740 Botmuira'a THBOBKM ON THE AVEIUGB DISTRIBUTION 



The velocity of the end /? would be 184'4 metres per second. If the tube 

 hydrogen at 0"C, the ratio of the density of the gas at B to the 

 at A will be *, or approximately 1 +*fo- 

 If it contains a gas whose chemical equivalent is p, the ratio will be 



JL 

 200' 



If the tube contains hydrogen and carbonic acid, and if a certain volume 

 of the tube at A contains 200 parts of hydrogen and 200 of carbonic acid, 

 then an equal volume of the tube at B will contain 201 parts of hydrogen 

 and 222 part* of carbonic acid. 



The time during which the experiment would require to be continued in 

 older to obtain a given degree of approximation to the ultimate distribution 

 of the mixed gases varies as the square of the length of the tube. 



Thus in Loschmidt's experiments on the diffusion of gases he used a tube 



about a metre long, and continued his experiments from half an hour to an 



hour in order to obtain the results from which he could best deduce the 

 coefficient of diffusion. 



In these experiments the inequalities of distribution of hydrogen and 

 carbonic acid were reduced to less than a third part of their original value 

 in hlf an hour, and if the experiment had gone on for two hours the 

 differences from the ultimate distribution would have been reduced to a hundredth 

 part of their original value. 



We may therefore consider two hours as ample time for an experiment 

 on the ultimate distribution of these two gases in a tube one metre in length. 



But if we make the whirling tube 20 centimetres long, the differences of 

 distribution from the ultimate distribution would be reduced to a hundredth 

 part of their original value in a twenty-fifth part of the time, that is to say 

 in 4 minutes 48 seconds. 



If it were found more convenient to have bulbs on the ends of the tubes, 



so as to be able to secure the gas at each end before it got mixed up by 



the violent commotion arising from the stopping of the whirling tube, we 

 should have to allow a longer time for the whirling. 



