on the Formula for measuring Heights by the Barometer. 225 
by means of a naked thermometer, and one having its bulb co- 
vered with moistened paper, coincided equally well with the re- 
lation between the tension of vapour, and the contemporaneous 
indications of the hygrometers of De Luc and Saussure, as de- 
duced from the observations of Du Long, and the investigations 
of Biot ; so that the formula I have proposed may be regarded 
as sufficiently accurate for ascertaining the hygrometric state 
of the atmosphere, by means of data which cannot, like those 
furnished by hygrometers formed of organic substances, be af- 
fected by the age of the instrument. All that is necessary for 
the successful application of the method, is Mr Dalton’s table 
of the elasticity of vapour, and two good thermometers. Lest 
the intricacy of the formula, however, should be considered as 
an objection to its use, I shall reduce it to a form which, with- 
out greatly affecting its accuracy, will render the analytical ex- 
pression involved by the problem, capable of solution as a sim- 
ple equation. For this purpose, let the expression 
2 = A (F — /) + B (F — f f be reduced to the form 
£ — A (F — f) -}- B (F — f) (F —f), and let the value of 
F — /'deduced from the first approximation £ = A (F — f) 
viz. a , be substituted for that quantity, in the term B (F — f) 
B ^ 
(F —jO, which will thus become — r- (F — f ), and we obtain 
A 
B 
%= A (F— /) + E£(F- 
A 
or>=(A + |*) (F — f). 
/); 
To ascertain to what extent the value of d was affected by 
changes in the atmospheric pressure, I inclosed the two thermo- 
meters in the receiver of an air-pump, and found, that, with va- 
rious degrees of exhaustion, the difference between them was al- 
most exactly in the inverse ratio of the density of the air. Hence, 
if the coefficients A and B be fixed at a pressure of thirty 
inches, we have, under any other pressure b y 
From this equation we derive 
b $ 
F 
SO 
(*+x) 
