” 
Temperature of Mercury in a Siphon Barometer. 261 
Frustum da”=5 (b, —b) [r?+[r-+(b, 8) sin. 0]? +rfr-+ 
(6,— 6) sin. &]?] (20.) 
It is evident, whatever may be the forms of the tubes, that 
capacity of D’D’=capacity of d’d” (21.) 
But, from the figure cap. D/D”=cap. DD” —cap. DI” 
cap. d’d’’=cap. dd” +-cap. dd’. 
Equating the second members according to (21,) and transpos- 
ing, we have 
cap. DD” —cap. dd’ =cap, DD’+ca 
or, denoting the sum of the second members of a and (18) by 
(I,) (22) 
the second member of (19) by (K,) (23) 
and the second member of (20) by (L,) (24) 
we have K—L=I (265.) 
In like manner, if the observations (a,,, ,,, t,,) (a5, 64; t,;) 
(a,, b,, ¢,,) be compared respectively as above with (a, b, ¢,) we 
shall have K/ —L/= Y, epee Bo =|", Kel’ =]"; (26) the 
terms of these equations being fhitietistis similar to dices of (25.) 
The four equations (25) and (26,) after correcting a readings, 
are sufficient to determine the unknown quantities ae 1 9, & and 
2 
aa +p" ) which these equations contain. 
From the minuteness of the angles (9,) (@,) we may use (4,) 
(#) in the places of sin. 6, sin. &; and neglect the terms which 
contain the second powers of those angles. ‘This will materially 
abridge labor without impairing the practical accuracy. 
As our limits will not permit us to discuss the general question, 
we will select that particular case only in which the two branch- 
sare cylinders of unequal diameters; and which is the most 
important, if not the only one that needs to be regarded in the use 
of the barometer. 
Here 6=0, #’=0 
K=2R?(a,—a) anes to (23) 
spread —b) 4) 
=78(R2p +r? p’) t3 ( 2) 
Substituting are in (25,) and dividing by (7r?,) we have 
R2 
= (4,—a)— (0,2) =+(~ pp’) (v4) Q7.) 
Vol. xx, No. 2.—Jan.-March, 1841. 34 
