198 REPORTS ON THE STATE OF SCIENCE.—1912. 
flow and density seems to be complicated and dependent upon the 
size and shape of the enclosure. In one experiment on a gas-engine 
of 11} inches bore, the jacket loss varied as (density)”* when the 
density at the moment of the explosion was varied from three times 
atmospheric to about six times.’ After an explosion in a cylindrical 
vessel 1 foot by 1 foot, the absolute rate of heat-loss is roughly 
twice as great when the initial pressure is 1} atmosphere, as when it 
is $ atmosphere, corresponding to the relation® (density)°"*. 
The relation between heat-loss and density in an explosion vessel 
is dependent upon two factors—namely, radiation and direct surface- 
loss by convection and conduction. To a first approximation it may 
be expected that the heat radiated from a given mass of gas at a 
given temperature will be independent of the volume which it occupies 
because the number of radiating molecules is the same. Thus, to 
obtain from closed-vessel experiments at atmospheric density an esti- 
mate of radiation in a gas-engine in which the ratio of compression is; 
say, 5, it would be necessary to experiment with a vessel of the same 
shape as the combustion chamber, but of five times the volume. From 
the work of David, however, it would appear that the radiation 
increases slightly with the density, so that the flame in the gas-engine 
would radiate a little more heat than an equal amount of gas at atmo- 
spheric density in the closed vessel.? The effect of the other element 
in heat-loss—namely, convection currents—is probably more affected 
by the density than is radiation, and may perhaps increase in propor- 
tion thereto. The heat-carrying power of the gas depends upon its 
capacity for heat per unit-volume, and this increases in proportion with 
the density. Thus it may be expected that the amount of heat trans: 
ferred to the walls from the interior by a given amount of ‘bodily 
movement of the gas will increase more or less in proportion to the 
density. It is therefore to be expected that the combined effect of 
these two factors, radiation and convection, will be to make heat-loss 
in a vessel of given form increase according to some fractional power 
of the density. 
The most important practical question connected with the relation 
between density and heat-loss is the effect of degree of compression on 
the working and efficiency of gas-engines. To put the matter in its 
simplest form we may suppose that the engine has a cylindrical com- 
bustion space and flat-headed piston, so that the enclosure containing 
the gas at the moment of firing is a cylinder. The length of this 
cylinder will in most cases be a fraction of the diameter, the ratio 
of diameter to length being of the same order as the compression 
ratio of the engine. The problem, then, is to determine how the 
amount and distribution of heat-loss to the walls is altered when the 
compression ratio of the engine is changed, say, by lengthening the 
connecting rod. In the ordinary case of a fairly high compression 
ratio, the effect of this alteration will be to reduce the length of the 
* Proc. Inst. Civil Hng., vol. 176, p. 234. 
® David, loc. cit. 
* David, loc. cit., p. 404. 
