348 Dr. Ure’s new experimental researches 
A, B, and C, will be affected by the heat, but the measuring 
column is beyond the reach of its influence. 
A surprising accordance will be perceived between my 
numbers, and those given by Mr. Dalton between 32 0 and 
212 0 , though mine were obtained with a different modification 
of apparatus. Above the boiling point, where the table of Mr. 
Dalton is deduced from calculation, the accordance soon 
ceases. But as my apparatus and mode of using it were pre- 
cisely the same as in the former part of the range, my results, 
if entitled to confidence in the one case, must be so in the 
other. At 280° Betancourt’s number and mine are not much 
different, the former 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 0 and 
212 0 , could not serve for the higher ranges,* I endeavoured 
to discover a simple rule of more general application. It is 
above 212 0 , indeed, that for the purposes 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 ioo°, 110°, 120°, 130°, 14,0°, and 150°, 
may be written in a series of which the 5th order of dif- 
ferences = o. Then if d ' d" d'" d iy d v , represent the first 
terms, in the first, second, third, fourth, and fifth order of 
differences, the n tb term of the series is 
* Dr. Young remarks oitDalton’s ratio, “ Itis certain that this cannot be the 
law of nature, since about 394 0 the elasticity would become uniform, and then 
decrease, if the law be true.” Young’s Natural Philosophy, 4L5. vol. ii. p- 398. 
