contraction must be rendered observable by expedients which
interfere with and render complicated its indications.
1347. DrebbeVs air thermometer. The air thermometer of
Drebbel, or according to some of Sanctorius, is represented in
j ^^ fig. 426. A glass tube, AB, open at one end, and
) & having a large thin bulb C at the other, is placed with
B its open end in a coloured liquid, so that the air
contained in the tube shall have a less pressure than
the atmosphere. A column of the liquid will there-
A fore be sustained in the tube AB, the weight of which
will represent the difference between the pressure of
\ the external air and the air inclosed in the tube.
If the bulb c be exposed to a varying temperature,
F <r 4s> *^ ie a ^ r included i n it will expand and contract, and
will cause the column of coloured liquid in the tube
A B to rise and fall, thereby indicating the changes of tem-
1348. AmontorCs air thermometer. Another form
of air thermometer is represented in^. 427. The
air included fills half the capacity of the bulb c, and
its expansion and contraction cause the coloured
liquid to rise or fall in the tube A B.
1 349. The differential thermometer. Of all forms
of air thermometer, that which has proved of greatest
use in physical enquiries is the differential ther-
mometer represented in fig. 428. This consists of
Fig 4^7 * wo Sl ass bulbs, A and B, connected by a rectangular
glass tube. In the horizontal part of the tube a
small quantity of coloured liquid (sulphuric acid, for example)
is placed. Atmospheric air is contained in the bulbs and tube,
10 O 10 SO
separated into two parts by the liquid. The instrument is so
adjusted that, when the drop of liquid is at the middle of the
horizontal tube, the air in the bulbs has the same pressure ; and,
having equal volumes, the quantities at each side of the liquid
are necessarily equal. If the bulbs be affected by different
temperatures, the liquid will be pressed from that side at which
the temperature is greatest, and the extent of its departure from
the zero or middle is indicated by the scale.
This thermometer is sometimes varied in its form and
arrangement, but the principle remains the same.
Its extreme sensitiveness, in virtue of which it indicates
changes of temperature too minute to be observed by common
thermometers, renders it extremely valuable as an instrument
of scientific research.
By this instrument, changes of temperature not exceeding
the 6000th part of a degree are rendered sensible.
1350. Pyrometers adapted to measure high temperatures.
The range of the mercurial thermometer being limited by the
boiling point of mercury, higher temperatures are measured by
the expansion of solids, whose points of fusion are at a very
elevated part of the thermometric scale. The solids which are
best adapted for this purpose are the metals. Being good con-
ductors, these are promptly affected by heat, and their in-
dications are immediate, constant, and regular.
Instruments adapted for the indication and measurement of
this high range of temperature are called pyrometers.
1351. Graduation of a pyrometer. To graduate a pyrometer,
let the metallic bar be immersed successively in melting ice
and boiling water, and let its lengths at these temperatures be
accurately measured. Their difference being divided by 180,
the quotient will be the increment of length corresponding to
6ne degree of temperature ; and this increment being multiplied,
the length corresponding to any proposed temperature may be
Let L express the length of the bar at the temperature 32.
Let L' express its length at the temperature 212.
Let i express the increase of length corresponding to 1.
We shall then have
~ 180 '
If L express in general the length of the bar at the tem-
perature expressed by T, we shall have
L = L + ZX (T-32),
which means nothing more than that the length at the tem-
perature T is found by adding to the length at the temperature
32 as many times the increment corresponding to 1 as there
are degrees in T above 32.
The instrument represented in Jig. 429. is one of the most
simple forms of pyrometer.
A rod of metal, t, is in contact at one end with the point of
a screw v, and at the other with a lever a, near its fulcrum.
This lever is connected with another so as to form a compound
system, such that any motion imparted by the rod to the point
on the lever a in contact with it is augmented in a high ratio,
according to the principles explained in (438). A lamp placed
under the rod t raises its temperature ; and, as it is resisted by
the point of the screw v, its dilatation must take eifect against
the lever a, which, acting on the second lever, will move the
index on the graduated arc c. The ratio of this motion to
that of the end of the bar acting on the lever being known
(438), the quantity of dilatation may be calculated.
1352. Temperature of metallic standard measures must be
observed. The standards used as measures of length for as-
certaining distances where great accuracy is required, such as
in measuring the bases in geographical surveys, are usually
rods of metal. But since these are subject to a change of
length with every change of temperature, it would follow that
the results of any measurement made by them would be at-
tended with corresponding errors.
For the common purposes of domestic and commercial
economy, such errors are too trifling to be worth the trouble
of correcting ; but this is not the case when they are applied to
scientific purposes. It is necessary in such cases to observe
the temperature of the rods at the moment each measurement
1353. Borders pyrometric standard measure. In the oper-
ation by which the great arc of the meridian in France was
measured, a very beautiful expedient was contrived by Borda,
in which the bar itself is converted into a thermometer which
indicates its own temperature. This expedient was again
rendered available for the series of experiments made by
Dulong and Petit, to ascertain the dilatation of bodies by heat.
A bar of platinum, PP', Jig. 430., was connected at one ex-
tremity with a similar bar of brass BB', of very nearly equal
The two bars, being screwed or rivetted together at the
extremity B, were free at every other point. Near the ex-
tremity P' of the bar of platinum, and immediately under the
extremity B' of the brass bar, a very exact scale was engraved,
the divisions of which marked the millionth part of the entire
length of the rod. The extremity B' of the brass bar carried
an index, which moved upon the divided scale. Over the point
of this was placed a microscope M, by which its position could
be ascertained, and by which the divisions of the scale could be
more exactly read off.
If the two bars, P P' and B B', were equally dilatable, it is
evident that the same change of temperature affecting both
would make no change in the position of the index ; but, brass
being more dilatable than platinum, the index pushed by the
expansion of the bar B B' would be moved towards P' through
a space greater than that by which the bar p p' would be
lengthened, and, consequently, it would be advanced upon the
scale through a space equal to the difference between the dila-
tation of the two bars.
The manner of graduating the scale upon p P' was as follows.
The compound bar being submerged in a bath of melting ice,
the position of the index was observed. It was then transferred
to a bath of boiling water, when the position of the index was
The interval between these two positions being divided into
180 equal parts, each part would represent one degree of tem-
perature ; or, if such division were too minute to be practicable,
it might be divided into a less number of equal parts, as, for
example, 36, in which case each division would correspond to
5. When the index, as most frequently happens, stands be-
tween two divisions of the scale, it is necessary to estimate or
measure its distance from one of these divisions, in order to
express its exact position. This is accomplished by a con-
trivance called a vernier, which, as it is of great use in all cases
where the observation of scales is necessary in science and the
arts, it may be useful here to describe.
1354. Construction and use of a vernier. The vernier is a
contrivance which, by a subsidiary scale, supplies the means of
estimating small fractions of the smallest
division marked on the principal scale.
Let A B, Jig. 431., represent a part of
the principal scale. Let c D be the sliding-
scale or vernier, which we will suppose
to consist of 10 divisions equal in their
total length to 11 divisions of the prin-
cipal scale. Each division of the vernier
will therefore be equal to eleven-tenths
of a division of the chief scale, and will
exceed a division of the chief scale by a
tenth of a division.
Let us suppose that the index, D, of the
vernier (which coincides with its zero),
stands, as in fig. 432., at M, between the
divisions marked 55 and 56, and that the
question is to estimate how much it is
above 55. Observe what division of the
scale coincides either exactly or most
nearly with a division of the vernier.
The number of the vernier which stands
at such division of the scale will express
the number of tenths of a division of the
chief scale between the index of the ver-
nier and the 55th division of the chief scale. In the present
case, the 4th division of the vernier coincides nearly with the
51st division of the chief scale. The point on the chief scale
indicated, therefore, by the vernier, is 55-4.
It is evident that the distance from the 55th division of the
chief scale to the point in, which coincides with the index or zero
of the vernier, is the difference between 4 divisions of the
vernier and 4 divisions of the chief scale ; and since a division
of the vernier exceeds a division of the scale by a tenth, 4
divisions of the vernier exceed 4 of the scale by four-tenths.
DILATATION OF SOLIDS.
1355. Solids least susceptible of dilatation. Of all the states
of aggregation of matter, that in which it is least susceptible of
dilatation is the solid state. This may be explained by the
energy of the cohesion of the component particles of the body,
which is the characteristic property of the solid state. It is the
nature of heat, by whatever hypothesis that agency be ex-
plained, to introduce a repulsive force among the molecules of
the body it pervades. In solid bodies -this repulsive force,
acting against the cohesive force, diminishes the tenacity of the
body. The component parts have a tendency to separate from
each other, and hence arises the phenomenon of dilatation ; but so
long as the body preserves the character of solidity, the separation
of the component molecules cannot exceed the limits of the play
of the cohesive principle ; and as these limits are very small, no
dilatation which is consistent with the character of a solid can
1356. Homogeneous solids dilate equally throughout their
volume. If a solid body be perfectly homogeneous, it will
dilate uniformly throughout its entire volume by an uniform
elevation of temperature. Thus, the length, breadth, and depth
will, in general, be all augmented in the same proportion.
1357. Dilatation of volume and surface computed from linear
dilatation. It is a principle of geometry, that when a solid
DILATATION OF SOLIDS. 23
body, without undergoing any change of figure, receives a small
increase of magnitude, its increase of surface will be twice, and
its increase of volume thrice, the increase of its linear dimen-
sions. That is to say, if its length be augmented by a thou-
sandth part of its primitive length, its surface will be augmented
by two thousandth parts of its primitive surface, and its volume
by three thousandth parts of its primitive volume. This is not
true in a strictly mathematical sense, but it is sufficiently near
the truth for all practical purposes.
Now, since all solid bodies of uniform structure, when affected
by heat, expand or contract without suffering any change of figure,
and since, while their change of their linear dimensions can be
easily and exactly ascertained, that of their surface or volume
would be determined with much more difficulty, the changes of
these last are deduced from the first by multiplying it by 2 for
the increment of surface, and by 3 for the increment of volume.
Thus, if it be found that a bar of zinc being raised from 32
to 212, receive an increment of length equal to the 340th part
of its length at 32, it may be inferred that its increment of
surface is two 340th parts, and that its increment of volume is
three 340th parts of its volume at 32.
1358. Dilatation of solids uniform between the standard
thermometric points. It is found that solid bodies in general
suffer an uniform rate of dilatation, through a range of tem-
perature extending from 32 to 212 ; that is to say, the incre-
ments of volume which attend each degree of temperature which
the body receives are equal. If, therefore, the entire incre-
ment of volume which such a body undergoes when it is raised
from 32 to 212 be divided by 180, the quotient will be the in-
crement of volume which it receives when its temperature is
raised one degree.
1359. Dilatation ceases to be uniform near the point of
fusion. When solids are elevated to temperatures much above
212, and more especially when they approach those tempera-
tures at which they would be fused or liquefied, the dilatations
are not uniform. As the temperature is raised, the rate of
dilatation is increased, that is to say, a greater increment
of volume attends each degree of temperature.
1360. Exceptional cases presented by certain crystals. There
are also certain exceptional cases in some crystallized bodies, in
which, notwithstanding they are homogeneous, the dilatation is
not equal in all their dimensions. Certain crystals are found
to suffer more dilatation in the direction of one axis than in the
direction of another.
1361. Tabular statement of the rates of dilatation of solids.
In the following table are given the rates of dilatation of solid
bodies according to the most recent and accredited authorities.
In the first column is given the limits of temperature between
which the dilatation has taken place; in the second is given the
increment of the linear dimensions, expressed decimally, the
linear dimension at the lower temperature being the unit.
In the third column the same is expressed as a vulgar
Table of the linear Dilatation of Solids,
Dilatation in Fractions.
Names of Substances.
According to Lavoisier and Laplace.
Flint glass (English)
32 to 212
Platinum (according to Broda)
Glass (French) with lead
Glass tube without lead
Glass (St. Gohain)
Steel (untempered) - r
Ditto . - .
Steel (yellow temper) at 65
Iron, soft forged -
Iron, round wire-drawn -
Gold (French standard) annealed -
Gold (Ditto) not annealed
Ditto - - -
Silver - -
Tin, Indian or -
DILATATION OF SOLIDS.
Dilatation in Fractions.
According to Smeaton.
Steel tempered -
Copper 8 parts, tin 1
Brass 16 parts, tin 1
Telescope speculum metal
Solder (copper 2 pints, zinc 1)
Solder white (tin 1 part, lead 2) -
Zinc 8 parts, tin 1, slightly forged
Zinc lengthened -p by hammering
According to Major-General Roy.
Glass (tube) - - 32 to 217
Glass (solid rod) -
Glass cast (prism of)
Steel (rod of) -
Brass (English) rod
Brass (English), angular -
According to Trougliton.
32 to 212
Steel wire drawn
According to Wollaston.
Palladium - -00 100000 ^
According to Didong and Petit.
32 to 212
32 to 572
32 to 212
32 to 392
32 to 572
Copper ... |
32 to 212
32 to 572
32 to 212
32 to 572
1362. Measure of the force of dilatation and contraction of
solids. The force with which solid bodies dilate and contract is
equal to that which would compress them through a space equal
to their dilatation, and to that which would stretch them through
a space equal to the amount of their contraction. Thus, if a
pillar of metal one hundred inches in height, being raised in
temperature, is augmented in height by a quarter of an inch, the
force with which such increase of height is produced is equal
to a weight which being placed upon the top of the pillar would
compress it so as to diminish its height by a quarter of an inch.
In the same manner, if a rod of metal, one hundred inches in
length, be contracted by diminished temperature, so as to render
its length a quarter of an inch less, the force with which this
contraction takes place is equal to that which being applied to
stretch it would cause its length to be increased by a quarter of
1 363. Practical application of the forces of dilatation and con-
traction in drawing together the walls of buildings. This prin-
ciple is often practically applied in cases where great mechanical
force is required to be exerted through small spaces. Thus, in
cases where the walls of a building have been thrown out of the
perpendicular either by the unequal subsidence of the foundation
or by the incumbent pressure of the roof, they have been restored
to the perpendicular by the following arrangement:
A series of iron rods are carried across the building, passing
through holes in the walls, and are secured by nuts on the
outside. The alternate bars are then heated by lamps until
they expand, when the nuts, which are thus removed to some
distance from the walls by the increased length of the bars, are
screwed up so as to be in close contact with them. The lamps are
then withdrawn, and the bars allowed to cool. In cooling they
gradually contract, and the walls are drawn together by the nuts
through a space equal to their contraction. Meanwhile the in-
termediate bars have been heated and expanded, and the nuts
screwed up as before. The lamps being again withdrawn and
transferred to the first set of bars, the second set are contracted in
cooling, and the walls further drawn together. This process is
continually repeated, until at length the walls are restored to
their perpendicular position.
1364. Moulds for casting in metal must be larger thantlie^ob-
ject to be cast. In all cases where moulds are constructed for
DILATATION OF SOLIDS. 27
casting objects in metal, the moulds must be made larger than
the intended magnitude of the object, in order to allow for its con-
traction in cooling. Thus the moulds for casting cannon balls
must always be greater than the calibre of the gun, since the
magnitude of the mould will be that of the ball when the metal
is incandescent, and therefore greater than when it is cold.
1365. Hoops and tires tightened by the contraction in cooling.
Hoops surrounding water-vats, tubs and barrels, and other
vessels composed of staves, and the tires surrounding wheels, are
put on in close contact at a high temperature, and, cooling, they
contract and bind together the staves or fellies with greater
force than could be conveniently applied by any mechanical
1366. Compensators necessary in all metallic structures. In
all structures composed of metal, or in which metal is used in
combination with other materials, such as roofs, .conservatories,
bridges, railings, pipes for the conveyance of gas or water, raf-
ters for flooring, &c., compensating expedients must be intro-
duced to allow the free play of the metallic bars in dilating and
contracting with the vicissitudes of temperature to which they
are exposed during the change of seasons.
These expedients vary with the way in which the metal
is applied, and with the character of the structure. Pipes
are generally so joined from place to place as to be capable of
sliding one within another, by a telescopic joint. The succes-
sive rails which compose a line of railways cannot be placed
end to end, but space must be left between their extremities
1367. Blistering and cracking of lead and zinc roofs. Sheet
lead and zinc, both of which metals are very dilatable, when
used to cover roofs where they are especially exposed to vicis-
situdes of temperature, are liable to blister in hot weather by
expansion and to crack in cold weather by contraction, unless
expedients are adopted to obviate this: zinc, being much more
dilatable than lead, is more liable to these objections.
1368. Metallic inlaying liable to start. When ornamental
furniture is inlaid with metal without providing for its expansion,
the metal, being more dilatable than the wood, is liable, in a
small room, to expand and start from its seat.
1369. Compensating pe?).dulum. It has been already shown
(547) that the centre of oscillation of a pendulum ought to be
kept constantly at the same distance from its point of suspen-
sion, since otherwise the rate of the time-piece regulated by it
would not be uniform. This object has been attained by con-
necting the bob of the pendulum with the point of suspension
by rods composed of materials expansible in different degrees,
so arranged, that the dilatation of one shall augment the distance
of the centre of oscillation from the point of suspension, while
the expansion of the other diminishes it.
Let s, fig. 433., be the point of suspension, and o the centre
of oscillation, and let s be supposed to be connected with o by
means of two rods of metal, s A and A o, which are
united at A, but independent of each other at every
If such a pendulum be affected by an increase of
temperature, the rod s A will suffer an increment of
length; by which the point A and the rod A o attached
o to it will be lowered ; but, at the same time, the rod
A o being subject to the same increase of temperature,
will receive an increment of length, in consequence of
which the point o will be raised to an increased dis-
tance above the point A, at which the rods are united.
If the increment of the length of the rod A o be in this
case equal to the increment of the rod s A, then the
<lg ' 433 ' point o will be raised as much by the increase of the
length of A o as it is lowered by the increase of the length
of s A, and, consequently, its distance from the point s will
remain the same as before the change of temperature takes
To fulfil these conditions, it is only necessary that the length