Conduction of Heat along Pipe through which Gas Flows. 109 



and affected with factors such that the mean of the com- 

 pounds is zero, while their mean square of deviation is 

 constant. Therefore (as in the case of oar digits sprinkled 

 with sines and cosines) the final velocities (with mean and 

 mean-square-of -error which will not be altered by continued 

 collisions) will be distributed normally. The distribution at 

 the time T was either not final, or not different from the 

 normal. 



It comes to the same if we place the epoch T before mole- 

 cular chaos has been set up ; and regard the u's and u's of 

 colliding molecules as elements taken at random from an 

 initial distribution of velocities which may be as different 

 from the normal frequency as the distribution of digits (less 

 by 4*5) above instanced. By parity of reasoning in the 

 course of repeated collisions the system will work down to a 

 stage in which the velocities are distributed according to the 

 normal law. It may be observed that in this view of the 

 proof the postulate (6) is replaced by one referring to an 

 initial stage. 



The reasoning is readily adapted to molecular motion in 

 three dimensions ; and to cases in which the centre of gravity 

 is not at rest. The reasoning may be extended to molecules 

 which are not spherical and not perfectly elastic ; provided 

 that the velocities consequent on repeated encounters continue 

 to be (at least approximately) linear functions of the com- 

 ponent velocities. When the mixture of molecules is not 

 complete, as the stage of perfect chaos is being approached 

 but is not yet reached, there is presumably fulfilled that 

 approximation to the normal law of frequency which has 

 been described as the Generalized Law of Error (see " The 

 Law of Error/ Cambridge Philosophical Transactions, 1905, 

 and " The Law of Great Numbers," Journal of the Statistical 

 Society, 1906, by the present writer). \ 



XL Note on the Conduction of Heat along a Pipe through 

 which Gas is Flowing, in its Relation to Measurements of 

 the Specific Heats of Gases. By W. F. G. Swann, D.Sc, 

 A.R.C.S., Assistant Lecturer in Physics at the University 

 of Sheffield*. 



A FEW years ago the author measured the specific heats 

 of Air and Carbon dioxide at constant pressure, and 

 the results, which have since been confirmed by other 

 investigators t, and which agree to one part in a thousand 



* Communicated by the Author, haying been read at the meeting of 

 the British Association, 1912. 



t Dugald Clerk, Report on Gaseous Explosions, B. A. Report, 1910 ; 

 Scheele and Heuse, Ann. d. Physik, vol. xxxvii. Dec. 29, 1911. 



