ON GASEOUS EXPLOSIONS. 311 



the first datum necessary for the investigations entrusted to the Com- 

 mittee, and is the principal subject of this repoi't. Before proceeding to 

 the discussion of this physical question, however, it is well to say some- 

 thing further about its bearing on practical engineering problems. 



The first requisite for predicting the performance of a gas-engine is to 

 know the rise of temperature and the consequent rise of pressure produced 

 by the explosion. The importance of this need not be insisted upon ; it 

 is not only the principal factor in the mean pressure developed, it also 

 determines in large measure the mechanical design of the engine and tlie 

 necessary strength of its parts. The part played by the energy function 

 in the calculation of this rise of pressure has been indicated in the last 

 paragraph. In proceeding further to analyse the indicator diagram given 

 by the engine with the object of accounting at each point for the heat 

 which has been put in, a knowledge of this function is again required. 

 The heat accounted for on the diagram is the work which has been done 

 plus the heat contained in the gas. The latter item can be calculated 

 from the temperature if the energy function be known. The balance 

 unaccounted for, which it is usually the object of such investigations 

 to find — whether in the steam-engine or the gas-engine — is the heat 

 which has been lost to the walls or has been suppressed owing to incom- 

 plete combustion. In fact, the internal energy of the gases at high tempera- 

 tures plays much the same part in the analysis of gas-engine phenomena 

 as does the total heat of steam in investigating the working of the steam- 

 engine. 



Again, from a table of internal energy, it is possible to predict the 

 pressure changes resulting from any series of operations such as occur 

 in the gas-engine, one item in which is an explosion subject to certain 

 hypothetical conditions which cannot be realised in practice, though 

 they can be indefinitely approached. An ideal diagram of this 

 kind, corresponding to the cycle of operations which is most usual in 

 present-day gas-engines, can, for example, be constructed for any given 

 combustible mixture on the assumption that the combustion is instan- 

 taneous and complete at the in-centre ; that there is no loss of heat 

 in compression, explosion, or expansion ; and that during expansion the 

 gases are at all times in thermal and chemical equilibrium. These con- 

 ditions can never be completely realised, but can in theory be approached 

 asymptotically by improvements in design carried on within certain defined 

 limits — namely, that the degree of compression and the nature of the 

 mixture are to be unaltered. For example, the heat loss may be reduced 

 by increasing the size of the engine and altering the nature of the cylinder 

 walls, and the attainment of thermal and chemical equilibrium may be 

 promoted by reducing the speed. Such an ideal cycle is, in fact, precisely 

 analogous to the Rankine cycle of the steam-engine, in that it takes account 

 of the actual physical properties of the working substance, but leaves out 

 of account such non-essential imperfections as heat loss to the cylinder 

 walls. It represents an ideal which the real engine may approach indefi- 

 nitely but can never attain ; and the closeness of the approach is a true 

 measure of the perfection of the engine. 



The ideal cycle which has hitherto been used in discussing the per- 

 formances of gas-engines is the well-known air-cycle. This is based upon 

 a special assumption as to the form of the energy function— namely, that 

 it is a linear function of the temperature at high, as it is known to be at 

 low, temperatures. The specific heat of the working substance is taken 



