1819.] and onthe Laws of the Communication of Heat. 119 
the heights of two columns of mercury contained in the two 
‘branches of a reversed glass syphon, while the one was kept 
at the temperature of freezing water, and the other raised to any 
determinate known temperature, it would be easy to deduce 
from this the dilatation required. 
If hand ji’ denote the vertical heights of the two columns 
producing equal pressures, at the temperatures ¢ and (’, we 
ought to have (calling d “ a ai commana: densities) : 
bd = \h" el’ 
But d and d’ are inversely as the volumes v and v’, which the 
same mass of liquid would occupy at the respective temperatures 
tand it’. Hence we have 
ev = a 
wings 
From which we deduce for the mean coefficient of the dilatation 
between ¢° and ¢’° 
hi —h 
hwo 
Hence the whole is reduced to the exact measurement of the 
temperatures and of the heights of the columns ; and it is needless 
to say that we obtain in this way the absolute dilatation of the 
liquid ; since the form of the vessels producing no influence | 
upon the pressure of the liquids ‘contained in them, their dilata- 
tion cannot produce any efiect. 
Boyle first pointed out the use which might be made of this 
principle for comparing the density of liquids with each other. 
Several philosophers have thought since his time of applying it 
to the measurement of dilatations; and it is probable that this 
very accurate method might be easily applied at low tempera- 
tures. But when we wish to apply it at temperatures of 306°, it 
becomes very laborious. 
To render the explanation of the apparatus which we employed 
more clear, we have drawn a perspective view of it (Plate 
LXXXIX, fig. 1), in which only the essential pieces are seen, 
the remainder being capable of bemg easily supplied. 
The recurved tube’ which contains the mercury consists of 
the two vertical branches, A B and A’ B’, communicating with 
each other by a horizontal tube, B BY’, carefully made, and 
preserving in its whole extent the same thickness of glass, and 
the same inside diameter. Care was taken by a prelimmary 
trial to ascertain that the pressure Was transmitted without 
obstacle from one of the colina to the other by means of the 
horizontal tube, and that the friction of the mereury against its 
inside did not prevent the level from being restored when the 
equilibrium had been disturbed. 
Each of the vertical branches is formed, as may be seen in the 
figure, by an assemblage of two tubes, of very different calibre, 
cemented together. By giving to the lower tube a small dia- 
meter, the total mass of mercury is much diminished ; and by 
) 
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