ing D with water and inverting it in the trough, let the air bubble into it from the tube by opening C and lowering B. When D is nearly full, close C so as to prevent the escape of the air, and read and record the volume as given by the graduation on D. Now decant the air from D into the flask A. Great care is Great care is necessary in this operation to prevent spilling, and it is best to practise a few times beforehand, until it can be transferred without allowing a single bubble to escape. Continue to empty B until all the air has been passed into A. The latter will then be nearly full of air, unless some has been lost. In the latter case do not give up the experiment, but keep on, retaining as much air as possible. Now holding the neck of the flask in the hand press the ground glass against it with the thumb, so as to retain what water is still in it, and taking it out of the trough stand it on the table right side up. Wipe the outside dry, and weigh it in its present condition; also when full of water, and when empty. Call the three weights m, n and o, respectively. The volume of air in cm.3, at the beginning of the experiment, will equal no in grammes; that at the end m. There are now four volumes of air to be compared. First the volume at the beginning of the experiment, when the air was moist and the dew-point was given; secondly, when transferred to B; thirdly, that found by adding the readings of D; and fourthly, that at the close of the experiment. Reduce all of these to the standard pressure and temperature by the method given below, when they should be equal if no air has escaped, otherwise the difference shows the amount of the loss. Great accuracy must not be expected, owing to the absorption of the air by the water, and for various other reasons.

n

REDUCTION OF GASES TO STANDARD TEMPERATURE AND PRESSURE.

tP

I. Dry Gas. Given a volume Vte of dry gas at temperature t, and barometric pressure P, to find what would be its volume Voн if cooled to 0° C, and the pressure altered to the standard H 760 m.m. Suppose that it is first cooled to 0°, without changing the pressure, and call its new volume VoP. We have by Gay Lussac's law for the expansion of gases, VP Vor (1+ at), in which a=, the coefficient of expansion of gas. Again, by

1

Mariotte's law we have, Vor: VOH H: P. Hence Vor

Vt (1 + at) H

=

VIP (273 +t) 760

tP

. (1).

For any other temperature t', and pressure P', we have,

273 P'

Voп=Ver' (273+ t') 760 '

он

P 273 +ť hence VIP VIP P'' 273 +t'

(2)

The first formula is used to determine the true quantity of gas present, that is, the volume at the standard temperature and pressure. The second, to compute the new volume when we alter both temperature and pressure.

II. Gas saturated with Moisture. Call p the pressure of aqueous vapor at the temperature t. Then of the total pressure P we have p due to the vapor, and Pp to the gas; substitute, therefore, P-p for P in equation (1), and we have,

273 (P-p)
(273 +t)760

(3).

III. Gas moist, but not saturated. Let the gas be gradually cooled, until the temperature becomes so low that the moisture can no longer be retained as vapor, but begins to condense on the walls of the vessel. This temperature 7 is called the dew-point; let p' be the corresponding pressure of the vapor. Then p: p' 1+at: 1+aT, or p = p(1+ at) ÷ (1+ a T'), and substituting this value in equation (3), we have

Apparatus. A balance AB, Fig. 15, capable of sustaining 5 kgrs. on each side, and turning with a tenth of a gramme under this load. Remarkably good results may be obtained with common balances, such as are used for commercial purposes, by attaching a long index to the beam, as in the figure. Several pounds of distilled water should be provided, a thermometer, a set of weights, and a rubber tube and funnel. Instead of a scale-pan, a counterpoise C is attached to one arm of the balance as a method of double weighing is to be used. The standard to be graduated, which we will suppose to be a tenth of a cubic foot, consists of a glass vessel D, whose capacity somewhat exceeds this amount. A

STANDARDS OF VOLUME.

53

1′′ steam valve is screwed into the cap closing the lower end which also carries a sharp brass point to form the lower limit of the volume. A ring is attached to the cap closing the upper end of the vessel, by which the whole is supported. A brass hook with the point turned upwards passes through this cap, in which a hole has been drilled to allow the air to pass in or out. The hook may be raised or lowered, and clamped at any height by a conical nut surrounding it, or by a set screw. Finally a millimetre scale should be attached to the upper end of D.

A

B

Experiment. Note the height of the barometer, the temperature of the room, also that of the distilled water. Fill D, by attaching the rubber tube, as in the figure, opening E and pouring in the water. When the vessel is full, close E and remove the rubber tube. Take care that no air bubbles adhere

to the side of the glass. Open E and

C

Fig. 15.

D

E H

F

draw off the water until it stands just on a level with the top of the scale attached to the glass. Counterpoise by adding weights to the scale-pan F, until the index stands at zero, first reading the directions for weighing, given on page 47. Draw off enough water to lower its level just one centimetre, counterpoise again, and repeat until the surface reaches the bottom of the scale. If too much water is removed at any time refill the vessel above the mark, and draw off the water again. Now bring the water level just above the point of the hook, and close E, so that the flow shall take place drop by drop. Use the hook as in Experiment 13, and as soon as the point becomes visible close E. Read the level of the water and counterpoise as before. Repeat two or three times, adding a little water after each measurement. Now open E, and let the water run out until the lower point just touches the surface. Measure the temperature of the water as it escapes. To counterpoise the beam nearly three

kilogrammes additional must be added to F. Make this weighing with care, and repeat two or three times, as when observing the upper point. Subtract each of the weights when the vessel was full, from the mean of those last taken, and the difference gives the weight of the water contained between the lower point. and each of the other observed levels.

Now to determine the volume, we have given by Kater, the weight of 1 cubic inch of distilled water at 62° F., and 30 inches pressure, equals 252.456 grains, and 1 gramme equals 15.432 grains. From this compute the weight of one tenth of a cubic foot. Two corrections must now be applied, the first for temperature, the second for pressure. Water has an expansion of about .00009 per 1° F. when near 62°, and glass .000008 linear, or three times this amount of cubical expansion at the same temperature; of course the apparent change of volume is the difference of increase of the water, and of the glass. Evidently at a high temperature less water would be required, hence this correction is negative if the temperature is above 62°. Practically in making standards it is best to keep the temperature exactly at 62°, adding ice or warm water if necessary, as this correction is a little doubtful, owing to the unequal expansion of different specimens of glass. The vessel D is buoyed up by the air, by an amount equal to the weight displaced, and this weight is evidently proportional to the barometric pressure H. Now 100 cubic inches of air at 30 inches weigh 2.1 grms., hence at 1 inch it would be, and if the pressure is changed from 30 to H, the change in weight would evidently be 2.1 × (30 — H) ÷ 30. The weights, however, are also buoyed up in the same way, but as the specific gravity of brass is about 8, the effect is only one-eighth as great. The true correction is then seven-eighths of this amount. The higher the barometer the greater the buoyancy, and the lighter the water will appear, or this correction will be negative for pressures above 30 inches. Both the corrections will be small, and in most cases can be neglected; but it is well to make them, in order to be sure to understand the principle. Having thus computed how much the tenth of a cubic foot ought to weigh, see if the distance between the points is correct, and if not, determine by interpolation

where the water level should be in order to render the capacity exact.

20. READING MICROSCOPES.

Apparatus. Three cheap French microscopes mounted on moveable stands, as in AB, Fig. 16. Two should have cross-hairs in their eye-pieces, while the third should contain a thin plate of glass with a very fine scale ruled on it. An accurate scale divided into millimetres is required as a standard of comparison, and since the division marks of those in common use are too broad for exact measurements, it is better to have one made to order, with very fine lines cut on the centre of one face instead of on the edge. The best material is glass, but copper or steel will do, especially if coated with nickel or silver. Several objects to be measured should be selected, as a rod pointed at each end, the two needle points of a beam-compass, and a scale divided into tenths of an inch, whose correctness is to be tested. Under the microscopes is placed a board D, on which the object to be measured C, is laid, and which may be raised or lowered gradually by screws, or folding wedges. Another method of supporting the microscopes, superior in some respects, will be found described under the Experiment of Dilatation of Solids by Heat.

C

A

Fig. 16.

Experiment. If a measurement within a tenth of a millimetre is sufficiently exact, use the two microscopes with cross-hairs. Place them at such a distance apart that each shall be over the end of the object to be measured, which should be laid on D. They should be raised or lowered until in focus, and then set so that their cross-hairs shall exactly coincide with the two given points. Remove the object very carefully, so as not to disturb their position, and replace it by the standard scale, bringing the zero to coincide with one of the cross-hairs. Now looking through the other microscope read the position of its cross-hairs on the scale, estimating the fractions of a millimetre in tenths. If the image of the scale is not distinct it may be focussed by slowly raising or lowering the board on which it is placed, taking great care not to disturb the microscopes. To get the whole number of millimetres, a needle may be laid down on the scale, and the right division distinguished by its point.

If greater accuracy is desired, use the third microscope, find