CORRECTION Or THE HEIGHT OF THE BAROMETER* 

 Z 4 2 6 



- + (aB + iA + c+3A(«A + 6) + 5Bo) 7 + 

 4 - o 



. . . , which must be equal to m x -^-, or to 2 to b z 3 -\- 



z 



(4mc + 2 m b A) 2 4 -f (6md+4mcA + 2mb B) z 6 

 a «A + 6 + 3 An. — S m b A 



+ . . • ; whence b zz 



and d zz 



Am 16 m 



aB+JA4-c + 3A (« A + 6) -f sB«- 



3b w 



?4mcA — I2m&B . , b b 3 



: anc l, by reduction, c zz —z — , 



J 16 »i 3 ' 



_ b 4Lb* <2]S _ b 302 b 3 



~~ 5?6 m* 45 to 45 * * "" 36864 m s ~~ " 26880 ??i x 



122 6 5 b 1 . , 4 , _ A 2 2 6* 



-1 , and A =z — 4 6 s , B = -1 , 



4032 TO 315 10m 15 ' 



t r — £ ; + - > and JJ zz — — - — . 4- 



672 m z 35 m 315 20736 to* 



493 b* b« 2 b* „ . .... 



-f- • Here we may observe, that 



45360 »#i 8 70 to 2835 



in the series for finding the value of y, the coefficients of 

 the terras involving the lowest powers of b are the same as 

 in the former case, and that there is a similar approxima- 

 tion to the ratios of 8 and ]6 in the neighbouring terms, so 

 that we may safely continue the series on these foundations: 

 the coefficients of the highest powers may be found by thig 



4 4 4 4 4 4 



progression, 1, , . — -, . . , which, 



1 s ' ' 3 . 4' 3 . 4 5 . 6 3 . 4 5 . 6 7 . S 



for the reason already mentioned, must represent the versed 



sine of a circular arc. In the series for x, the coefficients 



2 2 3 2 3 

 of the first terms form this progression: — , — . — , - . ■ — 

 10 3 5 12 7 12* 



523_57„2 3 5 79 

 4' 9 ' l c 2 3 ' 4* .', 5 



_ J_ a . _ _ _ o 1 1 



li 12 4 4 3 5 6 



2 3 5 7 9 11 , , 212 



— . — « • -* • - 2 • 7z • — • 2 3 • 3 2 . 4, or - . - , - 



13 12 s 4 4 5 3 Z 7 3 15 



3 2 3.5 



2.2.3 7 2.2.3.2.2.3 







3.5. 



9 



2. 2.3.2.2.3 





7.2 



