PAPER BY MAX MARGULES. 305 



Under the assumption that —= is a small quantity we have 



or 



h . h 2 





a a 2 



k~h 1 ' 



and when we retain only the first two terms of the exponential series 

 we obtain 



e = A QK + az ) siU (>™+ nt )= A (l^i+«) sin 27r (1 +X l)' 



For J>=4xl0 7 , 0=24x00x60, we obtain 



e=A (0.576+0.000125*) sin (mx+nt). 



The relative variations of pressure near the earth's surface increase 

 very slowly with the altitude. At the surface of the earth itself the 



variations of pressure are appreciably smaller in the ratio of i : -^ ? 



than in the example of the third section, where purely horizontal 

 vibrations occurred. A daily variation of temperature of 1° C. would 

 in the present case cause a pressure variation of 1.6 mm . The phases 

 of both vibrations occur simultaneously when L > c@. 



V. A SIMILAR COMPUTATION FOR THE CASE WHEN THE AMPLITUDE 

 OF THE TEMPERATURE VIBRATION DIMINISHES WITH THE 

 ALTITUDE. 



The differential equation (4) becomes 



*? + #* a jz gjt 2 - a ?z gd# 

 To the assumption r = Ae~ sz sin (mx + nt) there corresponds 



€ = (Be- S2 + Ke kz ) sin (mx+ nt) 



B(s 2 +as + h) = A (— - a 2 - as ) 



fe= 2~V4- ft 



h has the same meaning as before. K stands for ffj and K, disappears 

 under the same limitations as before, (namely, that the result is to be 

 applied only to altitudes that are slight in comparison to Z), 



. 80 A 20 



