8S New experimental Résearches 
being 105 inches, the latter 102. Being perfectly convinced, by. 
repeating the experiments in different circumstances, that Mr. 
Dalton’s ratio of progression, though apparently accommodated 
to the intervals between 32° and 212°, could not serve for the 
higher ranges*, I endeavoured to discover a.simple rule of more 
general application. It is above 212°, indeed, that for the pur- 
poses of art, the knowledge of the force of steam is required. 
I first tried the differential method, so useful for determining 
the distant links of a concatenated series. 
Without doing much violence to the above numbers, the forces 
corresponding to 100°, 110°, 120°, 130°, 140°, and 150°, may 
be written in a series of which the 5th order of differences =0. 
Then if d’ d” d” dv d*, represent the first terms, in the first, 
second, third, fourth, and fifth order of differences, the mth term. 
of the series is 
A n—2 , —— n—-2 n—3 
@+ nl dor. a", + F=1 Sey ipa yi 
n—2 n—3 n—4 
n—Il Teo ° Tee * rs * a", + &e. 
In the above series for steam, d’=0°65, d”’=0:19, d”= 
O04 ad =0:01. dv O.a= 102. 
Example \st. To determine the 8th term in the series, or 
the elastic force at 8 x 10, above 90°, (the first term 100° being 
included) or at 170°. 
Here 2»=S 
a+ jo. d’=1:92 +455 = 6:47 
fa Sd 4-08. 
n—l pct i. Bh = 1:40 
aorta eee Tt oa Be 
2 3 4 pte 
12°30 
Observation gives 12-05, forming a good accordance. 
Example 2. Required the 10th term, or n=10.. For 190° F. 
at n—Ii. d= ThT 
aA = a = 6:84 
n—1.~= sagas Or = 3°36 
n—-2 n—3 n—A4 PELL i) 
n— | To ° 3 Sing? . d a 1 26 
19:23 
At 190° experiment makes it 19-00, still coinciding. nearly. 
* Dr. Young remarks on Dalton’s ratio, “ It is certain that this cannot - 
be the law of nature, since about 394° the elasticity would become uniform, 
and then decrease, it the law be true.”— Young’s Natural Philosophy, 4to, 
vol, ii. p,.398. 
By 
