66. Dilatation of gases existing under different pressures. The following law has been deduced by Regnault: "Air and all gases except hydrogen have coefficients of dilatation which increase to some extent with their density."

Regnault has likewise enunciated the following very important law: "The coefficients of dilatation of the different gases approach more nearly to equality as their pressures become feeble, in such a manner that the law which is expressed by saying that all gases have the same coefficient of dilatation ought strictly to be considered as a law which applies only to gas in a state of extreme tenuity, but which is departed from as gases become compressed, or, in other words, as their molecules approach each other.”

A gas whose molecules are so far apart as not to exert any sensible influence upon each other may be called a perfect gas.

67. Air Thermometer. The present is a suitable opportunity to discuss the air thermometer, to which in our first chapter we promised to return.

If we have a series of thermometers with different liquids, such as mercury, alcohol, water, &c., and all enclosed in envelopes of the same description, and if each instrument has been accurately pointed off and graduated in such a manner that 1°C denotes the one hundredth part of the capacity of the capillary tube between o° and 100°, nevertheless these instruments, if plunged into the same liquid, will not all register precisely the same temperature.

But if we restrict our choice to thermometers with the same liquid, as, for instance, to mercurial thermometers made of the same kind of glass, we obtain instruments strictly comparable one with another, and which if plunged into the same liquid will all indicate the same temperature.

But though such instruments are comparable with each

other, we are not yet sure if their common reading accurately represents the true temperature; for there is no obvious reason why we should prefer a mercurial to an alcohol or water thermometer, which we have seen would both give slightly different indications. The mercurial thermometer stands therefore in the following position:- - different instruments of this kind may be made to give identical indications, but yet we cannot rely upon these for accurately measuring temperature; nevertheless we cannot suppose that they are very far wrong.

Let us now employ a gas or air thermometer, and confine in envelopes of the same material different gases of sufficient tenuity and not liable to be easily condensed, and let us suppose that we have the means of ascertaining accurately the pressure which they exert upon their envelopes; and let us also in the meantime disregard the expansion of these envelopes. Now if all these gases have a common pressure at o°C they will all have a common pressure at 100°C, or at any other temperature. If we make use of this pressure to determine the temperature, we have thus obtained different instruments whose indications are comparable with each other, even although the gases with which they are filled are different. Gases, if of sufficient tenuity, are therefore in this respect superior to liquids; and it only now remains for us to determine the precise law which connects together the temperature and pressure of a gas in order to make a perfect thermometer. We have various reasons for imagining the law announced by Gay Lussac to be correct, at least in the case of perfect gases. This law, taken in connexion with that of Boyle, asserts that if the pressure of a constant volume of gas be unity at o°C and 1.3665 at 100°C, then the pressure at 50°C will be the mean between these two numbers, or 1.18325. Strictly speaking, it is impossible to prove this law experimentally with precision,

for to do so implies the previous possession of an accurate instrument for measuring temperature. Now we have seen that the mercurial thermometer is not reliable, while for the purpose of this proof it must be presumed that the air thermometer does not yet exist, since in order to use it we must have a knowledge of this very law which we wish to prove. The case stands thus; if we employ mercurial thermometers (which we cannot imagine to be far wrong), Gay Lussac's law is found to give a near approximation to the experimental result. There is, however, a small difference, and the cause of this may be either that mercurial thermometers are not quite right, or that Gay Lussac's law itself is only an approximate expression of the truth. Now, in the first place, we know very well that mercurial thermometers are not absolutely correct, and in the next place, with regard to Gay Lussac's law, its extreme simplicity is in its favour, and we shall afterwards see that there are perhaps theoretical reasons for supposing it to be correct, at least for perfect gases.

In fine, we apprehend that a perfect gas obeys Gay Lussac's law, and may be made to furnish us with a perfect thermometer, and if we cannot procure a gas that is quite perfect, yet atmospheric air deprived of moisture and carbonic acid is a substance sufficiently good for all practical purposes.

Although the air thermometer is in principle peculiarly fitted for the determination of very high temperatures, yet there are considerable mechanical difficulties in the employment of the instrument in such cases. Regnault has lately invented two modifications of this instrument in order to render it suitable to measure the temperature of furnaces (see Annales de Chimie for September 1861). In one of these vapour of mercury is the gas employed, and the instrument is constructed as follows. There is a kind of

flask, either cylindrical or spherical, which may be either of cast or wrought iron, of platinum or of porcelain: the mouth is closed by a plate containing a small aperture. From 15 to 20 grammes of mercury are added to this flask, which is then placed in that part of the furnace the temperature of which we desire to know. The mercury soon boils, its vapour expels the air by the orifice, and the excess of mercurial vapour goes off by the same means. When the apparatus has acquired the temperature of the furnace the flask is withdrawn and made to cool rapidly, and the mercury which remains in the flask is weighed. It may be weighed directly, or, if it contains impurity, it is dissolved in acid and estimated as a precipitate. This weight is that of the vapour of mercury which filled the flask at the temperature of the furnace, and the volume of the flask as well as the density of mercurial vapour being known this temperature may thus be determined.

In conclusion, we append the results of a comparison made by M. Regnault between an air thermometer and a mercurial thermometer with an envelope of crown glass.

CHAPTER V.

Applications of the Laws of Dilatation.

68. Since all the bodies around us are subject to continual change of volume owing to their varying temperature, it is necessary to take account of this in very many operations and investigations whether of a scientific or strictly practical nature. Let us, in the first place, proceed to describe the influence which change of temperature exerts on our standards of length, weight, density and time.

STANDARDS OF LENGTH.

69. Supposing that a yard is taken to denote a certain absolute distance, and that the length of a bar is precisely one yard at the temperature 62° Fahr., it is clear that, owing to the expansion of the material of the bar, its length will be greater than a yard for temperatures higher than 62°, but less than a yard for temperatures below 62°.

If now we employ this bar as a standard by means of which to measure the absolute distance between any two points in terms of the yard as a unit of length, and if it be inconvenient or impossible to make this comparison at 62° Fahr., it will be necessary to know the precise temperature of our standard bar in order that we may know its real length.

The formation of a standard of length is an object of national importance, and we shall now shortly describe the respective standards authorised by the Governments of England and France.

70. English standard. The English standard of length was formerly the parliamentary standard yard executed by

F