BAROMETER. 
leather, if both ends *ere not hermetically 
sealed when it was made, and heated and 
rendered electrical by rubbing. 4. Unless 
the temperature of the air remain the same, 
the dimensions of a given quantity of mer- 
cury will be variable, and the altitude of 
the mercury is an uncertain measure of the 
weight of the atmosphere* because it is di- 
lated by heat, and contracted by cold, when 
perhaps the weight of the atmosphere is un- 
altered. If very great exactness be there- 
fore required, the difference of tempera- 
ture, at the different times of observation, 
and the depression or elevation of the mer- 
cury produced by it, must be ascertained, 
before the height of the column, raised by 
the weight of the atmosphere, can be disco- 
vered. See Weather, rules for judging of. 
The barometer applied to the measuring 
of altitudes. — The secondary character of 
the barometer, namely as an instrument for 
measuring accessible heights or depths, was 
first proposed by Pascal, and Descartes 
and succeeding philosophers have been at 
great pains to ascertain the proportion be- 
tween the fall of the barometer and the 
height to which it is carried ; as Halle, Ma- 
riotte, Shiickburgh, Roy, and more espe- 
cially by De Luc, who has given a critical 
and historical detail of most of the attempts 
that have at different times beeii made for 
applying the motion of the mercury in the 
barometer to the measurement of accessi- 
ble heights. And for this purpose serves 
the portable barometer already described, 
which should be made with all the accuracy 
possible. Various rules have been given by 
the writers on this subject, for computing 
the height ascended from the given fall of 
the mercury in the tube of the barometer, 
the most accurate of which was that of Dr. 
Halley, till it was rendered much more ac- 
curate by the indefatigable researches of 
De Luc, by introducing into it the cor- 
rections of the columns of mercury and air, 
on account of heat. This rule is as follows : 
M 
viz. 10000 X log. of — is the altitude in fa- 
m 
thorns, in the mean temperature of 31° ; and 
for every degree of the thermometer above 
that, the result must be increased by so 
many times its 435th part, and diminished 
when below it : in which theorem M denotes 
the length of the column of mercury in the 
barometer tube at the bottom, and m that 
at the top of the hill, or other eminence * 
which lengths may be expressed in any one 
and the same sort of measures, whether 
feet, or inches, or tenths, &c, and either 
English, or French, or of any other nation ; 
but the result is always in fathoms, of 6 
English feet each. The following rules must 
be attended to. 
1. Observe the height of the barometer 
at the bottom of any height or depth, pro- 
posed to be measured ; together with the 
temperature of the mercury, by means ot 
the thermometer attached to the barome- 
ter, and also the temperature of the air in 
the shade by another thermometer which 
is detached from the barometer. 
2. Let the same thing be done also at 
the top of the said height or depth, and as 
near to the Same time with the former as 
may be. And let those altitudes of mercury 
be reduced to the same temperature, if it 
be thought necessary, by correcting either 
the one or the other, viz. augmenting the 
height of the mercury in the colder tempe- 
rature, or diminishing that in the warmer, 
by its 9600th part for every degree of dif- 
ference between the two; and the alti- 
tudes of mercury so corrected, are what 
are denoted by M and m, in the algebraic 
formula above. 
3. Take out the common logarithms of the 
two heights of mercury, so corrected, and 
subtract the less from the greater, cutting 
off from the right hand side of the remain- 
der three places for decimals ; so shall those 
on the left be fathoms in whole numbers, 
the tables of logarithms being understood 
to be such as have seven places of deci- 
mals. 
4. Correct the number last found, for 
the difference of the temperature of the air, 
as follows ; viz. take half the sum of the two 
temperatures of the air, shewn by the de- 
tached thermometers, for the mean one ; and 
for every degree which this differs from the 
standard temperature of 3i°, take so many 
times the 435th part of the fathoms above 
found, and add them if the mean tempera- 
ture be more than 31", but subtract them if 
it be below 31° ; so shall the sum or difference' 
be the true altitude in fathoms, or being mul- 
tiplied by 6, it will give the true altitude in 
English feet. 
Ex. l. Let the state of the barometers 
and thermometers be as follows, to find the 
altitude; viz. 
Thermometers, 
detached. ] attached. 
Barometers. 
67 
57 
29.68 lower 
42 
43 
25.28 upper 
mean 49- 
dif.14 
