102 THE MECHANICS OF THE EARTH's ATMOSPHERE. 



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

 corresponding units of volume must remain unchanged. As correspoud- 

 ing units of volume, thos'e 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 — 1, then 



hi must increase as , / — 1= /' 



S2—SI 



Si 



hi must increase as h—(j^= - — —. 



For air and water at a temperature of 0-^ C. we have the ratio 



I 



ff= 



116 A 



For two strata of air whose ten)[)eratures are 0° and 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 ftx and (iz the values of 

 the quantities hi and hz in this last case, then we have 



Z>i = l 45.21 /i, 

 ^2=5.310/^2 



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

 waves of water, must be considerably dimiuisbed for the case of airial 

 billows. 



The value of the quantity 





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 i)lane boundary surface is given at least approximately according to 

 my computations, as 



P= 0.43 103. 



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

 the two media 



u'=hi-\-h2 



