102 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



must remain constant; that is to say, the ratio of the living forces of the 

 corresponding units of volume must remain unchanged. As correspond- 

 ing- units of volume, those must be used that hold good in the region of 

 rectilinear flow far from that of the wave surface ; but also for such 

 units of volume as have centers that are corresponding images for each 

 other the same proposition holds good. 



(3) If for a varied density the geometrically similar waves are to 

 have the same wave-length, namely, n=l, then 



b, must increase as „ / — 1= /-- — - 

 6 2 must increase as /l — a= ——. 



For air and water at a temperature of 0° 0. we have the ratio 



1 



G- 



1T6A 



For two strata of air whose temperatures are 0° aud 10° the ratio be- 

 comes 



273 



°" = 283 



If both boundary surfaces are to show congruent waves and therefore 

 also equal wave-lengths, and it I designate by /i ( and /i 2 the values of 

 the quantities bi and b 2 in this last case, then we have 



&! =145.21/?! 

 & 2 =5.316/j 2 



therefore both the velocities, especially that of the wind relative to the 

 waves of water, must be considerably diminished for the case of atrial 

 billows. 



The value of the quantity 



. S 2 ' °2 



1 ~~«i : 6i* 



which is invariable for any change in the material for a given form of 

 wave whose store of energy is equal to that of the rectilinear flow along 

 a plane boundary surface is given at least approximately according to 

 my computations, as 



p=0.43103. 



If by a wind-force w we understand the difference of the movement of 

 the two media 



w=&i+& 2 



