423 Researches respecting the Laws of the [June, 
d Ar 
“7 =O 7r0=a—K+20T + 30% 
a quadratic equation, the roots of which are 
1’ = —b+/P—3(a—Kjc, [7 = abo Vv PH 3 We 
3c q 3e 
These two roots will be both positive when the vessel is of a nature 
to dilate itself by heat; for since a is negative as well as c, the 
product 3 (a — K) c will in that case be positive. The value of the 
radicle will be then less than J, and as the denominator 3 c is nega- 
tive, the two roots will have the sign +. But the first is the only 
one which interests us; for it is the only one which is always very 
small, To calculate it exactly, and with facility, we must make c 
disappear from the denominator by multiplying the two terms of 
the fraction by 
b+V7F—3(a—K)c 
This gives us 
RIE Aas ae Ch a ee ot og 5 
b+ 7Yb—3(a—K)ec 
Nothing remains but to substitute for K its value in this formula, 
and we obtain the temperature T of the apparent maximum ot 
condensation. The absolute maximum of condensation will be 
found by making K = 0. This gives 
, a 
GOs b+ 7fh—3ac 
It was in this manner that we calculated in a preceding part of this 
paper. As the value of c is very small, if the temperature T of the 
maximum be low, we may obtain a near approximation, though 
we neglect the term 3c T? in the equation which determines this 
maximum, and then we obtain 
; K 
The apparent maximum T = — = est 
, ‘ . re: a 
The true maximum (T) = — 5; 
This gives us 
K 
T= (T) +35 
This result shows us how the apparent maximum depends upon the 
true maximum and upon the dilatation of the vessel. It shows us 
that, in order to obtain the temperature T of this maximum, we 
must necessarily have regard to the term which contains the square 
of the temperature in the law of the dilatation of water. But this 
simple result is only an approximation. ‘The true expression is 
et acon (a — K) 
b+ /B—3 (a—K)ec 
which may sensibly differ from the approximate one, when the 
vessels are very dilatable; for in that case the values of T and K 
