THE HYDROSTATIC PROBLEM FOR THE ATMOSPHERE. 87 



point of the virtual-temperature diagram for a vertical in the atmosphere passing 

 through the station. If the curve could be continued upwards somewhat from this 

 point, we should be able to solve the hydrostatic problem for a vertical of moderate 

 height. The solution would give a perfectly satisfactory accuracy in sufficiently 

 small heights above the station, but of course decreasing accuracy with increasing 

 height. Experience would gradually show to what height the extrapolation might 

 be ventured. 



As a guide for extrapolations of the virtual-temperature diagram, table i6m of 

 Meteorological Tables has been constructed. It has been obtained by a statistical 

 study of the results of the international balloon and kite ascents for the three years 

 1901, 1902, and 1903. The table gives the correction, which should be added to 

 the virtual temperature at the station in order to give the virtual temperature at the 

 heights above the station figuring as argument. The little table headed " Under 

 the earth's surface " gives the correction for extrapolations downwards, based upon 

 the common supposition of a decrease of the temperature of 0.5 degree per each 

 100 meters, used generally at present for " reductions to sea-level " of barometric 

 records. 



An observation being given, taken at a station at the earth's surface, table 16 m 

 thus enables us to draw the virtual-temperature diagram for a vertical through the 

 station. The ordinates being the heights, we have to use the method shown in 

 example 2, page 72, for calculating from this diagram the heights corresponding to 

 given pressures or the pressures at given heights, negative heights below the earth's 

 surface being also for theoretical reasons included. 



We emphasize that table 16 m should serve only as a guide in extrapolating 

 virtual temperatures, and that it must be used with caution. Preferably a table of 

 this kind should be made for each meteorological station, based solely upon data 

 from ascents in air from this station. Great differences, dependent on the situation 

 of the station, would probably be found. Thus for stations situated on high isolated 

 mountains the temperature inversions (positive temperature corrections) given in 

 table 1 6 m in case of high pressure during winter, would probably not be found, and 

 the gradients under ordinary conditions would probably be found smaller than 

 above low land. When these gradients are determined by ascents undertaken from 

 mountains, the value of meteorological observations at stations on mountains will 

 be very much increased. 



59. Extrapolation of Average Virtual Temperatures. The method devel- 

 oped in the preceding article is important, because it enables us to find the hydro- 

 static state of the atmosphere near the earth's surface every day by common 

 meteorological observations, quite independently of ascents in the air. Since it 

 therefore furnishes methods which at once might be introduced into the daily 

 meteorological work for the forecast of the weather, it will be important to simplify 

 the operations to be performed as much as possible. 



If the problem be to find completely the hydrostatic state, both as to the height 

 corresponding to any given pressure, and as to the pressure at any given height, no 



