1817.J Dilatation of Liquids at all Temperatures. 439 
Hence he properly concluded that this subsidence was owing to 
the dilatation of the vessel, which, conducting heat better than 
water, is heated sooner, and of course begins to dilate first. What 
proves this still better is, that the amount of this subsidence is 
nearly proportional to the cubic dilatation of the substances of 
which the vessels are composed. The pewter vessel alone seems to 
constitute an exception, because the subsidence indicated is a little 
less than that of brass, whereas it ought to be a little greater. But 
if this be not a typographical error, it may be owing to the great 
difficulty of making such delicate observations, and of measuring 
the sudden subsidence of the water before it has acquired any sen- 
sible increase of heat.* 
I shall finish these researches on the dilatation of liquids by 
pointing out a process, which results from them, and which ap- 
pears to me both simple and exact, for measuring the different 
dilatations of solid bodies. It consists in observing the apparent 
dilatation of a liquid; for example, mercury, in vessels composed 
of the substances which we wish to try, and to observe always be- 
tween two constant temperatures, as, for example, 0° and 80° 
Reaumur. ‘This apparent dilatation may be observed with facility 
as accurately as we please. When known for one species of vessel 
of which K is the cubic dilatation, we shall have between the true 
and apparent dilatations 0,, 4;, the equation 
4,41+ KTi{=3—KT 
which gives 
, fl+A,$TK = %,— 4, 
For another kind of vessel subjected to the same temperatures, we 
shall have, in the same manner, 
{1 + 47} TK’ = 3, — 4, 
3, will remain the same, because the same liquid was employed. 
Subtracting these equations from each other, this quantity disap- 
pears, and there remains 
14+ 4,} TK’ — {14 a TK = 4,— 4, 
¥ 
from which we obtain , 
K = K 4 rr srs als KTS 
ThA + art 
In the present state of science, the dilatation of the metals is 
known sufficiently to enable us to employ them to calculate the 
small correction dependant on K in the second member of the pre- 
ceding equation. Then substituting for 4,, 4,’ and T, their ob- 
served values, we shall find K’ — K. ‘The accuracy of these values 
will be so much the greater as 4, and 4, are observed in volumes, 
and as it is the difference of the cubic dilatations K’ — K which is 
given by this equation. Perhaps in experimenting on the most 
* M. Biot does not appear to know that pewter is not tin, but an alloy of tin 
with another metal, ts expansion is less than that of brass, but greater than that 
of tin. T. 
