104 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



depth, provided that the depth of the lower stratum iu the image varies 

 in the same ratio as the remaiuing linear dimensions of the waves. 



The velocity of propagation of such waves in shallow water depends 

 on the depth of the water. For water waves of slight height aud with- 

 out wind it can be computed by well-known formuke. When we iudi- 



2;r 

 cate the depth of the water by h and put « = -^, then is 



A 



which for h=y^ becomes 





H 'In 



aud for small values of /( becomes 



When however the depth of the water is not small relatively to the 

 wave length, then the retardation is unimportant, thus for 



'=^ the speed of propagation diminishes as 1:0.95768 



A 1 



=- the speed of propagation diminishes as 1:0.80978 

 4 



=— the speed of propagation diminishes as 1:0.394:27 



When it is calm at the earth's surface the wind beneath the trough of 

 the aerial billow is opposed to the direction of propagation, but un- 

 der the summit of the billow it has the same direction as that. Since 

 the amplitudes at the earth's surface are diminished in the proportion 

 g-«A. Y with respect to the amplitudes at the upper surface, therefore 

 these latter variations can ouly make themselves felt below when the 

 depth is notablv smaller than the wave-length. Variations of baro- 

 metric pressure are only to be expected when decided changes in the 

 wind are noticed during the transit of the wave. 



VIT. FUNDAMENTAL FORilULyi; FOR THE COMPUTATION. 



1 will here give the theory of the calculation ouly so far as is neces- 

 sary, so that any investigator familiar with analytical methods can 

 verify my results. I introduce two new variables, rf and 6^, which are so 

 connected with rectangular coordinates x and ythat 



e'"'+'" =«[C0S (6'-f ?;/) — cos £j (1) 



wherein w, «, and e are constants. The boundary line between the two 

 fluids corresponds to a constant positive value of //, namely : 



