by the Boiling Point of Water. 291 
point varies in a simple arithmetical proportion with the height, 
namely, 549°5 feet for every degree of Fahrenheit; so that 
the calculation of height becomes one of simple arithmetic, 
without the use of logarithms, or of any table whatsoever. 
When [ had ascertained this fact, I looked back to Deluc’s 
formula, and found my conjecture entirely confirmed. Its 
form is 
alogp+C=h, 
h being the ‘height of a thermometer plunged in boiling 
water under a pressure p; a and C constants. But the first 
side of this equation is the very form which gives elevations 
in terms of the barometric pressure. Hence the boiling 
temperature varies as the height. In other words, the 
pressure varies in a geometrical ratio, when the temperature 
of boiling water varies uniformly ; but the pressure varies 
geometrically when the heights above the sea vary uniformly ; 
hence the heights vary uniformly with the boiling tempera- 
tures. Sable 
It is very singular that: so elegant and simple a result 
should have escaped every writer on the subject (so far as 
I know) ; even Deluc himself, who proposed the logarithmic 
law, and Wollaston, who unawares adopted the true law as 
a first approximation, and then took a wrong one.* 
It is not to be supposed that the coincidence appears 
close, because the observations are not accurate enough to 
test it. Of seven observations between 195° and 210°, no 
one differs 80 feet of elevation from the mean line,—a 
* He says,—‘‘ Having occasion last summer of visiting Caernarvon, 
which would afford an opportunity of trying the instrument on the 
known height of Snowdon, and being aware that in 3550 feet the varia- 
tions of the boiling temperature were not to be considered uniform, as they 
might in small elevations, on which alone I had before tried the experi- 
ment, I wished to provide myself previously with a table for making the 
necessary correction, and from Dr Ure’s paper was supplied with data 
for calculation.”—Phil. Trans. 1820, p. 295. The table given from Ure’s 
law of tensions gives a gradually increasing number of feet, correspond- 
ing to every degree that the thermometer falls. 
Since this paper was first printed, I find that Sir John Leslie has re- 
marked the Arithmetical Law in his article, ‘‘ Barometrical Measure- 
ments,” in the Encyclopedia Britannica. 
