PAPER BY MAX MARGULES. 299 



the amplitude of the half day term will be <;reater than that of the 

 whole-day term." 



This predictiou is completely verified. When we execute the compu- 

 tation for an atmosphere considered as a rotating spherical shell in 

 which waves of temperature advance from meridian to meridian ac- 

 cording to the equation 



T = C sin GD sin {nt-\-\) 



(where oo = Polar distance, A = geographical longitude, n = velocity 



of the rotation of the earth), then we find for To=273" the wave of 



pressure 



*=6' sin {rit-\-X) [1.146 sin 09—0.423 sin^ a?— 0.370 sin^ ca— 0.100 sin'' oa 



-0.018 sin^ &3-0.002 siu^i oo— . . . ] 



When however at every place the wave of temperature repeats itself 

 twice daily and we assume 



T = C sin^ 00 sin (2u^+2/\) 

 then there results 

 £=-C sin (2w^+2A) [37.99 sin^ cc9+23.06 sin" oo 



+5.75 sia« gl»+0.81 sin^" 094-0.07 sin^^ fy+ . . . ] 



The law according to which the amplitude of the temperature wave 

 diminishes from the equator toward the pole has been assumed ditier- 

 <?utin the two cases only because of the easier computation; this how- 

 ever is of slight influence in the general result which is, that for ecpial 

 variations of temperature the resulting variations of pressure become 

 much greater in the double daily wave than in the single wave. 

 The coefficients of the first sine series vary OMly very slowly with T^ 

 (or with n when we, as Thomson does, consider the period as the 

 variable^. It is otherwise in the half-day wave ; here the factor of 

 4sin* oo in the neighborhood of To =208° passes, from — oo over to + xi 

 precisely as in the plane wave before considered when the ve- 

 locity of propagation of the forced vibration is made equal to that of 

 the free vibration. Thus slight semi-diurnal waves of temperature of 

 scarcely appreciable amplitude are sufficient to produce greai waves of 

 pressure in frictionless air if we assume the temperature of the spher- 

 ical shell to be in the neighborhood of 208°. 



Thus far the computation. Its application to the dail^- variation of 

 the barometer is only clear as to one i)oint. The semi-diurnal wave of 

 pressure may be considered as a consequence of a semi-diurnal wave of 

 temperature of small amplitude. Thus is explained the relative magni- 

 tudes (of the diurnal and semi-diurnal temperature and pressure waves) 

 but not the uniformity of the semi-diurnal variation of pressure over 

 the land and the ocean. This uniformity has led Hann to seek the ori- 

 gin of the phenomenon in the absorption of heat by the upper strata 

 of air. But the lower strata have also a semi-diurnal temperature va- 



