294 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



Every horizontal stratum moves alike, and tbe proportional variation 

 of density (p) is the same at all levels. Tbe possibility of such a motion 

 is evident beforehand, since on account of the assumption of Boyle's 

 law the velocity of sound is the same throughout. 



In the application to meteorology, the shortness of the more import- 

 ant periods of the vertical motion suggests that an "equilibrium 

 theory" of this motion may be adequate. For vibrations like those of 

 (28) there is no difficulty in taking account of the earth's curvature. 

 For the motion is that of a simple spherical sheet of air, considered in 

 my book upon the " Theory of Sound," § .'J33. If r be the radius of the 

 earth, the equation determining the frequency of the vibration corre- 

 sponding to the harmonic of order h is 



n 2 r 2 =h (h+l) a 2 (29) 



n 

 the actual frequency being - 9 — . If r be the period, we have 



_ 2?rr 



~aVh {h+l) (30) 



For h=l, corresponding to a swaying of the atmosphere from one side 

 of the earth to the opposite, 



2nr 



r '=^' < 31 > 



and in like manner for h=z2. 



2 nr ri 



T '= -T*~7l (32) 



To reduce these results to numbers we may take for the earth's 

 quadrant 



_ 7rr=10 e centimeters; 



and if we take for a the velocity of sound at 0° as ordinarily observed, 

 or as calculated upon Laplace's theory, viz, 33 x 10 3 cent ' meter .% we shall 

 find 



4xK> 9 

 r i= 777TT q.» w nn seconds=23.8 hours 



on the same basis, 



t 2 =13.7 hours. 



It must however be remarked that the suitability of this value of a 

 is very doubtful, and that the suppositions of the present paper are 

 inconsistent with the use of Laplace's correction to Newton's theory of 

 sound propagation. In a more elaborate treatment a difficult question 

 would present itself as to whether the heat and cold developed during 

 atmospheric vibrations could be supposed to remain undissipated. It 



