292 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



vations, is a "curve of condition," whereas the curves that I have 

 drawn in my memoirs on thermodynamics are "curves of changes 

 of conditions." 



The curves of dependence of temperature on altitude that are 

 always used in the description of individual balloon voyages are 

 in most cases, strictly speaking, neither curves of condition of the 

 vertical column of air nor yet curves of change of condition ; they are 

 rather representative of the successive conditions that the balloon 

 has met during its flight. 



If the ascent is very rapid (and the greater number relate specially 

 to the ascent), then the curve can be considered as approximately the 

 curve of condition along the vertical; but if the balloon floats in 

 equilibrium without any ascensive power and in company with the 

 air surrounding it then the diagram does actually present the curve 

 of change of condition. If the balloon has attained an altitude 

 where the diurnal period is very small and if the horizontal path is 

 not too long the curve will to a high degree of approximation pre- 

 sent the condition of the vertical column. 



These approximations may be pushed further especially when we 

 have observations at the points on the earth's surface immediately 

 below the balloon, which allow of a reduction of the individual 

 observations to a definite moment of time. The extent of the 

 error that may be made by the use or neglect of these reductions 

 can be seen exactly from the curves in dotted lines connecting the 

 values at the earth's surface with those observed simultaneously in 

 the balloons. Especially instructive in this respect are the curves 

 in Vol. II (of the Wissenschaftlichen Luftfahrten) for ascensions 

 No. 12, p. 136; No. 18, p. 188; No. 19. p. 202; No. 25, p. 274; 

 No. 32, p. 332, and others, which will be easily recognized by 

 examining the dotted straight lines. 



Where the results of many voyages are united in an average 

 value the curves that represent the connection between the values 

 and the altitude can be considered as appro ximately the mean curve 

 of condition for the vertical column of air above the lowlands of 

 Northern Germany. The small systematic error that might be 

 expected for the reason that the lower parts of the curves belong 

 largely to the late morning hours while the upper parts belong to the 

 midday or early afternoon, is of insignificant magnitude. 



Now, before I proceed to speak in detail of the curves of results 

 published in this work (Wiss. Luftfahrten, Berlin, 1900) it seems 

 proper to apply the just-mentioned difference between the curves 



