THE HYDROSTATIC PROBLEM FOR THE ATMOSPHERE. 67 



in the air with meteorological instruments. It will be evident that, the hydrostatic 

 results contained in these schemes being once worked out, a set of supplementary 

 results of general meteorological interest might easily have been obtained. We 

 may for instance mention temperatures and humidities at given heights tor given 

 pressures, or average values of these quantities for given height-sheets or pressure- 

 sheets. But in order not to complicate the schemes we have taken up only what 

 is of interest for as full an illustration as possible of the developed hydrostatic 

 methods. 



The examples are derived from the observations obtained by the celebrated 

 balloon ascent by Berson and Suring from Berlin July 31, 1901, to the greatest 

 height yet attained by man.* The height of the station, Tegel at Berlin, was 40 

 meters or 39 dynamic meters above sea-level. The observed quantities during the 

 ascent were time, pressure in millimeters of mercury, temperature centigrade, and 

 relative humidity. From the general remarks in the preceding articles and by the 

 small examples added to each table in the Meteorological Tables, the schemes will 

 easily be understood. We shall therefore content ourselves with a few general 

 remarks. 



In the first example (page 68) we have made a direct use of the observed data 

 only supposing the pressure to have been observed in millibars instead of in milli- 

 meters of mercury. 



This first example being worked out, we have constructed the second, consider- 

 ing the calculated heights (column 24 of table J) as observed quantities, column 2 

 of table K. We have preferred thus to derive example 2 artificially from example 

 1, instead of taking an independent example, where the heights have been really 

 observed; for the analogy and the contrast of the methods are better illustrated 

 when both are used to work out the same case of atmospheric equilibrium. Com- 

 paring the two schemes, we see that the difference amounts mainly to an inter- 

 change of the order of the columns, followed by a passage from direct methods to 

 methods of estimation, or vice versa. 



In connection with this second example it is important to emphasize that a 

 observed heights should be considered only those found according to rational geo- 

 metrical methods, as for instance when the height of a kite is determined by the 

 angle and the length of the kite-line. The use, on the contrary, of a barometer with 

 height-scale instead of pressure-scale is unscientific. It gives less trustworthy 

 results, and at the same time additional labor; for the working out of the results 

 according to example 2 is more laborious than the corresponding work according 

 to example 1. In some cases both pressure and height may be observed. The 

 observations then give directly the equilibrium relation between pressure and 

 height. But on account of the imperfections of the aneroid barometer, the relation 

 found in this direct way will be much less accurate than that found by one of the 

 above methods, the observations either of pressure or of height being provisionally 

 set aside. The derivation of the results according to both methods, once omitting 



* Verofr'entlichungen des K. Preussischen Meteorologischen Instituts. R. Assmann und A. Berson : Ergebnisse 

 der Arbeiten am Aeronautischen Observatorium 1900-1901. Berlin, 1902. p. 227. 



