328 



Intelligence and Miscellaneous Articles. 



cient of expansion under a constant pressure between and t, and 

 for the pressure/?. 



Putting iWL° =R P , — = a», we have 



pv = R p {*P + t), (1) 



a formula which combines the law of the compressibility and the 

 law of the dilatation of imperfect gases, and in which R^ and cc p 

 change with the pressure. Thus we have for R p the following 

 values : — 





P- 



r me- 

 <■ tre. 



0-76 

 metre. 



1 



metre. 



5 



metres. 



10 



metres. 



15 



metres. 



20 

 metres. 



Air 



Rp= 



29-222 

 19-329 



29-325 



19-388 



29-347 

 19437 



29-672 

 20-417 



30-007 



30-265 



30-446 

 25-915 



Carbonic acid. 



21-907 



23-867 



But, according to M. Clausius, we have also pv = -~, g being the 



acceleration due to gravity, and u the mean velocity of the progres- 

 sive motion ; then 



u= V3R^(a ; , + 0, (2) 



a formula which differs from that given by M. Clausius for perfect 

 gases in that R^ and ol p are not constant, but functions of the pres- 

 sure or volume. It may serve to determine the mean velocity of the 

 molecules in the different gases. In the case of air and of carbonic 

 acid, for which we have the requisite experimental data, we thus 

 obtain the following velocities, expressed in metres per second : — 



Pressure, 

 in metres. 



Air. 



Carbonic acid. 





* = 4°-8. 



£=100°. 



t=3°3. 



^=100°. 







0-76 



1 



5 

 10 

 15 

 20 



485-1 

 484-4 

 484-8 

 483-8 

 482-8 

 482-0 

 481-4 



566-9 

 566-9 

 5669 

 566-9 

 566-9 

 566-9 

 566-9 



393-3 

 3921 

 3918 

 385-0 

 374-5 

 362-9 

 350-4 



459*7 

 459-2 

 4590 

 456-4 

 452-8 

 449'4 

 446-2 



The velocities found for the pressure zero represent the ideal case 

 of a gas infinitely rarefied (that is to say, perfect), the attractions being 

 infinitely small. We see that the velocities diminish when the pres- 

 sure increases — that is to say, when the volume becomes small and 

 the attractions are more intense. For atmospheric air at 100° it is 

 necessary to carry the calculation to the second decimal place in 

 order to find the differences, which shows clearly the degree of 

 perfection that this gas reaches at that temperature. It seems 

 almost superfluous to remark that, in order that the numbers given 

 for air may have a real significance, we must consider air, not as 

 a mixture of two gases, but as a single ideal gas whose molecules 

 possess the physical properties of nitrogen and of oxygen in known 

 proportions. — Comptes Itendus, July 12, 1869. 





