Mr Galbraith's Barometric Measurements of Heights. 321 



This result 12058.6 feet is the approximate height without the smaller 

 corrections depending on the remaining terms of the series, or the effects of a 

 change of gravity depending on the latitude or the height of the upper baro- 

 meter. The effect of the remaining terms of the series may be found aa 

 follows : — 



10.634 S* 



49.(;94 - 0.214 - /3 ; therefore ^ = 0.015265 =± y 



g-'= 0.000410 = S 



H^ , * 



- = 0.000014 =- £ 



7 



Sum, =0.015698 =:}.+ 5 + £ 



"Whence 12060 X 0.015698 = 189.79 feet. As the coefficients in the for- 

 mula are derived from measurements adapted to the mean latitude of 45°, the 

 effect of the change of gravity depending upon the latitude should also, strictly 

 speaking, be allowed for, which is derived from the factor 1 + 0.00268 cos 2 x, 

 where X is the latitude of the place of observation. Since the latitude of the 

 Peak of Teneriffe is about 2^' N., this factor becomes 1 + 0.00268 x cos 57" 

 = 1 + 0.00268 X 0.545 = 1.00146. But 12058.6 + 189.8 = 12248.4 ; hence 

 12248 X 0.00146 = 17-9 feet to be added to 12248.4, making 12266.3 feet. 



If an allowance be made for the diminution of the force of gravity of the 

 air on account of the height of the upper barometer above the lower, it 

 would be a third proportional to the radius of the earth and the approximate 

 height • ; or if A; be the correction on this account, r the radius of the earth, 



and h the approximate height, k = —,r may in general be taken at 20887680 



feet. Hence k = -f 7.2 feet, which being applied, the height is 12273.4. feet. 



The last correction is the diminution of the gravity of the mercury for the 



height. It is a fourth proportional to the radius of the earth, the approximate 



height, part of formula (8.) or 48400 + 60 (i( + <')• Let k' be this correc- 



, A{48400+60(< + i')}. ^^ , . , 



tion; then ft = — ^^ Now, h is about 12270, and 



12270 X 56500 

 48400 + 60 (^ + t') is 56500 ; whence k' — — 20887680 ' ~ ^^-^ ^^^'' ^^'ich 



added to 12273.4, gives 12306.6 feet for the total height. 



It is therefore evident, that in great heights, where all the more minute 

 corrections are sensible, the operation becomes very tedious. II would then 

 be more convenient to have logarithmic and special tables calculated ex- 

 pressly for the purpose. But in all moderate heights, where these smaller 

 corrections become nearly insensible, the formula or rule may be very advan- 

 tageously employed. It may be interesting to show the correspondence be- 

 tween different methods of calculation by various authors. 



• Playfitii's Works, vol. iii. page TO. 



