PAPER BY PROF. HELMHOLTZ. 103 



then will for air and water 



-=0.069469 

 w 



, ... ..,. metres 



and it w =10 =- 



second 



A =0.208965 metre 



on the other hand for the two strata of air 



P* — n fi 



/*i+A 



0.67135 



audforzr=10 metres 

 seeond 



A=549 m .65 



Hence it results that when we would obtain for this form of atmospheric 

 wave the same wind velocity as for geometrically similar water-waves 

 we must increase the wave-length of the air wave in the ratio of 1 to 

 2630.3. 



This ratio becomes somewhat smaller when we execute the computa- 

 tion for the lowest waves for which 



This gives lor air and water 



p= 0.15692 



&2 =0.090776 

 w 



and for a wind velocity of 10 metres per second, 



A=0. n 'S3222 



The necessary magnification of the wave-length for equal strength 

 of wind would be 1:2039.6 which gives a wave-length of more than 900 

 metres for a wind of 10 metres per second. 



Since the moderate winds that occur on the surface of the earth, 

 often cause water-waves of a metre in length, therefore the same winds 

 acting upon strata of air of 10° difference in temperature, maintain 

 waves of from 2 to 5 kilometres in length. Larger ocean-waves from 

 5 to 10m long would correspond to atmospheric- waves of from 15 to 30 

 kilometres, such as would cover the whole sky of the observer and 

 would have the ground at a depth below them less than that of one 

 wave-length, therefore comparable with the waves in shallow water, 

 such as set the water in motion to its very bottom. 



The principle of mechanical similarity, on which the propositions of 

 this paragraph are founded, holds good for all waves that progress 

 with an unchanged form and constant velocity of progress. Therefore 

 these propositions can be applied to waves in shallow water, of uniform 



