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XIX. — On a Formula representing the Mean Height of the Barometer at the Level of 

 the Sea. By Professor Hansteen of Christiania, in a Letter addressed to 

 Professor Forbes, Secretary of the Royal Society of Edinburgh. 



Obsekvatoky near Christiania, 2Gth September 1846. 



Sir, — You have communicated to me, that the Royal Society of Sciences in 

 Edinburgh has done me the honour to elect me as a corresponding member. I 

 beg you to render my humble thanks to the Society, and to assure, that it shall 

 be my earnest wish to fulfil every task in my power which the Royal Society 

 should demand. 



That this letter may not reach your hands without any scientific communi- 

 cation, I subjoin the following : — From November 1822 to April 1824 inclusive, I 

 observed the height of the barometer in Christiania, and found the mean reduced 

 to 0° R., and to the level of the sea = 757"-763 = 335"'-913 lign. de Paris. As the 

 mean height of the barometer observed at Paris by Bouvard, and reduced to 0°, and 

 the level of the sea is = 337'"-53, 1 was surprised at the great difference of l'"-62 

 between Paris and Christiania. If jo denotes the pressure of the atmosphere at 

 the level of the sea, m and h the density of the mercury and its height in the 

 tube, g the force of gravity, we have^ = mgh, and, in another place, p'= mg'h'. 



If j/ =p is gh= g' h', or h' = - h. If, in the first place, the latitude is = (p, in the 



A., 1 9 1-0-0025911 cos 2d) , „ „„„, . • rh 



second, = (p', we have ^, = . ^^^^.^.^ ^, =1-0-0025911 (cos2 rf)-cos2 ^') ; 



y 1 — 00025911 cos 2 9 \ ~r ; •> 



h-h' ^ h, 0-0025911 (cos 2 <^ - cos 2 ^')- Taking (p = 0", (p' ^m\ we have 

 h -h' = l"'-74 ; and when <p = 48°-50' (Paris), (p' = 59°-55' (Christiania), we have 

 /* - h' = 0"'-32. But the observations have given for Paris and Christiania 

 h — h' = l"'-62 ; consequently, the mean pressure of the atmosphere is not the 

 in different latitudes (" Magazinfor Naturvidensk." 1824, page 282-291). 



Professor Schouw in Copenhagen has, in the Memoirs of the Royal Society 

 of Sciences at Copenhagen for 1832 (page 291-342), collected all the known obser- 

 vations of the mean height of the barometer, which, with exactness, could be re- 

 duced to the level of the sea, and to 0° R. In the following table I have added 

 the result of five years' observations here at the Observatory, and of the year 

 1844 at Bosekop. I have found that the observations can tolerably be represented 

 bythe formula 



^^ = 336"'-8097 + r"-3038 cos 2 ^ - 0"'-7478 cos 4 (i) - 0"'-9145 cos 6 ^ + 0"'-5435 cos 8 (p. 



VOL. XVI. PART. III. 3 O 



