196 REPORTS ON THE STATE OF SCIENCE.—1912. 
pressure), but a tenth of a second later, when the temperature has 
fallen to 1700° C., the radiation is only half as great. 
In a closed-vessel explosion the rate of heat-flow diminishes with 
very great rapidity as the gas cools down after ignition. Thus 
Hopkinson found that the products of igniting a mixture of coal-gas and 
air in a closed cylindrical vessel 1 foot by 1 foot lost heat at the rate of 
10 gramme calories per square centimetre per second at the moment of 
maximum pressure, when the temperature was 1760° C. One-fifth of a 
second later, when the mean temperature was 1300° C., the rate of 
heat-loss was reduced to 3} calories, or only one-third of its value at 
maximum temperature.* One cause of this is the fact that when the 
flame first touches the walls the heat is drawn almost wholly from the 
surface layer of gas in contact with them, and the flow is at first 
extremely rapid. This surface layer soon parts with its heat, and 
further supplies have to be drawn from the inner portions of the gas, 
the cool surface layer now acting as heat insulation. But it is pro- 
bable that the rapid reduction in radiation as the temperature falls is 
quite as important a factor in this phenomenon. In the gas-engine it 
is, of course, accentuated by the reduction of temperature consequent 
on expansion. ‘The closed-vessel experiments lend confirmation to the 
view already expressed, that in the gas-engine the rate of heat-flow per 
unit of area has fallen to a comparatively small value when the piston 
has moved a short distance out on the expansion stroke. 
An important practical consequence of radiation is the greatly 
increased loss of heat which occurs when the mean pressure in an 
engine is increased by increasing the strength of the mixture. The 
jacket loss and the metal temperatures are raised in a much greater 
proportion than the fuel consumption, and the efficiency is diminished. 
In very large engines this sets a fairly sharp limit to the possible out- 
put, which is as a rule considerably less than the maximum of which 
the engine would be capable if it were given all the fuel that it could 
take. If the load be in excess of this limit the engine overheats rapidly 
in consequence of the greatly increased heat-flow. 
3. The Effect of Cylinder Dimensions on Heat-flow.—At first sight 
it might appear that heat-flow is a surface phenomenon—that is, the 
number of calories per square centimetre per second passing into the 
walls of an engine or explosion vessel containing a gas at a given tem- 
perature and density should be independent of the volume. This view, 
which is rather widely held, is, however, certainly erroneous, and pro- 
bably to a considerable amount. The effect of radiation is necessarily 
to make the heat-loss per unit area from a large volume greater than 
that from a small volume, because the walls receive radiation from 
the inner layers as well as from the portions nearer to them. At some 
depth, of course, the radiation will cease to be sensible, and when that 
has been reached the radiation from the whole mass will not be 
increased by further increasing its volume. The experiments of David, 
to which reference has been made, show that the transparency of the 
products of an explosion while still at a high temperature is very great, 
* Proc. Roy. Soc,, A., vol. 79, p. 138. 
