and the Observed Velocity of Sound in Air and Gases. 27 



formula for correcting the influence of aqueous vapour (which 

 assumes the mutual action of the gases) gives results so accordant 

 with those deduced from experiments in the Arctic regions (where 

 the tension of vapour is almost nothing), as to afford a strong 

 confirmation of the view that the aqueous vapour of the atmo- 

 sphere does not transmit pulses independently of its other gaseous 

 constituents. Be this as it may, there can scarcely be any doubt 

 that the nitrogen and oxygen of the air do not transmit sounds 

 independently of each other. For if such were the case, although 

 the most usual and powerful sounds would be transmitted by 

 the nitrogen, yet it is hardly possible that the slower and feebler 

 pulses which would be propagated by the oxygen should entirely 

 elude observation. Considering the particles of these two gases 

 as completely and absolutely independent of each other, it is 

 easy to submit the question to a numerical test. Bearing in 

 mind that the velocity of sound in gases, ceteris paribus, is in- 

 versely proportional to the square root of their densities, and 

 assuming the value of k for both nitrogen and oxygen to be the 

 same as for air (the difference is very small), we have the follow- 

 ing results. 

 Let 



v = velocity of sound in dry air at 0° C. 



<tf = velocity of sound in nitrogen at 0° C. 



i/'= velocity of sound in oxygen at 0° C. 



d'= density of nitrogen, air being unity. 



d"=. density of oxygen, air being unity. 



Then 



, v 332 m «4117 QWn „ n 



v'= —p==f= — — — =337'279 metres per second, 

 Vd' \/0-971346 r 



and 



„ v 332 m -4117 Qi/Mo? , i 



v"= — ^=-= — = olo , lo7 metres per second. 



Vd" i/1-105612 



It thus appears that, if the nitrogen and oxygen of the air 

 transmitted sounds independently of each other, at the end of 

 one second the nitrogen sound would be more than 21 metres 

 (69*36 feet) in advance of the oxygen sound; and after the lapse 

 of ten seconds the former would be more than 211 metres ahead. 

 As the ear can readily appreciate intervals between sounds when 

 the distances traversed differ less than 30 metres, it is scarcely 

 possible to imagine that the duplication of distant and violent 

 sounds could have escaped the most ordinary observation, were 

 they transmitted independently by the gaseous constituents of 

 the atmosphere. 



c. Hence most physical philosophers have considered the atmo- 

 sphere as a mixture whose gaseous constituents exercise a mutual 



