Vibrations of an Atmosphere, 179 



from one side of the earth to the opposite, 



->=£* (31) 



and in like manner for h = 2, 



_ 2irr _ t, .„ 9 . 



To reduce these results to numbers we may take for the 

 earth's quadrant 



j7ZT=10 6 cm. ; 



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 

 cm. /sec, we shall find 



seconds = 23*8 hours. 



1_ v/2x33xl0 3 



On the same basis, 



r 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 atmo- 

 spheric vibrations could be supposed to remain undissipated. 

 It is evidently one thing to make this supposition for sonorous 

 vibrations, and another for vibrations of about 24 hours period. 

 If the dissipation were neither very rapid nor very slow in 

 comparison with diurnal changes — and the latter alternative 

 at least seems improbable — the vibrations would be subject to 

 the damping action discussed by Stokes*. 



In any case the near approach of t x to 24 hours, and of t 2 

 to 12 hours, may well be very important. Beforehand the 

 diurnal variation of the barometer would have been expected 

 to be much more conspicuous than the semi-diurnal. The 

 relative magnitude of the latter, as observed at most parts of 

 the earth's surface, is still a mystery, all the attempted ex- 

 planations being illusory. It is difficult to see how the 

 operative forces can be mainly semi-diurnal in character ; 

 and if the effect is so, the readiest explanation would be in a 

 near coincidence between the natural period and 12 hours. 

 According to this view the semi-diurnal barometric move- 



* Phil. Mag. [4] i. p. 305, 1851. 'Theory of Sound/ § 247. 



