On the Measure of Temperature, $c. 
374 
[Dec, 
increases rapidly as this excess augments ; and that it continually approaches the 
. m . i 
number 5,707 which is the limit, this being the value of the fraction r - rathe 
m 
case of glass compared with silver. This examination offers a new proof of the 
necessity of extending, to a very large interval of temperature, our inquiries with 
regard to certain phenomena of heat ; as it also well explains how Mr. Leslie us 
been led to results so different from those we have found. In fact, this cele >ra 
philosopher, beginning with observations made at low temperatures, V 011 ^ 
that the ratio in question would continue to diminish, until finally it won e ' 
unity ; so that, according to him, the total loss of heat in very elevated tempera > 
would be nearly independent of surface. But indeed the law* P ,0 P 0 ' s ; n ,rl e 
Mr. Leslie, by Mr. Dalton, or still earlier by Martin, may all be refute exC oss 
argument ; for all these laws make the rate of cooling depend solely °^| iereas es . 
of temperature of the body over that of the surrounding medium, ' »eratureof 
periment shows that this rate changes, in a marked degree, with the em 
the fluid which surrounds the body. , c or admitting 
It is, therefore, useless to enter into any discussion on the subjec , - llieo t, within 
even that the laws imagined by them did represent the results of exper ’ending 
— - — — — - — " **“***J5 • **VV« MJ VWVIO V* » V VWV»»W WMV# » | . I o 
the limits of their inquiries, it is certain, from all that precedes, t > a ’ g( j f ro ro the 
them beyond these limits, we should obtain results very f 31 ' re,rK 
truth. piously made 
We may, by considerations analogous to those of which we have P*" . Q case 
use, determine in what way the law of the total cooling effect c > 31 ^ ^ ag 
of any given body for a change in the nature or in the density 0 
The total effect of cooling is expressed by the formula 
m (at — I) -f- n$ 
an „tl,er pf« s " re ’ 
the 
If we suppose another gas, or even the same gas, under 
rate of cooling for the same bod)' will be 
m (at — 1) -f- «' t b . , 
for the co-efficient, n is the only one which, in this case, would r . becoUi eS . 
Comparing these two expressions, we shall find, that their ra 0 f c po 1 ^, e 
ke t = 0 or / =qo . Thus the total e . i e ag a,n ’ j, e w 
to unity, whether we make t = U or t =.<x> . Thus the ton* 1 i,j{ e 
different gases, becomes at high temperatures nearly the sainei ' sU fl5ces tc * j t 
lower part of the scale, the rates may be very different. Thi s /‘, 1 s jjc atte'*'! . e 
the iniipciirarff ... . «V. _ o ,1(1 1 «>* 1 - - 
to 
the inaccuracy of the proceedings by which Messrs. Dalton fl llC • {\uids j ‘ . ., t -ved 
compare the loss of heat, occasioned by the contact of various el^ s o0 ling> aS 0 gy a 
proceedings are founded on the supposition, that the total rates of c i . oe ratu re * ncU lar 
- whatever the J e ° P — ■ -- 
00} 
the P» 
icnce 
VppS 
coos eqlI ^ro* i ,n 
tbeff 
ate, 
in different gases, preserve the same ratio, wu»tcvc» 
singular coincidence, however, which it is unnecessary to d'^ 5 
temperature at which they operated, renders their error of le^ 
determinations are, therefore, as we have before observed, 5,1 fijose * IX " 
provided they are not extended to circumstances different fro* 0 s wb‘ cl 
were made. ftb eC8 . U a c °°* 
1 he necessity of separately determining the influence of ea c ^.° uS to t thought 
affect the procress of coolinv in nnv nnf havinrr b 3 ' ^ nat'U 3 
nected view 
gion^j 
progress of cooling in any body, not having allo' ve b a . g nati° 
w of the different laws to which we have been b’ 1 . wh‘ c ^,- s cus : 
that it might be useful to give a short recapitulation of the' 11 , 1 .. g of 
order of their sequence, often broken by accounts of expe* 1 * 1136 
r «us eS 
ar» te t e acb 
and of results, might he attended to. t be seP'V t [i»t 
Distinguishing, as we have done, the losses of heat due rC e* ve .\ylii c 
-5 
c j d* »» v nut uv/uv,^ t^Uv* lUSuCu Cl* liCflw U UO \y M * 
of conduction, by contact of fluids and radiation, it is soo a ^el at ‘°° S for eV lu 
of these effects has its own law. These laws must express tb® / c0 oli°J «e 
found between the temperature of the body, and its rate °l c ool l ^ r A e pf eS 
possible circumstance. It is to be recollected, that by rate u ld ° c * 
the number of degrees by which the temperature of the bod/ ' 
< uring a certain indefinitely small interval of time 
lsf Law . 
jo* 
•. - --r - ho dy p 5'd> in,S - 
tt it were possible to observe the cooling of 3 w° u 
'a 
r _ MW¥V . , pf Og re * 
cumn, bounded by non-radiating matter, the rate of° cook 0 ? jn 
geometnc progression, while the temperature diminished in ° r ‘ ^ V* c '^ t e irt 
, Fortlle S3me temperature of the matter enc' r ^ 0 f 
arithmpfi^. , co ° ir, £ body is placed, its rate of cooling, for exc<J sS *t fi c * 
Progression, would decrease as the terms of a g et>11 
