Encyclopaedia Britannica > Volume 15, PLA-RAM

P N E U M
Bar le’rr.
Tabes A.
rrm!,| Bulk * f Eitpan. f<jr j°
212^
202
192
182
172
162
152
142
J32
122
I 12
102
t;2
82
72
6,2
52
42
32
22
12
2
O
V',4388
30,4652
3°»44-y
3C>4159
30>3902
32,3638
3C»33^7
30,3090
30.2807
30,2518
3°rJ223
3C,t922
30,1615
3°,1302
30,0984
30,0661
30>°33 3
30,0000
29,9662
29»93f9
29,8971
29,8901
0,0000763
0,0000787
c, 0000810
0,00008? 3
0,0000857
0,0000880
0,0000903
0,0000923
0,0000943
0,0000963
0,0000983
0,000 FC03
G,‘>001023
0,0001043
0,0001063
0,0001077
0,0001093
0,0001 I 10
0,000 1127
0,0001 j 43
0,0001160
0,0000177
This table gives rife to feme reftettions. The fcale
of the thermometer Js conftru&ed on the fuppofition
that the fuceefiive degrees of heat are meafured by-
equal increments of bulk in the mercury of the ther¬
mometer. How comes it, therefore, that this is not ac¬
companied by equal increments of bulk in the mercury
of the column, but that the correfponding expansions
of this column do continually diminiih ? General Roy
attributes this to the gradual detachment of elaftie mat¬
ter from the mercury by heat, which preffes on the top
of the column, and therefore lh or tens it. He applied
a boiling heat to the vacuum a-top, without producing
any farther depreffion ; a proof that the barometer had
been carefully filled. It had indeed been boiled through
its whole length. He had attempted to meafure the
mercurial expanfron in the ufual way, by filling 30 inch¬
es of the tube with boiled mercury, and expoiing it to
the heat with the open end uppermoft. Rut here it
is evident that the expanfion of the tube, and its folid
contents, mull be taken into the account. The expan¬
sion of the tube was found fo exceedingly irregular,
and fo incapable of being determined with precifion
for the tubes which were to be employed, that he was
obliged to have recourfe to the method with the real
barometer. In this no regard was neceffary to any
circutnftance but the perpendicular height. There was,
befides, a propriety in examining the mercury in the
very condition in which it was ufed for meafuring the
pre ure o the atmofphere ; becaufe whatever compli¬
cation there was m the refults, it was the fame in the
barometer in actual ufe.
The moft obvious manner of applying thefe experi¬
ments on the expanfioir of mercury to our purpofe, is to
rC T-f c^erved height of the mercurv to what it
would have been if it were cf the temperature 32.
ms, uPP«fe that the obferved mercurial height is
9’2’ an the temperature of the mercury is 72°
1X1 e 3'-i1$Q2 : 30—29,2 : 29,0738'; This will be
A T I C S.
the true meafure of the demlty of the a‘r of the ftan-
dard temperature. In order that we may obtain the
exadt temperature of the mercury, it is proper that
the obfervation be made by means of a thermometer at¬
tached to the barometer-frame, fo as to warm and cool
along with it.
Or, tl is may be done without the help of a table,
and with fufficient accuracy, from the circumflance
that the expanfion of an inch of mercury for one degree
diminishes very nearly y^th part in each fucceeding de¬
gree. If therefore we take from the expanfion at 3 20
its thoufandth part for each degree of any range
above it, we obtain a mean rate of expanfion for
that range. If the obferved temperature of the mer¬
cury is below 32'’, we muft add this correction to
obtain the mean expanfion. This rule will be made
more exa£t if we fuppofe the expanfion at 32° to
be —0,0001127. Then multiply the obferved mer¬
curial height by this expanfion, and we obtain the cor¬
rection to be fubtraCted or added according as the tem¬
perature of the mercury was above or below 3 2°. Thus
to abide by the former example of 720. This exceeds
320 by 40: therefore take 40 from 0,0001127, and
we have 0,0001087 for the medium expanfion for that
range. Multiply this by 40, and we have the whole
expanfion of one inch of mercury, =20,004348. Mul¬
tiply the inches of mercurial height, viz. 29,2, by
this expanfion, and we have for the correction 0,12696;.
which being fubtraCted from the obferved height leaves
29,07304, differing from the accurate quantity lefs than
the thoufandth part of an inch. This rule is very eafily
kept in the memory, and fuperfedes the ufe of a table.
This correction may be made with all neceffary ex-
aCtnefs by a rule (till more fimple; namely, by multi¬
plying the obferved height of the mercury by the dif¬
ference of its temperature from 3 2°, and cutting off
four cyphers before the decimals of the mercurial height.
This will feldom err of an inch. We even believe
that it is the molt exaCt method within the range of
temperatures that can be expeCted to occur in mea¬
furing heights : for it appears, by comparing many
experiments and obfervations, that General Roy’s mea¬
fure of the mercurial expanfion is too great, and that
the expanfion of an inch of mercury between 20° and 70
of Fahrenheit’s thermometer does notexeeed 0,000102
pet degree. Having thus corrected the obferved mer¬
curial heights by reducing them to what they would
have been if the mercury had been of the Itandard tem¬
perature, the logarithms of the corrected heights are ta¬
ken, and their difference, multiplied by 10000, will
give the difference of elevations in Englifh fathoms.
There is another way of applying this correction,
fully more expeditious and equally accurate. The
difference of the logarithms of the mercurial heights is
the meafure of the ratio of thofe heights. In like
manner the difference of the logarithms of the obferved
and corrected heights at any itation is the meafure of
the ratio of thofe heights. Therefore this laft difference
of the logarithms is the meafure of the correction of
this ratio. Now the obferved height is to the cor¬
rected height nearly as 1 to i,sooio2. Tlie logarithm
of this ratio, or the difference of the logarithms of 1
and 1,000102, is 0,0000444. This is the correction for
each degree that the temperature of the mercury differs-
from 32. Therefore multiply 0,0000434 by the diffe¬
rence of the mercurial temperatures from 32, and the
prodnCU
125
Takinc
height*.
2JI
25*
*53