318 Mr Galbraith's Barometric Measurements of Heights. 



Wherefore substituting these values of c, m and e in formula (7), then 

 H = 52250 { 1 _ 0.0736 + 0.00115 + } A « = 

 52250 {0.9264 + 0.00115 (< + /')} /5 « = 



{484.04+60(i + <')} /3 s (8.) 



in which such a number of terms of s or of 1 + i /5* + | /3* + j /S* + &c. may- 

 be taken as are thought necessary. 



This formula (8.) gives the height when the mercury in the barometer is 

 reduced to the same temperature at both stations, either by a formula or ap- 

 propriate tables. The absolute dilatation of mercury from the recent deter- 

 mination of Dulong and Petit is '^tn * ft"" on^ degree of the centigrade scale, 



or gggQ equal to jqooo "^^''^J ^^ Fahrenheit. Whence if t be the tempera- 

 ture of the mercury at the lower station by the attached thermometer, and t' 



(r _ r') b 



that at the upper, then iqqqq must be added to the height of the baro- 

 meter at the colder station (generally the upper) to reduce it to the same 

 temperature as that of B at the warmer station. 



Now, this correction is in general a small fraction of an inch of mercury, 

 and it would simplify the operation to obtain its equivalent in feet to be ap- 

 plied to the approximate height, by finding the variation for 1 inch of mer- 

 cury, and of this taking a proportional part for the expansion for 1° of Fah- 



B — b 

 renheit. Thus K X -„ , , = PI' will give a result in any circumstances suf- 

 ficiently correct for the difference of an inch between B and b, iu which 



(,- ^\b 



K = 48400 +QO{t+t'); therefore iqqqq will give the fractional part of 



H' in feet, required to correct the result from formula (8) also in feet, for 

 the difference of the temperature of the mercury at the two stations. 



(<T r') S (t T')b 



Therefore 1 inch : ,,.»„„ : : H' : H' X iqooq ' ' ^^^^ i^ 



B — a (t— /)& _ K B — ^> 

 ^^B-l-6^ 10000 "lOOOO^B + fi^^'^~"^^ 

 Now, B — b and r — t' being each assumed at unity, 

 K B_i , ^,^ K6 



ioooo^B^Fl^(^— ^■'*^'''^°°'^'Iooo(r(BT4) (^•) 



But in this case also B, differing only by unity from b formula (9), becomes 

 without sensible error, 



K b K 



10000 ^26 20000 C^) 



K 48400 + CO (<+ Feet. t + 1' ,., .,, , „ 



°^ 20000 ~ 20000 ~ "^"333' °'^' ■*^°^'^" ^^"^ ^^ ionnA suffi- 



ciently accurate in practice, x being the co-efficient of r — t', then 

 t + i' 

 « = 2.42+3^ (!'•) 



Whence the complete formula will become 



Lai'lace made this . , which has been corrected as above. 



