PAPER BY MAX MARGULES. 315 



From this we develop the continued fraction as before, and compute 

 the ratios of the constants. But (u is not now indeterminate, but its 

 value is immediately found to he—Cq-,; hence [sfeFerrel, ]>. 320] 



«8= — C(/>Mt. • . . 



T=C »in^ comi {2nf-\-2X) i 



f=C'sin (2»/+2A)[a'48in*&94-a'6sin'^(i?4-o'8sin''cj+. .| ( * (^^^ 



For iJc = 40, = 10, = 5, Laplace has computed the constants. Only the 

 middle valae of these is of interest for our problem. I have in addi- 

 tion executed the computation for some neighboring values of l\ 



4Ji = 10. 10.94 11. 11.1 11.2 12. 



To=298o.7 2730.0 2710.5 269°. 1 2660.7 248^.9 



«4 -6.196 -37.99 -55.00 -247.8 101.8 . 8 270 



a^ -3.247 —23.06 -33.68 —154.2 64.3 5.919 



a^ -0.724 - 5.75 - y.46 - 39.2 16.5 1.(162 



orio- 0.092 - 0.81 - 1.20 - 5.6 2.4 0.2G0 



^,2-0.008 - 0.07 - 0.11 — 0.5 0.2 0,026 



These numbers confirm Thomson's expectations, that the period of 

 the free vibrations of this kind, for a rotating spherical atmosphere 

 of ordinary temperature, lies very near 12 hours. Instead of so de- 

 terminiugthe velocity of rotation of the earth that the period shall agree 

 ■exactly with a half-day, we can choose a corresponding tem])eratiire. 

 It lies near to 268°. At this ])oiut a^ passes from — x over to + x. 

 In the neighborhood of this value forced vibrations must lead to enor- 

 mously great amplitudes. Therefore a slight semi-diurnal wave of 

 temperature would sufi&ce to produce a very great wave of pressure of 

 the same period. At temperatures below 268° the phases of both are 

 in agreement; in other cases they are opposed. 



For 4A;=10, or To=298.o7, we obtain at the equator 



£=-10.26 C sin {^nt+'lX) 



298 7 

 Therefore, a temperature amplitude of 0.038°= =7— — :^7i-7Tr. would suf- 

 ' ^ 760 X 10.26 



fice in order to produce a pressure amplitude of 1 mm. 



The comparison of the atmosphere with a spherical shell having a 

 •constant temperature of 298°.7 gives, as we shall see, the lunar tide on 

 the equator much larger than it is, as deduced from observations. Sim- 

 ilarly one must require corresponding large temperature amplitudes 

 in order to produce the observed semidiurnal pressure amplitude of 

 1 mm at the equator. In view of the great imperfections in the as- 

 sumptions no importance can be attached to the numerical values. 



This computation only shows that in order to produce semidiurnal 

 variations of pressure of the same amount as the diurnal variation much 

 smaller temperature variations will suffice. 



