1830.] 
and the Communication of Heat. 
373 
in' (a e — 1) + ntK 
a quantity which is no longer proportional to 
in ( a 1 — 1) + nt b . 
W LeVufinm.h S e how the ratio of these rates of cooling varies ; and snppose. for 
clearness, that * is greater than that is to say, that it refers to the body, 
''we nniy easily satisfy ourselves, by the rules of the differential calculus, that 
the fraction 
m ( a * — 1) *1“ lift- 
in' [a 1 — ij nt IJ . 
in 
becomes equal to 
when t = 0 or co 
in' 
If we suppose t very small, the quantity a 1 — 1 becomes equal to t lo D . a, an 
the preceding ratio, dividing b} T t log. a 
n 
m -f- 
losr. « 
t {b— I) 
in' + 
n 
log. a 
obXul'!^' stated at the t^repidto 
bulb ; as also the ratios between them : 
Excess of 
temp. of the 
thermome- 
ter. 
Kate of cooling 
Of the therm 
with naked 
bulb. 
260° 
240 
220 
200 
180 
160 
140 
120 
100 
80 
60 
40 
20 
10 
24°, 42 
21 ,12 
17 ,92 
15 ,30 
13 ,04 
10 ,70 
8 ,75 
6 ,82 
5 ,56 
4 
Of the therm 
with silvered 
bulb. 
,1a 
2 ,86 
1,74 
0 ,77 
0 ,37 
10°, 96 
9 ,82 
8 ,59 
7 ,57 
6 ,57 
5 ,59 
4 ,61 
3 ,80 
3 ,06 
2 ,32 
1 ,60 
0 ,96 
0 ,42 
0 ,19 
Ratios 
2°, 23 
2 ,15 
2 ,09 
2 ,02 
1 .98 
1 ,91 
1 ,89 
1 ,80 
1 ,81 
1 ,78 
1 ,79 
1 ,81 
1 ,85 
1 ,90 
r imtiprs contained in the last column, fully confirms 
The mere inspection of the ^ ber that the ratios of the rate of cooling of 
lie fact above announced, s»c v for exQes3es 0 f temperature comprised 
ue two thermometers remain much tue resulte f ro m this, that after dimm- 
etween 40° and 120°. This circun i ’ c0lltr ibuted to persuade Mr. Dalton, that 
shing, the ratios augment, has pronau } bo dies. If this senes were pro- 
he law of cooling in th^air is the sm . g ftlready 2 ,23 for an excess of 260 
onged, we should liud that tl 
