334 REPORTS ON THE STATE OF SCIENCE. 



based upon these experiments. It cannot be regarded as having a secure 

 foundation until the various doubtful questions in regard to heat loss 

 and delayed combustion, which have been raised above in this connection, 

 have been satisfactorily determined. 



The Committee think that they can usefully continue their work in 

 the direction of suggesting, and to some extent organising, research 

 on the lines which have been foreshadowed in this Report. Research 

 of this kind is expensive, and the Committee are of opinion that their 

 work would be greatly facilitated if they had some funds at their 

 command. They therefore recommend that they be reappointed, and 

 ask for a grant of lOOl. 



APPENDIX. 



The Deviation of Actual Gases Jrom the Ideal State, and on Exjierimental 

 Errors in the Determination of their Specific Heats, By Professor 

 H. L. Callendab, M.A., LL.D., F.ll.S. 



1. The equation ^j?;=R^, where 6 is absolute temperature, is the 

 characteristic equation of a fluid which (1) obeys Boyle's Law at all 

 temperatures, and (2) has the difference of its specific heats constant 

 and equal to R. The specific heat at constant volume or pressure may 

 vary in any manner with temperature, provided that the difference of 

 the two is constant ; but both specific heats must be independent of the 

 pressure or density. 



For the majority of common gases or vapours (excluding those which 

 polymerise, like sulphur) the deviations from Boyle's Law, as measured by 

 the defect {'KOIp—v) of the actual volume from the ideal volume, at 

 moderate pressures (say up to ten atmospheres) are to a first approxima- 

 tion a function of the temperature only, and diminish rapidly with rise 

 of temperature. On this assumption tables of correction for the gas- 

 thermometer have been independently calculated by Callendar ' and 

 D, Berthelot ^ for various gases when employed in the usual manner. 

 The corrections are very small, and agree very closely, though calculated 

 on slightly different assumptions. The differences are much too small 

 to be taken into account in gas-engine experiments. 



In dealing with a mixture of gases and vapours at high temperatures, 

 the method of procedure is necessarily somewhat different from the case 

 of the gas-thermometer, and the tabulated corrections do not apply. The 

 effective temperature of the mixture is calculated from the value of 

 the product pi'/R, assuming that the composition of the mixture is 

 known, and that the constant R has the same value per gramme molecule 

 for each of the constituents as for an ideal gas. The errors involved in 

 this method will be small, and will diminish with rise of temperature, 

 provided that the constituents do not dissociate or polymerise. The. 

 experimental evidence at present available with regard to dissociation 

 would indicate that the error of this assumption is certainly less than 

 1 per cent, for a gas-engine mixture at 2000° 0., if the composition of 

 the products of combustion is known. 



' Phil. Mag., January 1903. ■ Trav. ct Mem. Bur. Lit., Paris, 1903. 



