PAPER BY MAX MARGULES. 297 



observational material from all lauds and oceans with the object of 

 establishing a basis for a further matbematico-physical theory. 



In order to attain this, one must first treat the phenomenon under 

 assumptions that simplify the labor. I believed that some computations 

 as to the variations of pressure in air that is periodically heated would 

 contribute to the better understanding of the diurnal variation of the 

 barometer. In the course of the work, it appeared that the computa- 

 tion must not be confiued to the si.nplest cases if one would make it 

 useful to a certain degree. For this reason the investigation has grown 

 to a larger size than was desired by me. 



Before giving the detailed computations let the review of certain 

 results take precedence. Let T and p indicate the absolute tempera- 

 ture and the pressure of the air when at rest; T '(l + r) and p (l + £) 

 indicate temperature and pressure of air in motion. When r is given 

 as a periodic function of the time t and of the locality x then e will also 

 appear as such a function. 



Let a wave of temperature 



with constant amplitude move in the direction— x in a plane layer of 

 air upon which no other forces are acting. 

 This will produce a wave of pressure 



L 2 „•_ 9 /' t , x 



where c indicates the velocity of propagation of a free vibration when 

 the process is strictly isothermal; in air at the temperature 273° we have 

 c=280 metres per second. 



If we assume the length of the wave to equal the circumference of 

 the equator then for a period whose duration is one day and for a pres- 

 sure p expressed as 760 millimetres of the barometer a variation of 

 temperature of one degree will produce a variation of pressure of 4.4 

 millimetres. 



Both temperature and pressure vibrations have the same phases 



when their velocity of propagation fv—^ J is greater than c, but op- 

 posite phases when it is smaller than c. If V=c then will e be indefi- 

 nitely large, as must occur in the case of a frictionless medium when 

 the forced vibrations have the same period as the free. Again, 

 let a wave of temperature similar to the preceding advance in a 

 plane stratum of air, subject to the influence of constant gravity. The 

 air now moves horizontally in the direction of the progress of the 

 wave and also vertically. The pressure wave on the ground is given 

 by an equation similar to the preceding only in the numerator c 2 & 2 is to 

 be substituted for JA For the equator, the day and 760 millimetres, a 



