312 REPORTS ON THE STATE OF SCIENCE. 



to be constant and equal to 19 foot-pounds per cubic foot, or 4-8 calories 

 per gi-amme molecule. In the state of ignorance as to the real form of 

 the energy function which prevailed until quite recently, this assumption 

 was as good as any other, since it was impossible to say that the value of 

 the energy derived from it was further from the truth than any other value 

 which might be assigned to it. So far as was known, the differences between 

 the indicator diagram of a real engine and the corresponding air-cycle 

 diagram might have been wholly, or almost wholly, due to what have been 

 called above 'non-essential imperfections' — that is, to lieat loss and to 

 incomplete combustion. In other words, there was no conclusive evidence 

 that the air- cycle was not for practical purposes a true ideal cycle in the 

 sense defined above and equivalent to the Rankine cycle for the steam- 

 engine. Under these circumstances its extreme simplicity made it the 

 best available standai'd of comparison for judging the performance of a real 

 engine. Recent researches, however, on the properties of the gases at 

 high temperatures have definitely .shown that the assumption of constant 

 specific heat is erroneous, and have given suflicient information about 

 the magnitude of the error to show that it is of material importance. They 

 have shown that the air-cycle cannot be regarded as equivalent to the 

 Rankine cycle in the steam-engine, inasmuch as it does not take account 

 of the properties of the actual working fluid, but postulates a hypothetical 

 fluid which has no real existence. It is as though in the theory of the 

 steam-engine the total heat of the steam were to be taken as equal to its 

 latent heat, the sensible heat of the water being neglected. This assump-. 

 tion would lead to a simpler formula for the ideal efficiency for the steam- 

 engine, but it would be erroneous in the same way and to about the same 

 extent as the air-cycle formula for the gas-engine.' Tlio closer approxi- 

 mation to the real cycle which is made by taking account of the actual 

 properties of the working fluid — in the steam-engine the total heat of 

 the steam instead of only the latent heat, in the gas-engine the true 

 value of the energy instead of that based on the assumption of constant 

 specific heat — though it leads to some complication of formulte gives 

 compensating advantages of real practical value. It .sliows the engineer 

 what are the limits to the iuiprovements which can be eflfected by changes 

 of design or increase of size, and it enables him to judge whether it is 

 better that the lines of development should proceed in such directions or 

 in the direction of radically modifying the cycle of operations. 



Measurement of the Internal Energy or Specific Heats of Gases at 



High I'emjyeratures. 



The results of most experiments on the energy of gases have been 

 expressed in the form of tables or formulae giving tlie specific heat 

 (referred to unit mass of the gas) in terms of the temperature. It 

 would appear preferable for most purposes to exhibit them in terms 

 of internal energy per unit volume. That is the form most convenient 



' If the sensible heat of the steam can be neglected in comparison with its latent 



T -T, 

 heat the Rankine cycle reduced to the Carnot cycle, with efficiency —hf^ — •", for do 



beat is then necessary to warm the water from the condenser to the boiler tempera- 

 ture, and the whole process becomes reversible. The efficiency of the Carnot cycle 

 usually exceeds that of the corresponding Rankine cycle by about one eighth 

 part, - r 



