338 M. V. Begnault on some Apparatus for determining 



a function of the temperature and of the pressure, the numerical 

 coefficients of which have been deduced from experiment; in 

 other terms, the density is one of the coordinates of a surface, of 

 which the two others represent the pressure and the temperature. 



2. Theoretical or limit densities. — These are what would be 

 found by operating on temperatures so high, and under pres- 

 sures so feeble, that the gas or vapour would follow exactly the 

 same laws of expansion and elasticity as atmospheric air under 

 an increase of temperature or a diminution of pressure to which 

 it is subjected. These limit densities obtain with all gases, 

 and with all vapours when they are subjected to an extreme 

 expansion, and if the temperature is sufficiently high. They 

 are the only ones which could be of use in studying the com- 

 position of a compound gas expressed in volume relatively to the 

 volumes of the simple gases of which it is formed. 



Thus, when the densities of gases and vapours are determined 

 simply with reference to the constitution of bodies, the limit 

 density, or one nearly approaching it, ought to be sought. It 

 is hence desirable that the apparatus with which densities are 

 determined should be so constructed as to be easily used to 

 ascertain whether if, starting from the temperature and pressure 

 which prevailed in the apparatus during the experiment in 

 which a density is to be deduced, the gas or vapour follows the 

 same laws of expansion and elasticity as atmospheric air, for 

 small variations of temperature and pressure to which it is 

 subjected. 



To satisfy these conditions in determining the density of a 

 gas, and of that of the vapours of bodies which only boil at very 

 high temperatures, I constructed some years ago the apparatus 

 represented in figs. 12, 13, 14, Plate II. The receiver in which 

 the gas or vapour is measured consists of a tube A B, 3 or 4 centi- 

 metres in diameter, terminating below in a tube B c, 2 centimetres 

 in diameter, and above in a capillary tube A b, provided with a 

 steel stopcock r. The lower tube is hermetically fixed in an ap- 

 paratus of cast iron, cdef In the piece cdef there is a second 

 tubulure ef, in which the long open tube C D is fixed; cdef is 

 firmly screwed on an iron tripod M N P Q, which is furnished 

 with lcvelling-screws V, V. A strong plate of sheet iron, pqs, 

 the shape of which is seen in fig. 13, is fixed on cdefhy means 

 of the screws u, u and of red-lead cement. Lastly, a semi- 

 cylinder, g h i, of sheet lead, of which one side is a wrought- 

 iron frame, E F G H (fig. 12), is fixed on the sheet-iron plate 

 x x x by means of red-lead cement. The open face of the cy- 

 linder is closed by a pane of plate-glass, fixed by means of a 

 second iron frame exactly like the first, fastened down by screws 

 z } z } z (fig. 12). A plait of hemp, well stuffed with red lead, is 



