THE HYDROSTATIC PROBLEM FOR THE ATMOSPHERE. 63 



273 -\-t instead of 9, r being the virtual temperature counted from the freezing-point 

 of water, we get this expression for the thickness of the standard sheet: 



() H nn _ x = 28.7 (273 + T nn _ x ) nat. log. 



1 



Height (2) can evidently be found as the sum of a certain number of heights given 

 by formula (a). 



The determinations of the heights (1) and (3) are different forms of one problem, 

 namely, the determination of the distance H np from a certain standard suriace of 

 pressure n to any isobaric surface of pressure p. By the fundamental formula this 

 distance is 



H, P = 28.7(273 + t) nat. log. j 



t iP being the average virtual temperature for the sheet of air between the isobaric 

 surfaces n and p. This formula containing two continuously variable quantities, 

 T p and p, is not immediately suited for tabulation. But it may be written as a 

 sum of two terms, a principal term H containing only one variable p, and a cor- 

 rection term A// containing two variables, namely, H and t. We thus write 



(b) H n , v = // + AN 



giving H and A// respectively the values 



b') IT, = 7835 nat. log. ^ 



Thus, tabulating the three formulae (a), (b'), and {b"), we shall easily be able to 

 calculate the height from any isobaric surface p a to any isobaric surface p b , the 

 required values of the virtual temperature being given. Only three tables would 

 therefore be necessary. But for practical reasons, however, we shall give two dif- 

 ferent tabulations of formula ('), arranging the table in a special form for the 

 important case of p a being the pressure at the earth's surface. Thus in the second 

 tabulation of formula (b') the height (1) is the height from the ground to the 

 nearest standard surfaces. We then get the following four tables. 



(A) Table 9 m. Mutual distances measured in dynamic meters between 

 standard isobaric surfaces. This table contains nine small tables in succession, 

 each giving, according to formula (), the thickness of one of the standard sheets 

 of the atmosphere for practically occurring values of the average virtual temper- 

 ature. These successive tables are separated the one from the other by horizontal 

 lines representing standard surfaces, the pressures of which are added in millibars. 



(B) Table 10 m. Distances in dynamic meters, measured from the stand- 

 ard isobaric surfaces to points of given pressure, the average virtual temper- 

 ature of the sheet being o C. This table contains ten small tables in succession, 

 calculated according to formula (b r ). Each gives the distance from one standard 



