438 Researches respecting the Laws of the (June, 
term of the true maximum once, among other examples, at 1*78° 
R., while our formula for pure distilled water gives the true maxi- 
mum at 2°74° R., nearly 1° higher than the observation of Dalton. 
Mr. Dalton observed, likewise, that in his vessels the water stood 
at the same height by equal changes of temperature above and 
below that which corresponded to the apparent maximum of con- 
densation. This is another consequence of our formula. The 
general expression of the apparent dilatation A, in these low tem- 
peratures is 
A, = (a—K)T+06T? +cT 
and calling T’ the temperature of the apparent maximum of con- 
densation, we have seen that this temperature was given by the 
equation 
O=a—K+2b0T 4+3cT* 
Let us make in general 
T=T+é# 
that is to say, let us reckon the temperatures above and below the 
apparent maximum of condensation. Substituting this value of T 
in A,, we shall have 
A= (ae Oa 4 vO Tag te va 
+(a—K)t +2bT7¢43cT?’¢ 
ok eh te Bee 
+40? 
The first line is constant; it is the value of the dilatation A, at the 
epoch of the maximum of condensation. We will represent it by 
A,-. The second line is all multiplied by the first power of t. 
When we unite all its terms, the factor of ¢isa — K +2)7T’ + 
3 c T”, and this factor is null, because T’ is determined precisely 
so as to render it null. Hence the whole expression of A, hecomes 
A, = Ay +ib+ 36TH O+c8 
We have seen that the coefficient c is very small; for we have c = 
— 0°00000002708. Hence if we extend the comparison of heights 
to 20° Reaumur on both sides the maximum, we shall have ¢ = + 
20, and there result c 2? = = 0°0002166; that is tosay, that this 
term would not alter the statement more or less than +53, of the 
whole volume of the water at0. If we take ¢ = 10, the effect 
will be eight times less; so that unless the experiments be almost 
mathematically exact, the effect of this term will not be perceived ; 
but if we neglect it, the value of A, will be reduced to 
bp = by + fb 4+ 3cT? #2 
then it remains the same when ¢ has equal values either positive or 
negative. Now this is the property observed by Mr. Dalton, 
The same philosopher has observed, likewise, the quantity that 
water sinks suddenly in vessels of different kinds when plunged into 
a hot liquid. He found this quantity to vary with the vessel, and to 
increase with the dilatability of the vessel. 
