obtained experimentally is 

 about half of that calculated from the heat developed, 

 allowing for change of volume in combustion and with 

 values of Q and C v derived from experiments under steady 

 conditions. 



Four suggestions have been made to account for this 

 difference — (1) that there is rapid cooling by the cylinder 

 walls (Hirn) ; (2) that there is dissociation of the gases 

 formed (Bunsen) ; (3) that the specific heats rise greatly 

 with the temperature (Mallard and Le Chatelier) ; (4) that 

 there is " afterburning " (Clerk). 



Evidence has been given that the first three do not explain 

 all the observed difference. Clerk's argument is largely 

 based on the fact that in certain cases the pressure in the 



* Communicated by the Author. 



