174 Dulong and Petit on the Measure of Temperatures, [Marcw, — 
uniform mode of calculation which we always employed, in order 
to render our results more easily comparable. 
Suppose we observe, at equal intervals of time, every minute 
for example, the excess of temperature of a body above the sur- 
rounding medium, and that for the times 0, 1’, 2’, 3’, &c. ...-v, 
the excesses are A, B, C.....T. If the law of geometrical 
progression held good, we should have B = Am, C= Am? 
....1 = Am'; m beimg a fraction which will vary from one 
body to another. This law never holds exactly, especially when 
the temperatures, A, B, C, are high. But it is clear that we may 
always represent a certain number of the terms by an expression 
of the form A m*'+s", by determining properly the coefficients 
m,a, 8; and by means of that formula, we may calculate very 
nearly the value of the time ¢, corresponding to any excess of 
temperature T, provided that this excess be comprehended in the 
portion of the series which has served for the interpolation. 
This same expression gives us the means of determining the 
rapidity of cooling corresponding to each excess of temperature ; 
that is to say, the number of degrees which the temperature of 
a body would sink in a minute, supposing the rate of cooling 
uniform during that minute. We have in fact for that velocity, 
dT 
raat = (log. m).T.(a+ 28%) 
This quantity must always exceed the real loss of temperature 
during the time, since the rapidity of cooling diminishes during 
its whole duration, how short soever it may be. 
It was not, as may be easily conceived, to correct the smalk 
difference of which we have just spoken that we employed this 
process. But it is obvious that when a series is divided into 
several parts, represented each by empirical formulas, which 
correspond as exactly as possible with the numbers observed, 
the velocity of cooling deduced from these formulas for the 
different excesses of temperature, are always disengaged from 
the uncertainties and inaccuracies which the crude results of 
the observations always present. | 
Let us return now to the first comparison, of which we spoke 
a little ago; and for this, let us examine how the velocity of 
cooling has varied in the three series, the calculated results of 
which are contained in the following table : 
Excess of “temper-|v cigeity of,cooling of Ditto of thermomé-/Ditto of thermdme- 
a eae ae rcnyticar rina ed ter B re ter © 
100° 18-92° 897° 5-00° 
80 14-00 6-60 3°67 
60 9-58 4:56 2°52 
40 5:93 2:80 1:56 
20 2:75 130 0°73 
