PAPER BY MAX MARGULES. 309 



with the following relation between A and B 



With the same constants as before 1° variation of temperature on the 

 equator gives G.U mm. variation of pressure. 



On tlie occasion of the computation for the rotating sphere we shall 

 again have opportunity to explain that the particular integrals that 

 we, in both cases, have given as the solution ot the difi'erential equation 

 (11) contain the complete solution for the whole spherical shell. 



If we put ©1 for the duration of the vibration for single waves for 

 which B is infinitely large, and similarily 02 for the double wave, then 

 we have 



2 ;r 2 7tS 



©1 = 

 = 



2 7t 2 7t S 



-«2~ vitrt: 



These are the values of the periods of free vibrations of a spherical 

 shell. Lord Kayleigh {L. E. I). Phil. Mag. Feb. 1890) investigates only 



such and finds (by putting-Ji^^'o -^ for the velocity of propagation 



instead of -/ iiJ To) for the atmosphere on the earth at rest ©i = 'SS.S 

 hours and ©j = 13.7 hours ; theretbre the first is much nearer to 24: than 

 The second is to 12 hours. He remarks however that it is doubtful 

 whether one ought to adopt the Laplaciau velocity of propagation for 

 vibration of such long duration. 



Therefore the relative magnitudes of the semi-diurnal variation of 

 the barometer still remains a riddle. But this is so only so long as we 

 confine the calculations to the sphere at rest. 



VIII. CALCULATION FOR A ROTATING SPHERE. 



Diurnal wave. — In this case also the calculation will be carried out 

 only for air in a spherical shell whose thickness is small in comparison 

 with the radius S of the sphere, and also under the further assumption 

 that the movements are horizontal, and that therefore a=0. [This lat- 

 ter assumption and the omission of the first of equations (10) are cer- 

 tainly not unobjectionable; they are imitated from the analogous pro- 

 cesses in the theory of the tides.] The difference between the sidereal 

 day and the solar day is not considered, and r=n. 



B To c)f :)b o 



p-^-^— =^— 2nc cos 00 



8 ^00 dt 



_?^^Jl—=^l+2nhco8co ) . . . (10a) 

 S sin oodX dt ' 



^s dr\ , 1 ( cM^sin a?) Jc » _ 



o/^_^A_, l_ i Hbsm g?) c'c » ^^j 



\:)t dtj'^siuoo} ;)oo """^/l ♦ 



