larity in their clock-rates, have removed the clocks themselves to a place where the change of temperature is extremely small.

80. Compensation balance for chronometers. If a ribbon or bar be made of two metals of different expansion firmly attached to one another, and if the temperature rise, then one of these metals will expand more than the other. Under these circumstances the ribbon will bend so that the most expansible metal will form the outside or convex surface of the curve, and the least expansible the concave. In like manner should the temperature fall the most expansible will form the inner or concave surface.

Fig. 18.

Now if the balance-wheel of a chronometer be formed as in Fig. 18, not with one continuous rim, but with a broken rim of several separate pieces, all of which are fixed at one end and free at the other, the free ends being loaded; and further, if each piece be composed of two metals, of which the most expansible is placed without; then it is evident, from what we have just said, that on a rise of temperature the loaded ends will approach the centre. This may be so arranged as to counteract the effect produced on the rate of the chronometer by the matter of the wheel being thrown from the centre on account of the radius being lengthened through expansion. In practice, however, this method of compensation is very seldom perfect, and the rate of the best chronometer probably varies a little from one temperature to another. In the Greenwich and Liverpool Observatories the temperature corrections of chronometers are ascertained; and Mr. Hartnup, of the Liverpool Observatory, has given some very interesting examples of his method of applying a temperature correction to these instruments.

OTHER APPLICATIONS OF THE LAWS OF DILATATION.

81. Breguet's metallic thermometer. A very sensi

tive thermometer has been

made by M. Breguet on the principle just mentioned. It consists of a spiral (Fig.19) composed of silver, gold, and platinum rolled together so as to form a very fine ribbon. In this state it is sensitive to an exceedingly small change of temperature, becoming coiled or uncoiled, owing to the different expansion of the metals of which the compound ribbon is made. A

needle attached to one extremity of the coil points to a scale which is graduated experimentally by the aid of an ordinary thermometer.

82. Reduction of barometric column. When the pressure of the atmosphere is expressed in the number of inches of mercury which it is capable of supporting, in order to render the statement complete it is necessary to know the temperature of the mercury, since this fluid has a different density at different temperatures. Thus we find (Art. 52) that one inch of mercury at o°C will denote the same atmospheric pressure as 1.005393 inches at 30°C.

Another thing to be noted is that the scale, by aid of which we read the column of mercury, even if correct, yet only denotes true inches and parts of an inch at 62°Fahr., if it be of English make, so that at any other temperature allowance must be made not only for the change in density of the

mercury but for the change in length of the divisions of the scale.

Example.-Suppose that an English barometer with a brass scale, correctly graduated, reads 30 inches at 45° Fahr., what is the pressure in true inches of mercury reduced to the specific gravity it has at 32° Fahr.?

Since the scale is only correct (Art. 70) at 62° Fahr., and since brass expands very nearly .00001 for 1° Fahr., it follows that 30 apparent inches at 45° Fahr. =

30

1.00017

=

29.995

true inches. Also the density of mercury at 32° Fahr. (or o°C) is to its density at 45° Fahr. (or 7°.2C) as 1.001294 to I. Hence the atmospheric pressure in mercury at 32° Fahr. will be

29.995 1.001294

=

29.956 inches.

In French barometers, on the other hand, the indications of the scale are correct at o°C, the same temperature to which the mercurial column is reduced, while the scale itself represents millimètres.

In comparing an English and a French barometer together it is therefore necessary to reduce the indications of each to 32° Fahr.; that is to say, to find by the one the pressure of the air in inches of mercury at 32° Fahr., and by the other the same in millimètres of mercury at o°C. If both instruments are correct, their indications should then bear to one another the same proportion as inches to millimètres.

83. Expansion and contraction of metals. It requires the application of very intense pressure to produce the same change of volume in a solid or liquid body as that which is occasioned by a very small change of temperature. It follows from this that the forces exerted by solids in contracting or expanding, or by liquids in expanding, must be very great. If a strong vessel be entirely filled with a liquid and then sealed tightly, the vessel will burst if there be a considerable rise of temperature.

In like manner it has been calculated, that a bar of wrought iron whose temperature is 15° Fahr. above that of the surrounding medium, if tightly secured at its extremities, will draw these together with a force of one ton for each square inch of section on cooling down to the surrounding temperature.

In the arts it is of great importance to bear in mind the intensity of this force, sometimes with the view of guarding against its action, and sometimes in order to make it useful. Thus bars of furnaces must not be fitted tightly at their extremities, but must at least be free at one end. In making railways also a small space must be left between the successive rails.

Allowance must also be made for expansion and contraction in the case of tubular and lattice bridges. The reader who has visited the Menai tubular bridge will recall the arrangement made for this purpose.

For a similar reason water or gas pipes are fitted to each other by telescopic joints; and, generally speaking, the effects which may follow change of temperature must always be present before the mind of the constructor or engineer.

As an instance of the advantage which may be derived from the force of contraction, we may mention the familiar method by which tires are secured on wheels;-the tire is put on hot, when it fits loosely, but when it has contracted on cooling, it grasps the wheel with very great force.

It is probably also owing to the sudden change of volume from rapid cooling that tempered steel acquires that hardness which renders it so invaluable in the arts.

CHAPTER VI.

Change of State.-Liquefaction and Solidification.

84. Very many of the substances with which we are acquainted may be made to appear before us, either in the solid, the liquid, or the gaseous condition; but there are others that cannot be made to change the state in which we find them, or can only be compelled to do so with very great difficulty.

Thus we have not yet been able to freeze pure alcohol, nor have we been able to liquefy atmospheric air.

Heat is the well-known agent which causes change of state; and it always acts in such a manner that a substance passes from the solid to the liquid, and from the liquid to the gaseous state, by the addition of heat, and back again in the reverse direction by the withdrawal of this agent. This law is quite universal, and the order is never reversed; so that, although we cannot as yet solidify alcohol, we are quite sure that our only chance of success lies in abstracting heat from this liquid; and in like manner, although we have not as yet succeeded in melting some substances, we are sure that if we ever succeed it will be by the application of great heat.

85. Let us in the first place study the passage of bodies from the solid to the liquid state.

The characteristics of these states are too well known to need description. We are all acquainted with the rigidity and permanence of form which denote a solid, and with the excessive mobility of a liquid which enables it readily to assume the form of the vessel in which it is placed; never