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numerical indications of measurement of the changes of tem-
perature.

1323. Preparation of the mercury. For this purpose it is
necessary, in the first instance, that the mercury with which
the tube is filled shall be perfectly pure and homogeneous.
This object is attained by the same means as have been already
explained in the case of the barometer (715.).

1324. Selection of the tube. In the selection of the tube it
is necessary that it be capillary, that is to say, a tube having an
extremely small bore, and that the bore should be of uniform
magnitude throughout its entire length.

The smallness of the bore is essential to the sensibility of the
instrument, as already explained ; and its uniformity is necessary
in order that the same change of volume of the mercury should
correspond to the same length of the column in every part of
the tube.

The uniformity of the bore of the tube may be tested by
letting into it a small drop of mercury, sufficient to fill about a
third of an inch of the tube. Let this be made to fall gradually
through the entire length of the tube, stopping its motion at
intervals, and let the space it occupies at different parts of the
tube be measured. If this space be everywhere the same, the
bore is uniform ; if not, the tube must be rejected.

1325. Formation of the bulb The bulb, whether spherical

or cylindrical, can be formed upon the end of the tube by the

B 4



8 HEAT.

ordinary process of glassblowing. The sensibility of the ther-
mometer requires that the capacity of the bulb should bear a
large proportion to the calibre of the tube. If, however, the
capacity of the bulb be considerable, the quantity of mercury it
contains may be so great that it will not be affected by the
temperature of the surrounding medium with sufficient promp-
titude.

A cylindrical bulb of the same capacity will be more readily
affected by the temperature of the surrounding medium than a
spherical bulb, since it will expose a greater surface.

The glass of which the bulb is formed should be as thin as is
compatible with the necessary strength, in order that the heat
may pass more freely from the external medium to the
mercury.

1326. Introduction of the mercury. The tube to be filled
is represented in Jig. 425., where B A c is the tube, and c D a
reservoir formed at the top for the purpose of filling
D it, which is to be afterwards detached. Let the tube
be first dried by holding it over the flame of a spirit-
e lamp, so as to evaporate and expel all moisture which
may be attached to the inner surface of the glass. To
fill it, let a quantity of purified mercury be poured
into the reservoir c D. This will not fall through
the bore, being prevented by the air included in the
reservoir A B and in the tube. To expel this, and
cause the mercury to take its place, let the tube be
placed in an inclined position over a charcoal fire or
the flame of a spirit-lamp, so that the air shall be
heated. When heated it will expand, force itself in
bubbles through the mercury in c D, and escape into
B the atmosphere. This will continue until all the air
in the bulb A B and in the tube A c has been expelled.
The pressure of the atmosphere acting on the mercury
in c D will then force it through the tube into the bulb A B,
which, as well as the entire length of the tube, it will ultimately
fill. If a sufficient quantity of mercury be supplied to the
reservoir c D, the bulb A B, the tube A c, and a part of the re-
servoir c D, will be filled with mercury after all the air has
been expelled.

When this has been accomplished, let the tube' be removed
from the source of heat, and allowed gradually to cool. A file



THERMOMETRY. 9

applied at c, where the top of the tube is joined to the superior
reservoir, detaches that reservoir from the tube, which remains
with the bulb A B completely filled with mercury.

In this state the instrument would give no indication of
change of temperature, no space being left for exhibiting the
play of the mercury by dilatation and contraction.

To obtain space for this, let the bulb A B be exposed to a
temperature higher than any which the instrument is intended
to indicate. The mercury dilating will then overflow, and will
continue to overflow until the mercury acquires the extreme
temperature to which it is exposed.

A jet of flame being now directed by a blow-pipe on the end
C, it will be hermetically sealed ; after which, being allowed to
cool, the mercurial column will subside, the space in the tube
above it being a vacuum, since the air is expelled. The column
will continue to subside until the mercury assumes that state
which corresponds to the temperature of the air surrounding the
instrument.

1327. Thermometric scale arbitrary. The variation of the
height of the mercurial column in such a tube will in all cases
correspond with the changes of temperature incidental to the
surrounding medium ; but, in order that it may supply a nume-
rical expression and measure of such changes, a scale must be
attached to the tube, by which the variations of the column
may be indicated, and the divisions or the units of such scale
must correspond to some known change of temperature. It is
evident that such a scale, like all other standards for the arith-
metical measure of physical effects, must be to some extent ar-
bitrary. We accordingly find different scales and different
thermometric units prevailing in different countries, and even
in the same country at different times.

1328. Standard points. Division of scale. Whatever
thermometric unit be adopted, it is necessary that two standard
temperatures be selected, to which the mercury can be reduced
at the times and places where thermometers may be required to
be constructed or verified. The instrument being exposed to
these two temperatures, the points at which the mercurial
column stands are marked upon the scale. The space upon
the scale between these points is thus divided into a certain
number of equal parts, which are called degree?, these degrees
being the thermometric unit. The same divisions are then

B 5



10 HEAT.

continued upon the scale above the higher and below the
lower standard point, and such divisions may be continued in-
definitely. The scale is then complete.

In this process, the number of equal parts into which the
space between the standard points is divided, is altogether
arbitrary.

1 329. Numeration of scale. Zero point. It now remains
to number the scale ; and, for this purpose, a zero point must
be selected. If there existed a minor limit to temperature, a
temperature below which no body could possibly fall, then such
a temperature would supply a natural thermometric zero, and
the scale might be numbered upwards from it.

1330. No natural zero. In that case, although the thermo-
metric unit would still remain arbitrary, the zero of the scale
would not be so. But no such natural thermometric zero exists.

There is no natural limit either to the increase or diminution
of temperature. The zero, therefore, of the thermometric scale,
like the thermometric scale itself, must be arbitrary.

1331. Phenomena fit to supply standard points Thermal

phenomena present great varieties of standard temperatures, by
which thermometric scales may be established, and which may
serve equally as terms of temperature for the purpose of dis-
tinguishing the indications of different thermometers constructed
at different times and places. Thus, the temperatures at which
all solid bodies fuse, and those at which all liquids congeal, are
fixed. For different bodies these are different, but always the
same for the same body. In like manner, the temperatures at
which all liquids boil under a given pressure are invariable for
the same liquids, though different for different liquids. The
temperature of the blood in the human species presents another
example of a fixed temperature.

1332. Freezing and boiling points of ivater adopted by
common consent. Now any two of these various temperatures
naturally fixed might be taken as the thermometric standards,
the choice being altogether arbitrary. Thus, it appears that
the arithmetical division of the scale, and consequently the
thermometric unit, the position of its zero, and, in fine, the
standard temperatures by which alone the indication of different
thermometers can be rendered comparable, are severally arbi-
trary. Unanimity, nevertheless, has prevailed in the selection
of standard temperatures. The temperature at which ice melts,



THERMOMETRY. 11

and that at which distilled water boils, when the barometer
stands at 29-8 inches, have been adopted in all countries as the
two temperatures with reference to which thermometric scales
are constructed.

1333. Determination of these points. The bulb and tube, as
already described, being filled with pure mercury, and a blank
scale being attached to the tube, the instrument is immersed
successively in melting ice and boiling water, and the points
at which the mercurial column stands in each case are marked
upon the scale. The former is called the freezing point, and
the latter the boiling point.

1334. Different thermometric units and zeros. Fahrenheit's,
scale. The same unanimity has not prevailed either as respects
the unit or the thermometric zero. In England, Holland, some
of the German States, and in North America, the interval be-
tween the freezing and boiling points is divided into 180 equal
parts, each part representing the thermometric unit. The scale
is continued by equal divisions above the boiling and below the
freezing points.

The zero is placed at the thirty-second division below the
freezing point ; so that, on this scale, the freezing point is 32,
and the boiling point 32 + 180 = 212.

This scale is known as Fahrenheit's, and was adopted about
1724.

The reason for fixing the zero of the scale at 32 below the
freezing point is, that that point indicated a temperature which
was at that time believed to be the natural zero of temperature,
or the greatest degree of cold which could exist, being the most
intense cold which had been observed in Iceland.

We shall see hereafter that much lower temperatures, natural
and artificial, have been since observed.

The divisions of the interval between the freezing and boiling
points into 180 equal parts was founded upon some inexact
supposition connected with the dilatation of mercury.

The divisions of this scale are continued in the same manner
below zero, such divisions being considered negative, and ex-
pressed by the negative sign prefixed to them. Thus, + 32
signifies 32 above zero, but 32 signifies 32 below zero.

133o. Centigrade scale. In France, Sweden, and some
other parts of Europe, the centigrade scale prevails.

In this scale the interval between the freezing and boiling

B 6



12 HEAT.

points is divided into 100 equal parts, and the zero is placed at
the freezing point.

1336. Reaumur's scale. In some countries the scale of
Reaumur is used; in which the interval between the freezing
and boiling points is divided into eighty equal parts, the zero
being placed at the freezing point.

1337. Methods of computing the temperature according to
any one scale when the temperature according to any other is
given. As all these scales are used to a greater or less extent
in different parts of the world, it will be necessary to establish
rules by which the temperature expressed by any one of them
may be converted into the corresponding temperature expressed
by any other.

Since the numbers of degrees into which the interval between
the freezing and boiling points is divided on the three scales
are 180, 100, and 80 respectively, it follows that 18 Fahren-
heit are equal to 10 centigrade and to 8 Reaumur ; or that
9 Fahrenheit, 5 centigrade, and 4 Reaumur are represented
by equal lengths of the scales. Hence are inferred the following
rules :

1. To reduce any number of Fahrenheit degrees to an equivalent number
of centigrade or Reaumur degrees, divide by 9, and multiply by 5 for cen-
tigrade, and by 4 for Reaumur.

2. To reduce any number of centigrade degrees to an equivalent number
of Fahrenheit or Reaumur, divide by 5, and multiply by 9 for Fahrenheit,
and by 4 for Reaumur.

3. To reduce any number of Reaumur degrees to an equivalent number
of Fahrenheit or centigrade, divide by 4, and multiply by 9 for Fahrenheit,
and by 5 for centigrade.

If it be required to reduce any temperature expressed by
one scale to the equivalent temperature expressed by another,
the preceding rules will be. sufficient for the centigrade and
Reaumur, inasmuch as they have the same zero. But when it
is required to reduce the temperature of Fahrenheit to the
equivalent temperature on the other scales, it is necessary first
to subtract from the temperature of Fahrenheit 32 (the distance
between the two zeros), and then apply the preceding rule, or if
it be required to reduce a temperature on the centigrade or
Reaumur to an equivalent temperature on Fahrenheit, first
apply the preceding rules, and then add 32.

These principles are expressed briefly by the following for-



THERMOMETRY.



mulae, in which F, c, and K express the same temperature upon
the three scales :

c = x(F-32),

R =4 x(F-32),

F = I x C + 32 = - x R + 32.

Two or all the three scales are sometimes attached to the
same thermometer, so that equivalent temperatures are evident
on inspection.

Sucli reductions may also be facilitated by the following table,
showing the temperatures by the scales of Fahrenheit and
Reaumur which are equivalent to those of the centigrade.

Table for converting the Centigrade Thermometer into Degrees
of Reaumur and Fahrenheit's Thermometer.



Cent


Reau.


Fahr.


Cent.


Reau


Fahr.


Cent.


Keau. | Fahr.


Cent.


Reau. ] Fahr.


100


80-


212


64


51-2


147-2


29


23-2


84-2


6


4-8


21-2


99


79-2


210-2


6.J


50-4


145-4


28


22-4


x-2'4


7


5-6


19-4


98


7 - 4


2(i8'4


6.'


49-6


143-6


27


21-6


80-6


8


6-4


17-6


97


77-6


2066


61


48-8


141-8


26


20-8


78-^


9


7-2


15-8


9tt


76-8


204-8


60


48-


140-


25


'2G-


77-


10




14-


95


76-


203-


59


47-2


138-2


24


19-2


75-2


11


8-8


li-2


94


75-2


201-2


58


46-4




23


18-4


73-4


12


9-6


10-4


93


74-4


190-4


57


45 '6


1346


22


17-6


71-6


13


10-4


8-6


92


73-6


197-6


66


41-8


132-8


21


16-8


69-8


14


11-2


6-8


91


72-8


195-8


55


44-


131-


20


16


68-


15


!"'


5-


90


72-


194-


54


43-2


129-2


19


15-2


6<i-2


16


12-8


3-2


89


71-2


192-2


53


42-4


127-4


18


14-4


64-4


17


13-6


1-4


88


704


19(1-4


52


41-6


125-6


17


13-6


62-6


18


14-4


0-4


87


696


18*6


51


40-8


123-8


16


12-8


CO-8


19


15"2


2"2


86


68-8


186-8


50


40-


122-


15


12-


59-


20


16-


4-


85


6S-


185-


49


39-2


1202


14


11-2


57-2


21


1 -8


5-8


84


(i7-2


1S3-2


48


38-4


1184


13


10-4


85-4


22


17-6


7-6


83


664


181-4


47


37-6


116-6


li


9-6


536


23


18-4


9-4


82


6.V6


179-6


46


36-8


114-8


11


8-8


5l-8


24


19-2


11-2


81


64-8


177-8


45


36-


113-


1


8-


50-


25


20-


13-


80


61-


176-


44


35-2


111-2




7-2


48-2


26


208


14-8


79


6.1-2


174-2


43


344


109-4




64


46-4


27


21-6


16-6


78


624


172-4


42


33-i


1076




5-6


44-6




22-4


18-4


77


61 6


170-6


41


32-3


105-8




4-8


4i-8


89


232


20-2


76


60-8


168-8


40


32-


104-




4-


41-


30


24-


22-


7fl


0-


167-


39


31-2


102-2




3"2


?9-2


31


24 8


i3-8


74


59-2


H;5 2


3S


30-4


lOil-4




2-4


374


32


25-G


V5-6


73


5S-4


If .3-4


37


29-6


186




1-6


356


33


21-4


27-4


72


57-6


161-6


36


2X-8


96-s




0-8


3.*-8


24


27-2


29-2


71


56-8


I59-s


35


58-


95




0-


32-


35


28-


3i-


70


5V


15S-


34


57-2


9<-2





0-8


302


ae


2s-8


32-8


(19


55-2


156-2


33


264


91-4




1-6


28-4


37


V9-6


34-6




:>4'4


151-4


32


2.v<;


896




2-4


V6-6


38


30-4


36-4


67


536


152-6


31


24-8


87-8




3-2


24-8


39


Sl-2


3S-2




5i-8


1508


30


24-


86-




4-


23-


40


32-


40-


6->


52-


149-





















1338. Rate of dilatation of mercury. It has been ascertained
by experiment, that mercury, when raised from 32 to 212,
Buffers an increment of volume amounting to 2-lllths of its
volume at 32. Thus, 111 cubic inches of mercury at 32 will,
if raised to 212, become 113 cubic inches. From this may be
deduced the increment of volume which mercury receives for



U HEAT.

each degree of temperature. For, since the increase of volume
corresponding to an elevation of 180 is yfy of its volume at
32, we shall find the increment of volume corresponding to
one degree by dividing r 'j^- by 180, or, what is the same,
by dividing ^ - j^- by 90, which gives -g^Vo- I* follows, there-
fore, that for each degree of temperature by which the mercury
is raised, it will receive an increment of volume amounting
to the 9990th part of its volume at 32. It follows, therefore,
that the weight of mercury which fills the portion of a ther-
mometric tube representing one degree of temperature, will
be the 9990th part of the total weight contained in the bulb
and tube.

1339. Its dilatation uniform between the standard points,
In adopting the dilatation of mercury as a measure of tem-
perature, it is assumed that equal dilatations of this fluid are
produced by equal increments of heat. Now, although it is
certain that to raise a given quantity of mercury from the
freezing to the boiling point will always require the same
quantity of heat, it does not follow that equal increments of
volume will correspond to equal increments of heat throughout
the whole extent of the thermometric scale. Thus, although
the same quantity of heat must always be imparted to the
mercury contained in the tube to raise it from 32 to 212, it
may happen that more or less heat may be required to raise it
from 32 to 42, than from 202 to 212. In other words, the
dilatation produced by equal increments of heat, in different
parts of the scale, might be variable. Experiments conducted,
however, under all the conditions necessary to ensure accurate
results, have proved that mercury is uniformly dilated between
the freezing and boiling points, or that equal increments of
heat imparted to it produce equal increments of volume. The
same uniform dilatation prevails to a considerable extent of the
scale above the boiling and below the freezing points ; but at
extreme temperatures this uniformity of expansion ceases, as
will be more fully explained hereafter.

1340. Use of a standard thermometer. A thermometer
having once been carefully graduated may be used as a standard
instrument for graduating other thermometers, just as good
chronometers once accurately set are used as regulators for
other time-pieces. To graduate a thermometer by means of
such a standard, it is only necessary to expose the two instru-
ments to the same varying temperatures, and to mark upon the



THERMOMETRY. 15

blank scale of that which is to be graduated two points corre-
sponding to any two temperatures shown by the standard ther-
mometer, and then to divide the scale accordingly.

Thus, for example, if the two instruments be immersed in
warm water and the column of the standard thermometer be
observed to indicate the temperature of 150, let the point at
which the mercury stands in the other thermometer be marked
upon its scale.

Let the two instruments be then immersed in cold water and
let us suppose that the standard thermometer indicates 50.
Let the point at which the instrument to be graduated stands
be then marked. Let the intervals of the scale between these
two points, thus corresponding to the temperatures of 50 and
150, be divided into one hundred equal parts ; each part will be
a degree in the scale, which may be continued by like divisions
above 150 and below 50.

1341. Range of the scale of thermometers varies with the
purpose to which they are applied. The range of the scale of
thermometers is determined by the purpose to which they are
to be applied. Thus, thermometers intended to indicate the
temperature of dwelling-houses need not range above or below
the extreme temperatures of the air, and the scale does not
usually extend much below the freezing point nor above 100;
and thus the sensitiveness of the instrument may be increased,
since a considerable length of the tube may represent a limited
range of the scale.

1342. Qualities which render mercury a convenient ther-
moscopic fluid. Mercury possesses several thermal qualities
which render it a convenient fluid for common thermometers.
It is highly sensitive to change of temperature, dilating with
promptitude by the same increments of heat with great regu-
larity and through a considerable range of temperature. It
will be shown hereafter that a smaller quantity of heat produces
in it a greater dilatation than in most other liquids. It freezes
at a very low and boils at a very high temperature. At the
temperatures which are not near these extreme limits, it expands
and contracts with considerable uniformity.

The freezing point of mercury being 40, or 40 below
zero, and its boiling point + 600, such a thermometer will
have correct indications through a very large range of tem-
perature.

1343. Bulbs liable to a permanent change of capacity, which



16 HEAT,

renders correction of scale necessary. It has been found that,
from some physical causes which are not satisfactorily ex-
plained, the bulbs of thermometers are liable to a change of
magnitude after the lapse of a certain time. It follows from
this that a thermometer, though accurately graduated when first
made, may become at a later period erroneous in its indications ;
since a diminution of the capacity of the bulb would cause the
standard points and all other temperatures to be raised upon the
scale. To obviate this, thermometers used for purposes re-
quiring much precision ought to be verified from time to time
by comparison with well-constructed standards, or by exposure
to the standard temperatures.

It is also found that a change of magnitude is produced in the
bulb of a thermometer by sudden changes of temperature, which
render verification necessary.

1344. Self -registering thermometers. It is sometimes needed,
in the absence of an observer, to ascertain the variations
which may have taken place in a thermometer. Instruments
called self-regulating thermometers have been contrived, which
partially serve this purpose by indicating, not the variations of
the mercurial column, but the limits of its play within a given
time. This is accomplished by floating indices placed on the
mercury within the tube, which are so adapted that one is
capable of being raised with the column, but not depressed,
and the other of being depressed but not raised. The con-
sequence is, that one of these indices will remain at the highest,
and the other at the lowebt point which the mercurial column
may have attained in the interval, and thus register the highest
point and lowest point of its range.

The self-regulating thermometers on this principle which are
the best known are Sykes and Rutherford's.

13-15. Spirit of wine thermometers. Alcohol is frequently
used as a thermoscopic liquid. It has the advantage of being
applicable to a range of temperature below the freezing point of
mercury ; no degree of cold yet observed in nature or attained
by artificial processes having frozen it. It is usually coloured
so as to render the column easily observable in the tube.

1346. Air thermometers. Atmospheric air is a good ther-
moscopic fluid. It hns the advantage over liquids in retaining
its gaseous state at all temperatures, and in the perfect uni-
formity of its dilatation and contraction. It is also highly
sensitive, indicating changes of temperature with great promp-



THERMOMETRY. 17

titude. Since, however, it is not visible, its expansion and



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