1817.) Dilatation of Liquids at all: Temperatures. 375 
ee aban sab 
Finally, if we substitute for D, the general expression AT + BT* 
+ C T°, which we have verified, we obtain 
ge {AT+ BI?+ CT 41+ KT} 
*=KT+D Speak NLT SE PC 
or, by actual multiplication, 
{B+ AK} {C0 + BK} 
a DA wp + 5 2 ¢ 5 
ir Kp) tia DT bz Dl ot 
K Cc D T* 
80 ; 
The term containing ‘T* is always insensible, unless we suppose 
the experiments extremely exact. It would not give for water 
roeesos Of the primitive volume, even supposing T = 80. There- 
fore, neglecting this term, when the total dilatation, D, for a liquid 
is known, we must substitute its value in this formula. Making 
q = DAK, b= DiB+AKS, c= Dic+ BK 
89 80 80 
we have for every other temperature the true and absolute dilatation 
3, by this general formula, 
Car + ol oe 
which is that which we announced in beginning this investigation ; 
but if the experiments employed could be regarded as excessively 
precise, perhaps the term involving T* might become sensible, 
Then it would be necessary to introduce a term of the fourth order 
in calculating D, from the observations. I must remark that, our 
degrees being expressed according to the thermometer of Reaumur, 
we must take likewise for K the cubic dilatation of the vessel for one 
of these degrees. 
All the experiments of Deluc were made in glass thermometer 
tubes. According to the experiments of Lavoisier and Laplace, the 
cubic dilatation of this species of glass is 0°0000262716 for each 
degree of the centesimal thermometer. Therefore, if we multiply 
it by 42, or add to it one fourth of the amount, we shall obtain the 
dilatation for each degree of Reaumur, which will be 
K = 0:00003284 
Hence we have only to determine by experiment the total and ap- 
parent dilatation D, Unfortunately, we cannot say that there are 
any liquids the dilatations of which are known with that precision 
with which philosophers at present conduct their experiments, 
In this uncertainty I shall endeavour at least to calculate the dila- 
tations of water and alcohol from the experiments on these two 
liquids made by Blagden and Gilpin, introducing the dilatation of 
the vessel. ‘These experiments, indeed, do not extend beyond 0 
and 302 Reaumur ; but as they were made with very great care, 
