bi 
a 
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)=3H, 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(H+h 
—H’—’); and from equation (10) we should have 
a’ —b’ —(a—b)+B(H+h—H’—h’)=(A - A’) (t’—2,) 
a’ — 6” —(a—b)+B(H+h—H,—h,)=(A—A’) (t’—t); H, 
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, 
tegarding its vertex as the origin of coordinates, Soy?dz=7By?x. 
1—B dr ? 
Differentiating, &c. 1) Bare Integrating and returning to 
SE: 
numbers, we have 
2B 
Cry 5; in which (C) is the correction. This is a parab- 
ola, if | —F is positive, which becomes the common one, when 
B=3. If ak is negative, it is an hyperbola; which is the 
tommon one, if B=—1. But the hyperbolic form, it is evident, 
cannot subsist in a mercurial barometer. Various consequences 
from the above formule, 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. 
