On Diurnal Variation of Birometric Pressure. 21 



when tlie lieating is effected sufficiently rapid, we may take (2) as 

 a rougli approximation. Next, let us assume that d is of tlie form 



where dX^) is ^^^^ variation of temperature at sea-level and is a 

 function of x and t only, while A^^) is the function of z only. Tlie 

 latter assumption amounts to saying that the variation of tempera- 

 ture at z level is proportional to tlie variation at sea-level. Then 

 we have 



To simplify the matter, we idealize the case still further and assume 

 that the elevation C is nearly constant for a siuall finite altitude 

 near the surface. Then, if we are considering only the initial stage 

 of the motion where the pressure gradient near the earth' s surface 



is still insignificant, we may put u=o^ -^ — =o at z=o. Hence 



we have 



_g dd. 



tjyj?'d'M''- ^'^ 



In this integral, p{z) may for the present purpose be considered to 

 ])e the mean value independent of the variable part of the temper- 

 ature. It may therefore be regarded for the rough approximation, 

 as the function of ,~ onl}^, say -^^), 



""^'^ = IaO-'^IM''- ^'^ 



Then the total fiow of mass througli tlie infinite vertical plane 

 parallel to yz, is given by 



U = l^updz = -^^---?^f^'oF(z)dz. (5) 



Jo /J- dxJo ^ 



The latter integral is a constant and may be denoted by /. The 

 rate of cliange of the barometic pressure p at sea-level will be ap- 

 proximately given by 



