* Temperature of Mercury in a Siphon Barometer. 253 
* 
To appreciate the temperature of the mercurial column through- 
out its whole extent, in a siphon barometer of which the two 
branches are cylinders of equal diameters, I propose the follow- 
ing method. ——- gs? 
‘Let ABC represent the tube of a siphon barometer, of which 
those portions at least within the ranges of the mercurial surfaces 
are cylinders of equal diameters; and let O be the zero point of 
the scale DB, which is supposed to be inexpansible by heat. 
Suppose the summits of the convex surfaces Fig. 1. 
of the column in the two branches, at any time, © : 
are at D, d; and put OD=upper reading =a 
Od=lower reading=6 
temperature =¢ 
If the temperature increases to (t’,) while the 
atmospheric pressure remains unchanged, the 
masses of mercury in the two branches will ev- 
idently not be altered, and the surfaces will rise 
to some points D’, d’. Suppose now the tem- 
Perature (¢’) to be constant, and the atmospher- 
ic pressure to increase. For the sake of refer- 
ence to the. figure, we have supposed the tem- 
perature and pressure, whenever they change vy 
0 increase ; but this can lead to no error when. 
the contrary is the case, as aff erroneous suppo- 
sition would be corrected by the sign. Conse- 
quent upon this increase of pressure, the sur- 
face d’ will descend to some point d”, and the 
surface D’ will ascend to some point D’”. Since 
the tube D’D” contains a volume of mercury B 
equal to that which d’d” did under the first E F 
Pressure with the temperature (¢’,) and since the diameters of 
these tubes are equal, their altitudes must be equal, and therefore 
DD’ =d/d” ; (1.) 
If (#) represents the ratio of expansion in height of mercury in 
4 cylindric glass tube, due to one centigrade degree ; and (p,) (p’) 
the altitudes of cylinders having diameters equal to those of the 
rometric tube within the ranges of the mercurial surfaces, and 
Capacities respectively equivalent to the volumes of mercury in 
the longer and shorter branches of the siphon at the epoch of the 
first observation when the temperature was (¢;) we have 
Vol. x1, No. 2.—Jan.-—March, 1841. 33 
= 
+ 
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