THE HYDROSTATIC PROBLEM FOR THE ATMOSPHERE. 65 



earth's surface gives by means of table iim an approximation~value H of the 

 height above the station of the lowest standard isobaric surface. By means of this 

 approximate value we may, with sufficient precision, take from the diagram the 

 average virtual temperature of the sheet. This temperature used in table 12M 

 gives the correction h, which added to the approximation value If gives with 

 sufficienfcorrectness the height of the surface above the station. Adding the height 

 of the station we get the height of the surface above sea-level. This height being 

 known, we estimate a value for the height to the next standard surface. This is 

 easily done with fair approximation by the inspection of the virtual-temperature 

 diagram and by comparison with the 'corresponding heights in table 9M. For this 

 estimate of height the value of the average virtual temperature is taken from the 

 diagram. Using this value in table 9M, we generally find the height to the next 

 standard surface with sufficient precision. Otherwise the operation may be 

 repeated, giving for every repetition a more accurate value. The final value of 

 the height found in this manner added to the height of the first standard surface 

 gives the height of the second standard surface. Then the distance to the next 

 standard surface is estimated, the corresponding average virtual temperature deter- 

 mined from the diagram, and this temperature used to find a better value for the 

 distance by means of table 9M, and so on. 



To complete the solution of the problem we finally determine the distance H nv 

 from one of the standard surfaces, the height of which is found, to a neighboring 

 isobaric surface of the given pressure p b . An approximation value H of the height 

 is found at once from table iom. Using this approximate value we find the average 

 virtual temperature of the sheet trom the diagram, and by means of this temperature 

 we find from table 12 m the correction A.I1, which, added to the first approximation 

 value H , gives the required height H nv . 



The second of the problems defined in section 49 is thus solved. 



53. Calculation of the Pressure at a Given Height. Let H be the given 

 height at which the pressure is to be found. We then determine first, as described 

 jn the preceding section, the height of the standard isobaric surfaces. Now, let -p n 

 be the standard surface whose height H n is nearest the given height h. The prob- 

 lem is then reduced to finding the pressure p at the height H H n above the 

 standard surface of pressure n. 



Now, the height H H n is the quantity tabulated in table iom, and the argu- 

 ment is the corresponding pressure p. Then if the average virtual temperature 

 of the sheet of air between the heights H n and // happens to be o C, table iom 

 used inversely immediately gives the required pressure. 



As a rule, however, this average temperature wilT have [another value, t. This 

 temperature being known, we can avail ourselves of a simple artifice, determining 

 a difference of height H' H n defined by the property of being the height, which, 

 used in table iom, gives the required pressure^. 



The difference of pressure corresponding to a given difference of height is in 

 inverse proportion to the specific volume of the sheet of air between the two heights, 



