( 584) 



Grenander. Les gradients verticaux de la temperature dans les minima 

 et les maxima barométriques. Arkiv för Matematik, Astronomi och 

 Fjsik. Band 2. Hefte 1—2 Upsala, Stockholm. 



Of the results which Hann has given, up to a height of 12 kil., 

 I have taken the means of groups of 3 months, which are printed 

 in table I by the side of the values I had obtained ; the agreement of 

 the two results, which for the greater part have been deduced 

 from different observations, is very satisfactory. 



Grenander in his paper chiefly considers the relation between the 

 changes of temperature and the barometer readings; his results cannot 

 therefore be compared with mine directly, but probably we are most 

 justified in comparing the variations of temperature at barometer 

 maxima, with those which I have computed for clear weather. For 

 great elevations, till nearly lb kil., GRENANDER also obtains with 

 increasing height a small decrease of temperature. 



It is difficult to state with what degree of precision the tempe- 

 ratures of table II represent the mean values for the different seasons; 

 the deviations, especially at greal heights, may perhaps amount to 

 some degrees, hut certainly they represent the mean distribution of 

 temperature better than the values adopted in the various theories 

 of refraction, and we can therefore derive from them more accurate 

 values for the refraction. 



4. Tt is hardly possible to represent the relation between the 

 temperatures in table II and the heights by a simple formula, and 

 to form a differential equation between the refraction, the zenith distance 

 and the density of the atmosphere at a given height, which can be 

 easily integrated. 



Therefore I have followed another method to determine the refrac- 

 tion corresponding' to the distribution of temperature I had assumed. 



According to Radau's notations (Essai sur les refractions astrono- 

 miques. Annates de l'Observatoire de Paris. Mémoires Tome XIX), tlie 

 differential equation of the refraction, neglecting small quantities, is : 



fl- l ±(y-Ss^dm 



Is = a" ; ^— ^ ; rrr • (0 



\/ 



«*»* + 2^(y-«»)- (|y-2J 



an 

 R 



Here is : 



R radius of the earth for 45° latitude, 

 r radius of the earth for a given point, 

 h height above the surface of the earth, 



