Temperature of Mercury in a Siphon Barometer. 265 



These formulas may be used, not only to determine the tem- 

 perature of the mercury, but, supposing this to have been ascer- 

 tained by any other means, to verify the correctness of the ob- 

 servations ; as for example, the correctness of the readings and 

 temperature (a',) {b',) (t^,) would be verified by their satisfying 

 equation (38.) 



If, in any case, doubt should be entertained as to the parabolic 

 form of the meniscus which in (12,) makes F(H)=^H, we can 

 put F(H)=BH ; B being an indeterminate co-efficient. Then as 

 from (12) to (16,) a'—b' would be changed to a'-b'-\-B{B.-{-h 

 — H' — /i') ; and from equation (10) we should have 



a'-b' -{a-b)-i-B(HL+h-B.'-h')={A- A') (f—t,) 

 a'^-b''-{a-b)+B{B.-j-h-lI,-h,) = {A-A'){f'-t)-JI, 

 and h, being the altitudes of the meniscuses for a/^, b". 



These two equations give the numerical value of B — . To de- 

 termine the form of the meniscus from this value of B, we have, 

 regarding its vertex as the origin oi o^Qoi^msX^^^ fny^ dx=.nBy'^ x. 



1 — Bdxdy 

 Differentiating, &c. -nB = — Integrating and returnmg to 



numbers, we have 



2B 



cx=y ~ ; in which (C) is the correction. This is a parab- 



2B 



ola, if . _p is positive, which becomes the common one, when 



2B 

 B=J. If 1 _ p is negative, it is an hyperbola; which is the 



common one, if B= — 1. But the hyperbolic form, it is evident, 

 cannot subsist in a mercurial barometer. Various consequences 

 from the above formulee, and remarks relating to the construc- 

 tion of the barometer, and the necessary precautions to be taken 

 in observing, my limits compel me to omit. 



