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. 



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 D^'B, which is supposed to be inexpansible by heat. 



Suppose the summits of the convex surfaces Fig. i. 



of the column in the two branches, at any time, 

 are at D, d; and put 0D-= upper reading = a 

 Oo?= lower reading =6 

 temperature =i 



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 {t') 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 

 to increase ; but this can lead to no error when 

 the contrary is the case, as an 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 

 equal to that which dfd" did under the first k f 



pressure with the temperature [t',) and since the diameters of 

 these tubes are equal, their altitudes must be equal, and therefore 

 !)'}:>" = d'd"; (1.) 



If (e) represents the ratio of expansion in height of mercury in 

 a cylindric glass tube, due to one centigrade degree ; and {p,) {p') 

 the altitudes of cylinders having diameters equal to those of the 

 barometric 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 {t ;) we have 



Vol. XL, No. 2.— Jan. -March, 1341. 33 



O" 



d" 



