Temperature of Mercury in a Siphon Barometer. 263 



R2 t'''-t 



t" — t 



t" -t 



— ;(35) 



a"-a-jr/T—^{a"'-a) 



which is the same as (32). 



In hke manner, substituting in (31,) and resolving for {f — t), 

 we have 



t'=t-{-. 



^tn_t)\a/-a-^X^'-b)] 



r- 



(36.) 



a" - a-^{b" - 5) + {t" - t)e'[a" -a' -^^ {b" - b')] 

 Neglecting the fourth term in the denominator from its minute- 



ness, we have 

 t'=t-\-- 



t"-t 



- [a'-a~^,{b'-b)l (37) 

 a"-a-^,{b"-b) 



In these last four equations («',) [a",) {b',)(b",) are the read- 

 ings after being corrected, if necessary, for the heights of the 

 meniscuses. These formulae are sufficient for determining the re- 

 lative diameters of the two branches of the siphon, and the mean 

 temperature throughout the mercurial column. 



An example will serve to illustrate the process. , 

 To test No. 366 Bunten's mountain barometer, and to deduce 

 the formula for the temperature of the mercurial column, I made 

 the following observations. 



The second observation is any one of which the temperature 

 is demanded. The remaining three were taken agreeably to the 

 suggestions under (10.) And it is farther important in this case, 

 that at least two of the upper readings should differ considerably 

 from each other in value ; which may be effected by observing 

 at the base, and on the summit of a hill, or under different at- 

 mospheric pressures at the same place. In this example, how- 

 ever, owing to the accidental loss of the barometer, the difference 

 between any two upper readings, is not so great as it ought to be. 



