--

the two tubes is b b' cm., the pressure of the enclosed air is now measured by h− (b — b'). Again alter the position of the sliding tube and make a similar set of ob servations. Now write down from a table, or by actua calculation, the reciprocals of the pressures, and then plot curve, taking as abscissæ lines proportional to the additiona volume (a - b) of the tube occupied by the air, and fo ordinates the reciprocals of the pressures or numbers pro portional to 1/ {h − (b −b')}.

"

FIG. 16a.

P

If the measurements be made with care, it will be foun that the curve obtained by joining the points thus foun is a straight line suc as PBA in fig. 164 cutting the vertica axis in B and th horizontal axis in a point on the nega tive side of the or gin. Now O B is th reciprocal of the or ginal pressure, th additional volume zero, the actua

B

N

X

volume is v, and the barometric height is given by 1/01 At A the reciprocal of the pressure is zero; the pressure i therefore infinitely large, and the actual volume infinitel small. Thus the distance o A is v, and the distance A measures the actual volume v + a (a - b), when the reciproca of the pressure is P N.

But since the curve given by the experiments is a straight line, A N is proportional to PN, or the volume is inversely proportional to the pressure; in other words, the product of the pressure and volume is constant.

Before taking any readings to determine the difference f pressure it is well to wait a few minutes and notice if the

If they do, we may feel sure there

of the levels remain the same. Again at is no leak at the joints.

imilar se

e, or by ar

(2) To determine by means of the Volumenometer the and the Density of a Solid.

the add

The method is useful in the case of solids soluble in or he air, and affected by water. The solid should be broken into fragnumbers ments sufficiently small to go into the flask E. Determine the volume of the flask and a small portion of the tube D E will be fe down to some convenient mark, as above. We can do this is thus for from one pair of observations if we assume Boyle's law to ight lines be true, for then we have

the neg

Now weigh the solid, and place it in the flask; deterof the mine as before the volume of the portion of the flask not O B is toccupied by the solid, together with that of the tube DE f the orlown to the same mark; let this volume be v'.

ure, the

Then v-v' is the volume of the solid in cubic centiolume metres. But the mass of the solid has been found in actual rammes; dividing this by the volume, we have the density 1/0 B. grammes per cubic centimetre.

sure is

If the second form of apparatus be used with the bulb and nitely innel, it is best to make two marks on the tube, one at F, e AN etween the bulb and funnel, the other at G, just below the Tocal lb, and to determine the volume between these marks in > same way as the volume of part of the tube was found. t this volume be v c.c.

is a e is the

ence

the

Then in using the instrument to measure the volume of solid it is filled with mercury up to the upper mark F at the atmospheric pressure, and then, the funnel being closed, the sliding tube is lowered until the mercury falls to the lower mark. Thus the volume of the contained air

increases by v, which takes the place of a (a - b) in the

The method will give accurate results only in the case in which the volume of the solid is considerable; it should nearly fill the flask.

Experiments.

(1) Test Boyle's law, and measure the volume of the small flask attached to the volumenometer.

(2) Determine the density of the given glass beads.

Enter results thus :

Area of cross section of tube 101 sq. cm.

Four observations of increase of volume and corresponding

pressures, made and plotted on curve shewn.

Volume deduced from diagram .

Division to which tube is filled, a
Division to which mercury falls, b
Level of mercury in sliding tube, b'
Height of barometer, h

155 c.c.

Volume by calculation from one observation:

a-b

b-b'

Volume

154'5 c.c.

H. Capillarity.

To Measure the Surface Tension of a Liquid by the height it rises in a Capillary Tube.

If a narrow tube is dipped into a liquid which wets it, the liquid rises in the tube and stands at a higher level than in the containing vessel. From this we infer that the Articles of the liquid in the neighbourhood of the surface

a different condition from those in the interior of its

mass, and, in consequence, possess a greater amount of potential energy (see Maxwell's 'Theory of Heat,' chap. xx).

The effect may be represented by supposing that the surface film of any liquid is under tension, so that if we draw any line across it we may conceive the portion of the film on one side of the line to act on the portion on the other side with a definite force. The amount of this force per unit of length is found to be a constant for the surface of separation of any two given fluids, and it may be shewn to be equal to the amount of surface energy per unit of area which the fluids possess.

FIG. xvii.

Toc

If now we have three fluids meeting at a point, there will at that point be three definite forces-the tensions of the three surfaces of separation, and in order that there may be equilibrium the surfaces must meet at definite angles. Now let one of the substances c be a solid, and let a and b be the other two. Let Tab (fig. xvii) represent the tension between the surfaces of a and b, and let this surface at o make an angle a with the surface of c. Then, resolving the forces at o parallel to the surface, we have for equilibrium

Tab COS a = TheTea

Τα

A

Tea

a

This equation determines a, the angle of capillarity. If Toe-Tea is greater than Tab, no such angle as a can be found; the liquid is said to wet the surface of the solid, and will run all over it unless prevented by other forces, such as gravity. The system of two fluids and the solid tends to set itself, so that its whole energy is as small as possible.

And since the surface energy of the water-air surface is less than that of the air-glass surface in the case of water in contact with glass, the water tends to cover the glass. If the glass surface be vertical the water as it creeps

up the surface gains potential energy, and equilibrium is reached when the gain of potential energy due to the rise of water is equal to the loss due to the diminution of air-glass surface.

To determine the surface tension of a liquid we require to know the density of the liquid, the diameter of the tube, the angle of contact, and the height the liquid rises.

Let the section of the tube be a circle of radius r. The circumference of this is 2 r, and at each point of this circumference there is a force T per unit of length acting at an angle a with the vertical. The total vertical force is 2. T Cos a. If h be the height of the volume of liquid raised, measured from the flat surface of the liquid in the vessel to the bottom of the meniscus in the tube, and the

weight of the very small portion forming the meniscus be neglected, then the weight of liquid raised is Tr2 hp g.

.. 2π Tr COS α = πpgr3h, ..pgrh sec a dynes per cm.

In practice the method is only used with a liquid, such as water, which wets the glass, and then a = o, sec a = 1,

..Tpgrh dynes per cm.

To perform the experiment a finely divided scale (A B, fig. xviii) must be placed in a vertical position, with one end dipping into

the beaker c, which is to contain the liquid; the scale may most conveniently be of glass divided into millimetres and