On Diarnnl Variation of Earometic Pressure. 



13 



of ß(z) and thence the vakie of /, nor upon the influence of h(;x) 

 wliicli we assume small, and carry through the application a little 

 further on some appropriate actual problems, to see how far the 

 formula may be utilized for the explanation of the phenomena in 

 question. __ 



4. Suppose a temperature wave proceeding toward the posi- 

 tive direction of x, West say, over the earth's surface idealized as 

 in the preceding paragraph, such that 



O-r 



6, = aco^-^{t—^ + <f\ 

 1 V 



(7) 



where T=2,4: hours and ?;=2rr/24 per hour. Taking the origin of 

 time at noon at the origin of x, —<p gives the retardation of the 

 temperature maximum after noon. Let us assume f constant and 

 only a as a function of x. Then 



I dp _ d-d _/ d-a 



/ T \ Ü J dx T \ V V. 



{-^+.), 



(8) 



G dt dx'- ^ dx' 

 Integrating, we obtain 



2-/ \ (d'a \ • 2-/, X , \ r^da 2-/ 



- — P — P'. = — a sm t — + if —2 cos 



CT\^ ^ I \dx' J T \ V ^1 dx T \ X 



Avhere j9o is the mean value of p. Putting the expression of p—]jj 

 in the form as given by Angot, and transferring the origin of time 

 to midnight, we have 



p—Po = «1 cos(??i + ^j) 



where 



(9) 



(10) 



V dx 

 If a be constant in a special case, and (p be —2'''-', we obtain 

 'Pit' ~^'^^ or 240°, i.e. the maximum must occur at 8'' a.m.'-* 



1) Taking into account the retardation of the temperature maximum in higher levels, 

 — 3'' may have been preferable, which gives '1/1 = 225°, i.e. the maximum occurs at 9'' a.m. 



2) The result is not v. ry far from truth, except for some elevated stations and for high 

 latitude. The inversion of the phase in the latter case will be considered later. 



