the steam rising from boiling water, as in the hypsometer. A suitable arrangement is not difficult to make if the laboratory can furnish a hypsometer somewhat wider than the usual ones, with a good wide opening in the top of the cover.

(2) To obtain the coefficient of expansion of a piece of metal-iron, for example-relatively to glycerine, we take a bar of the metal whose volume is obtained from a knowledge of its weight and specific gravity, and place it in the tube before the neck is drawn out.

The bar should be bent so as only to touch the tube at a few points, otherwise it will be impossible to fill the tube with the glycerine.

The tube is filled after having been weighed when empty, and the weight of glycerine in it at a known temperature is determined. Let the temperature be o° C. It is then raised to say 100° C. and the weight of the glycerine within again determined. The difference between these two gives the weight of glycerine expelled.

Let us suppose we know the specific gravity of glycerine; we can obtain the volume of the glycerine originally in the tube by dividing its weight by its density. Let us call this v1 We can also find the volume of the glycerine expelled; let this be v, and let v, be the volume of the iron, at the lower temperature, v, the volume of the thermometer, t, the change in temperature, a, the coefficient of expansion of the glycerine, B, the coefficient of expansion of the metal, y, the coefficient of expansion of the glass.

When the temperature has risen to the volume of glycerine is v1(1+ at) and that of the metal is v2(1+ẞt); thus the whole volume of glycerine and iron will be v1(1+at)+ V2(1+ẞt). The volume of the glass is v(1+y).

The difference between these must clearly give the volume of glycerine which has escaped, or v.

V1(1+at)+V,(1 +ẞt) −v(1+y)=v.

Thus

V1(a-y) is the volume of glycerine which would have been expelled if the volume of the tube had been v1; that is to say, if the tube had been such as to be filled entirely with the glycerine which was contained in it at the first weighing. This can be calculated from the knowledge of the weight and specific gravity of the glycerine and of the value of the coefficient of expansion of the glycerine relatively to the glass. Subtract this from the volume actually expelled. The difference is the increase in volume of the metal relatively to glass for the rise in temperature in question. Divide the result by the volume of the metal and the rise in temperature; we get the coefficient of relative expansion of the metal.

Thus, let the original weight of glycerine be 11222 gms., then the amount which would be expelled, due to the rise of temperature of the glycerine only, will be 457 gramme, since the coefficient of expansion of glycerine relative to glass is 0005. Suppose that we find that 513 gramme is expelled. The difference, 056 gramme, is due to the expansion of the metal. Taking the specific gravity of glycerine as 130, the volume of this would be 043 c.c. Suppose that the original volume of the metal was 5 c.c. and the rise of temperature 100° C., the coefficient of expansion is given by dividing 043 by 500, and is, therefore, o00086.

Experiments.-Determine the coefficient of expansion of the given liquid and of cubical expansion of the given solid.

38. The Constant Volume Air Thermometer.

Determina

tion of the Coefficient of Increase of Pressure per degree of Temperature of a Gas at constant Volume.

The air is contained in a closed flask or bulb, which can be heated to any required temperature. From this a tube, after being bent twice at right angles, passes vertically downwards to a reservoir of mercury, into one end of which a plunger is fitted. A second and longer vertical tube is also screwed into this reservoir. On the tube connecting the bulb with the reservoir is a mark, which should be as near the bulb as it can conveniently be.

By means of the plunger the level of the mercury in this tube is adjusted until it coincides with the mark, the bulb being kept at o° C. by immersion in melting ice. The mercury at the same time moves in the other tube, and the difference of level of the two columns is measured by means of the kathetometer or of scales placed behind the tubes.

Let this difference be 5'62 cm., and, suppose the height of the barometer to be 75 38 cm., then the pressure on the enclosed gas is that due to a column of mercury 81 cm. in height.

It is of the greatest importance that the air in the bulb should be free from moisture. The bulb inust, therefore, have been thoroughly dried and filled with dry air by the use of the three-way cock, drying tubes, and air-pump, as already described, (§ 16). In Jolly's air-thermometer the three-way cock is permanently attached to the tube which connects the bulb with the reservoir.

The bulb is next immersed in a vessel of water which is made to boil, or, better still, in the steam from boiling water. The mercury is thus forced down the tube connected with the bulb, but by means of the plunger it is forced back until it is level again with the mark. At the same time it rises considerably in the other tube. When the water boils and the conditions have become steady, the

difference of level in the two tubes is again noted. Suppose we find it to be 34'92 cm., and that the barometer has remained unchanged.

The air is now under a pressure due to 110°3 cm. of mercury, its volume remaining the same. The increase of pressure, therefore, is that due to 29'3 cm., and the coefficient of increase per degree centigrade is

In this case it is important that the lower temperature should be o° C., for to determine the coefficient we have to divide by the pressure at o° C., and the difference between this and the pressure at the temperature of the room, say 15°, is too great to be neglected, as in the case of a solid or liquid.

If greater accuracy be required, allowance must be made for the expansion of the glass envelope, and for that portion of the air in the connecting tube which is not at the temperature of the bath.

The same apparatus can be used to determine the coefficient of increase of volume at constant pressure per degree of temperature.

In this case make the first observation as before, noting at the same time the height at which the mercury stands in the marked tube. Now heat the bulb. The air will expand and drive the mercury down the one tube and up the other, thus increasing at the same time the volume of the air and the pressure to which it is subject. By withdrawing the plunger the mercury is allowed to sink in both tubes. It must, however, sink faster in the one open to the external air, and after a time a condition will be reached in which the difference between the levels in the two is the same as it was originally. The air in the bulb is under the same pressure as previously, but its temperature has been raised to 100° C. and its volume altered. Observe the level of the mercury in the tube connected with the bulb. If

the bore of this tube be known, the change of level will give the increase of volume; hence, knowing the original volume, the coefficient of expansion per degree of temperature can be found.

Owing to the large amount of expansion produced in a gas by a rise of temperature of 100° C., a tube of large bore is required.

The method, however, as here described will not lead to very accurate results, for it is almost impossible to insure that the air in the bulb and that in the tube should be all at the same high temperature. In the first method, on the other hand, the portion of tube occupied by air can be made very small, so as easily to be jacketed along with the bulb and kept at an uniform high temperature.

The method is open to the objection that the air in contact with the mercury, and therefore the mercury itself, is at a different temperature in the two parts of the experiment. The density of the mercury, therefore, is different and the increment of pressure is not strictly proportional to the difference of level. This error will be but small.

We have described the experiment as if air was the gas experimented with. Any other gas which does not attack. the mercury may be used.

Experiment.- Determine for the given gas the coefficient of the increase of pressure per degree of temperature at constant volume.