( MS ) 



and, following Hergesell's advice, I have used only the temperatures 

 observed during- (lie ascents, a* during the descents aqueous vapour 

 may condense on the instruments. 



It is evident that for the determination of the refraction, as a cor- 

 rection to the results of the astronomical observations, we must 

 know the variations of the temperature at different heights with a 

 clear sky. For the temperatures, especially of the layers nearest to 

 the surface of the earth, will not be the same with cloudy and 

 uncloudy weather, as in the first case the radiation of the earth will 

 lower the temperature of those layers, and so cause an abnormal 

 distribution of temperature. It is even possible that in the lower 

 strata the temperature rises with increasing height, instead of lowering, 

 as is usual. 



For this reason I have divided the balloon ascents into two groups, 

 1 st those with a cloudy sky, 2 nd those with a clear or a partly 

 clouded sky. 



In working out the observations, I have supposed that for each 

 successive kilometer's height the temperature varies proportionally 

 to the height, and after the example of meteorologists, I have deter- 

 mined the changes of temperature from kilometer to kilometer. For 

 this purpose, I have selected from the observations, made during each 

 ascent, the temperature-readings on those heights, which corresponded 

 as nearly as possible with a round number of kilometers, and I 

 have derived the variations of temperature per kilometer through 

 division. 



The available differences of height were often less than a kilo- 

 meter, especially at the greatest elevations; in those cases I adopted 

 for the weight of the gradient a number proportional to the difference 

 of heights. Sometimes on the same day, at short, intervals several 

 ascents have been made at the same station, or at neighbouring 

 stations, from which the variations of temperature at the same heights 

 could be deduced. In these cases I have used the mean of the 

 results obtained, but I assumed for that mean result the same weight 

 as for a single observation, as the deviations of the daily results 

 from the normal distribution of temperature are only for a small 

 part due to the instrumental errors, and for the greater part to 

 meteorological influences. 



3. The observations which I have used, were the following: 

 from publication I, 31 ascents of which 12 had been made in pairs 

 on the same day, so that 25 results were obtained ; from publication 

 II, 38 ascents all on different days; and from publication III, 170 



39* 



