606 TKANSACTIONS OF SECTION A. 



confroDted witn the bewildering complexity of the phenomena which he registers, 

 asks for some theoretical clue which shall help him to analyse these and to reduce 

 them to something like order. In particular he considers that he has indications, 

 in various cases, of distinctly periodic fluctuations of atmospheric pressure, and he 

 requires some corresponding theory. Under these circumstances, perhaps the 

 most useful course will be to attempt a review of such results in the existing 

 theory of wave-motion as may conceivably have an application to meteorological 

 conditions. 



We may consider in the first case the oscillations of the atmosphere as a whole. 

 J.f we assume, for simplicity, isothermal conditions, these are closely analogous to 

 the oscillations of a liquid ocean of uniform depth covering the globe. The 

 velocity of propagation for waves of mainly horizontal displacement is in fact 

 equal to ^(ffH), where H is the height of the 'homogeneous atmosphere.' If we 

 put H = 29500 feet, the most important type of free oscillation on a non-rotating 

 globe has a period of about 16 hours, the type being that of the semi-diurnal 

 tidal oscillation of an ocean of uniform depth. When we take account of the 

 rotation, the modes of oscillation and the periods are considerably modified. The 

 problem is virtually the same as in Laplace's dynamical theory of the tides, with 

 this advantage, that owing to the absence of barriers to the aerial ocean the results 

 are much more closely applicable to the actual circumstances. The calculations of 

 Hough (with the preceding value of H) show that the principal free oscillation 

 has now a period of about 12 hours. This result is of interest in relation to the 

 well-known semi- diurnal Aariation of the barometer. This is of very regular 

 type, uniform along each meridian, with maxima at 10 A.M. and 10 P.M. An 

 oscillation of this character might (except as to the phase) be regarded as a 

 forced solar semi-diurnal tide, whose period is very nearly coincident with that of 

 one of Hough's free oscillations. This would explain the comparative smallness 

 of the solar diurnal atmospheric tide, and might even be consistent with the small- 

 ness of the lunar semi-diurnal tide, since the amplitude of the 'resonance' falls ofl" 

 with extreme rapidity as the ditt'ereuce between the free and forced periods 

 increases. The difficulty is, however, in the phase, which is accelerated instead of 

 retarded. This cannot be accounted for by friction ; and the magnitude of the 

 phase-interval also appears far too great to be attributed to such a cause. There 

 seems to be no alternative but to adopt Lord Kelvin's view that the semi-diurnal 

 variation is a temperature eflect. The diurnal variation of temperature does not 

 follow the simple harmonic-law, and when analysed by Fourier's method will 

 have constituents whose periods are respectively i, ^, ^,...of a solar day. The 

 semi-diurnal constituent will be mainly operative owing to approximate co- 

 incidence with the free period already referred to. The phase remains to be 

 accounted for, but there does not appear to be any prima facie difficulty as to 

 this. It should be mentioned that the Ibrced oscillations due to variation of tem- 

 perature have been discussed mathematically on the basis of Laplace's theory by 

 Margules. 



We have next to consider the possible types of local and (relatively) small 

 scale oscillations of the atmosphere. The most obvious locus of such oscillations 

 is at the common horizontal boundary of two strata of dirterent densities. The 

 circumstances are here very nearly the same as if the fluids were incompressible, 

 and we may quote Stokes' formula for the velocity of propagation of waves on 

 the common boundary between two liquids in equilibrium, viz. : — 



" V IL • jTp}' 



where X is the wave-lengch, and p, p' are the densities of the lower and upper fluids 

 respectively. When p' = 0, we have V = v'(^X/2jr) as in the ordinary theory of 

 deep-water waves ; in the present case the potential energy of a given deforma- 

 tion is dimini.shed in the ratio {p-p')lp, whilst the inertia is increased in the ratio 

 (p + p')lp. VVhenp— p' is relatively small, the oscillations are exceedingly slow, 

 as in the case of a flask half-filled with oil and half with water, a phenomenon 



