CORRECTION OF THE HEIGHT OF THE BAROMETER. 



-f- • • . : or, if we express x in the powers of y, x zz b y 1 -f> 



2 l y 3 



+ ... . For example, in the case of water 



3 q + 24mb 



rising in a tube an inch in diameter, q being # ]51, and b — 



— — - — 6*55, we have, for an arc of 30°, Sin. 30° — 



2 m 2 r 



•5 = 13*1 2 — 50 z % — 145*6 z 3 , whence z — '05, or perhaps 

 •0505, x = -0l6l, and y — -0483. But for this value of 

 y, x ought to be but about *0153 : and this difference, as 

 well as the numbers obtained from the properties of the 

 cubic parabola, shows onty that it would be better to ex- 

 tend the calculation to an arc of 70° or 80* by the first se- 

 ries, if great accuracy were required. According to Mr. 

 Gay-Lussac's experiments, m is more correctly, in the case 

 of water '0115 ; in that of pure alcohol *0047. 



For a surface of simple curvature, the primary equation Surface of ska 

 is fy x A/U 1 + /) - mj, and the coefficients of the first P le curvatl "~ 



series become b — - , c zz b 3 -I , and d zz <2 b s 4~ 



2 m 12 m' 



\ — t. r *• the ratios of the last terms being , 



30 m 360 m* ° 5.6m 



, and so forth : and n = 4 b x 3 + i c x 5 -\- i , d x -4- . . . : 



7.8m. 



and from this series we may calculate the elevation of a fluid, 

 between two plane surfaces. 



I am, Sir, 



Your very obedient servant, 

 3 Sept. 1809, . E.F.G. H. 



II. 



