242 Dulong and Petit on the Measure of Temperatures, [APRIL, . 
Having thus determined for each excess of temperature and 
for different densities the quantities of heat carried off by the 
air, we observed that they followed a simple law, by means of 
which we determined with sufficient precision the corrections 
which the calculated velocities ought to undergo. The numbers, 
therefore, which we shall give in the subsequent part of this 
chapter, may be considered as differing exceedingly little from 
those which would be obtained by making the experiments in an 
absolute vacuum. 
Let us now proceed to the examination of the different series 
calculated and corrected, and let us begin with that in which 
the balloon was surrounded by melting ice. The thermometer 
preserved its natural vitreous surface. y 
Excess of the therm, above Correspondiug velocities. 
the balloon. of cooling. 
OO ae oe ge et 10-69° 
Le SND ack ERT OR Ee DEMS Beser eins wien mic 8°81 
OE in sam tase era sehen eiousbenst s se asiarh 7°40 
LBD ya. siwicgs ene PONE AAE oe Tighe ee 6:10 
DE TRE wie fe Slee stehe > « eee e heats 4°89 
it Ue ee fake he Sa oo oa entetee ates 3°88 
POE sethaesd wrap ps « hat é-0. ae pe ate mone « 902 
TOG". be ots PS RCN «eh eee el 2°30 
BO yaa win ore ie Reape eh enw iS falta a, nie hi 1-74 
The first column contains the excesses-of temperature of the 
thermometer above the walls of the balloon ; that is to say, the 
temperatures themselves since the balloon was at 0°. The 
second column contains the corresponding velocities of cooling, 
calculated and corrected by the methods already pointed out. 
These velocities, as we have already observed several times, are 
the number of degrees that the thermometer would sink ina 
minute, supposing the cooling uniform during the whole minute. 
This first series shows clearly the inaccuracy of the law of 
Richmann ; for, according to that law, the velocity of cooling at 
200° should be double-that at 100°; whereas we find it more 
than triple. When we compare in like manner the loss of heat 
at 240° and at 80°, we find the first about six times greater than 
the last; while, according to the law of Richmann, it ought to 
be merely triple. 
Nothing would be easier than by a formula composed of two 
or three terms to represent the results contained in the preced- 
ing table, and to obtain in this way an empirical relation between 
the temperatures of bodies and the corresponding velocities of 
cooling. But formulas of this kind, though without doubt they 
are useful when we wish to interpolate, are almost always mac- 
curate beyond the limits within which the observations have been 
made, and never contribute to make us acquainted with the laws 
of the phenomena which we study. gst Bs 
ee 
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