272-274] ATMOSPHERIC TIDES. 495 



The tidal variations of pressure due to the gravitational action 

 of the sun and moon are very minute. It appears from the above 

 analogy that the equilibrium value s of the condensation will be 

 comparable with HJJ-L, where His the quantity defined in Art. 177. 

 Taking H=l SO ft. (for the lunar tide), and H = 25000 feet, this 

 gives for the amplitude of s the value 7 2 x 10~ 5 . If the normal 

 height of the barometer be 30 inches, this means an oscillation of 

 only -00216 of an inch. 



It will be seen on reference to Art. 206 that the analogy with 

 the oscillations of a liquid of depth H is not disturbed when we 

 proceed to the tidal oscillations on a rotating globe. The height 

 H of the homogeneous atmosphere does not fall very far short of 

 one of the values (29040 ft.) of the depth of the ocean for which 

 the semi-diurnal tides were calculated by Laplace*. The tides in 

 this case were found to be direct, and to have at the equator 

 11*267 times their equilibrium value. Even with this factor the 

 corresponding barometric oscillation would only amount to 0243 

 of an inchf. 



274. The most regular oscillations of the barometer have solar diurnal 

 and semi-diurnal periods, and cannot be due to gravitational action, since in 

 that case the corresponding lunar tides would be 2*28 times as great, whereas 

 they are practically insensible. 



The observed oscillations must be ascribed to the daily variation in tem 

 perature, which, when analyzed into simple-harmonic constituents, will have 

 components whose periods are respectively 1, J, J, J, ... of a solar day. It 

 is very remarkable that the second (viz. the semi-diurnal) component has a 

 considerably greater amplitude than the first. It has been suggested by 

 Lord Kelvin that the explanation of this peculiarity is to be sought for in 

 the closer agreement of the period of the semi-diurnal component with a free 

 period of the earth s atmosphere than is the case with the diurnal component. 

 This question has been made the subject of an elaborate investigation by 

 Margules J, taking into account the earth s rotation. The further consideration 

 of atmospheric problems is, however, outside our province. 



* See the table on p. 361, above. 



t Cf. Laplace, &quot;Recherches sur plusieurs points du systeme du monde,&quot; Mtm. 

 de VAcad. roy. des Sciences, 1776 [1779], Oeuvres, t. ix., p. 283. Also Mecanique 

 Celeste, Livre 4 me , chap. v. 



J This paper, with several others cited in the course of this work, is included in 

 a very useful collection edited and (where necessary) translated by Prof. Cleveland 

 Abbe, under the title : &quot; Mechanics of the Earth s Atmosphere,&quot; Smithsonian Miscel 

 laneous Collections, Washington, 1891. 



