372 
On the Measure of Temperature, 
[Dec. 
Thus the law we have announced, as representing the loss of heat, occasioned by 
the contact of air, is confirmed, when we extend our researches to greater excesses 
of temperature. The results already tabulated, will furnish even the means of veri- 
fying the law of cooling in vacuo. It is sufficient for this purpose to deduct from 
the total effect in the air, the rate which would be occasioned bv the sole contact 
of air, that is to say, the successive values of v. The several remainders will 
evidently be the rates of cooling as due to radiation, or which comes to the same 
thing, those which would be observed in vacuo. 
We shall here give the numbers determined in this way for the thermometer, 
with naked bulb, and also the rates calculated from the law of pooling in vacuo. 
These rates are, we know, expressed by the formula 
tn ( a 1 — I.) 
t being the excess of temperature of the body ; vx a constant coefficient, which 
must be determined for each case, and which here is equal to 2,61 j and finally* 1 
being the exponent 1,0077 common to all bodies. 
Excess of tem- 
perature. 
Hates of cool- 
ing in vacuo 
deduced from 
observations 
in the air. 
Rate of cooling 
in vacuo , as 
calculated. 
260° 
16°, 32 
16°, 40 
240 
13 ,71 
13 ,71 
220 
11 ,31 
11 ,40 
200 
9 ,38 
9 ,42 
180 i 
7 ,85 
7 ,71 
160 
6 ,20 
6 ,25 
140 
5 ,02 
4 ,99 
120 
3 ,93 
3 ,92 
100 
3 ,04 
2 ,99 
eo 
2 ,22 
2 ,20 
It will be seen by the example just given, that we may, by observing directly 
the cooling process in the air, determine separately the loss of heat due to contact 
of the air and to radiation, and that to effect this purpose we must observe th e 
co> ling of the same body with different surfaces. 
But this method of calculation depends, in the first place, on the supposition, that 
the quantity of heat taken up by the air is independent of the nature of the surface 
of the body ; and in the second place, on this principle, that bodies of different sur- 
faces, preserve at every temperature, ibe same ratio between their radiating poWd'S’ 
These two propositions are rigorously true, but they could not possibly be estab- 
lished except by direct experiments ; such, in fact, as we have given an account o( 
in this paper. And though Mr. Leslie has adopted them in the use he has made ot 
the principle we have above explained, his results are not the less inaccurate, as b e 
has always calculated the rate of cooling after the law of Newton. 
I he laws relative to each of the two effects which are combined in the cooling ° { 
a body plunged in a fluid, having been separately established, it is sufficient to c o&" 
bine them to have the total cooling effect. 
The rate v then ol this cooling, for an excess of temperature, t will he expressed 
by the formula r 
m ( a * — 1 ) + 
_ a an( i ^ for all bodies, and in every fluid, be equal to 1,007'. 
its s„rf * ■* ,e , co ‘ e fficient »i will depend on the size of the body and nature 
? S We ^ as on tl ! e temperature of the surrounding matter. The co- et ' 
will, h w> ln< ependent of this temperature as of the nature of the surface, will v# 1 ? 
p j f.,* 1Ks,on us well as with the kind of gas in which the body will be immef 5 ' 
f lese vaUH tions will follow the laws we have already explained, 
this mom 1 ^ U f s lmv ® us > in the first place, as we have stated in the beginning 0 
surface °t 1 * c * at , aw co °i* n g in elastic fluids changes with the nature of tb e 
serve their ” ? Ct ' w, ‘ en change takes place, the quantities a, b> and », pfC' 
power of th V>i U r. S> >U * ^ ,e co ‘ e fficient vi varies proportionally to the radiating 
will become 6 surtace * ^ tIie new value be represented by m[ the rate of cooli^ 
