From which, since x and x, are given, æ, may be calculated from the first equation since & has been determined. Having found 1, x is calculated from the next equation, and so on successively for all the corrections. If the calculations have been carried out correctly the calculated value of an should agree with that assumed.

A tube is given to you divided into millimetres (Fig. 11). It

Fig. 11.

is to be calibrated between points 16 cms. apart, the errors being required for points at a distance of 2 cms. apart. That is to say, assuming the first and seventeenth centimetre division to be known, the errors at the third, fifth, &c. division are to be found.

The most difficult part of the operation consists in obtaining a mercury thread of the required length. It may most easily be accomplished by slipping a short piece of indiarubber tubing over one end of the glass tube. The free end of the rubber tube is then compressed between the finger and thumb of the right hand, so as to close it completely, the end of the glass capillary tube dipped into clean mercury, and then the rest of the rubber tube compressed between the finger and thumb of the left hand to expel a little air from it. On releasing the left hand, a thread of mercury is drawn up.

The capillary tube should then be quickly placed nearly horizontal with the lower end over the mercury in the bottle, and the end of the rubber tube released. By gently tilting the tube, the thread may be moved from end to end of the tube, and it should be noted whether it moves freely without leaving

portions of mercury behind, or the ends of the thread ceasing to be convex. If this is not the case the thread should be removed from the tube and the tube cleaned, first with a little dilute acid, then with water, then with alcohol, and thoroughly dried. A thread of mercury should then be drawn up into the tube, made to approach the lower end of the tube, and a small drop of mercury forced out and cut off with the finger-nail or a knife.

By carrying out this operation several times the thread may be diminished in length till it occupies between 19 and 21 of the small scale divisions, i.e. within 1 mm. of 2 centimetres.

When this is the case, move the thread till its left-hand end nearly coincides with the division on the left at which the calibration is to commence.

Place the tube on a strip of mirror glass and read both ends of the mercury thread by means of a magnifying lens, avoiding parallax by placing the eye so that its image is covered by the part read, and then slipping the lens into position between the eye and the scale. The excess of the observed length of the thread over 20 scale divisions is the 8 of the preceding equations.

Now move the thread forward 20 small scale divisions so that its left-hand end nearly occupies the position of the righthand end in the previous case, and obtain §1 as before.

Continue the operation till the ends have been read in eight successive positions, and then take readings as the thread is moved backwards. The means of the Ss observed at each part of the scale going and returning should be used in the calculations, which should be carried out and tabulated as shewn below.

A check for some of the intermediate points may be obtained by taking threads 4 and 8 cms. long. Calling the first division 0, the 4 cms. thread will give the corrections at the points 4, 8 and 12, while the 8 cms. thread will only give the correction at the division 8.

To calculate the corrections it is necessary first to find 8, from x, xn and the quantities 80, 81, &c. If these are tabulated as shewn below and & found, the differences 8-80, 8-81 may be written down as in the fifth column and the corrections obtained by successive addition.

Arrange your observations and calculations as follows, giving the mark on the label attached to the tube so that it may be identified :—

+010=x0

1.98 to 4.04=2.06

-04 to 2.03=2.07-05 to 2.0=2.08 2.075 ⚫075 -.0315 +007=x2

-.043=x4

Taking the readings along the tube as abscissae and the corrections at these readings as found by the first measurements as ordinates, above or below according as the correction is positive or negative, plot a "Calibration Curve" for the tube as shewn below, Fig. 12.

Do the same for the second and third sets of readings, taking the same abscissae.

If l is the length of the mercury thread in any position, and

A the mean area of the cross section of the tube within the part occupied by the mercury thread, Al is the volume of the thread. As this volume remains constant as the thread is moved, the length of the thread varies inversely as the mean area of cross section within its length. Hence by taking again dis

tances along the tube as abscis

eft

Fig. 12.

eft

VA

sae, and erecting at the different points occupied by the centre of the mercury thread ordinates inversely proportional to the observed lengths of the threads, we get a representation of the way in which the cross section of the tube varies.

Plot these reciprocals as shewn below, Fig. 13.

The most important practical application of the preceding exercise occurs in the calibra

tion of thermometer tubes. All thermometers used for accurate work should be calibrated either by the maker or by the observer. Information as to the methods of breaking off a mercury thread and complete methods of calibration will be found in Guillaume's Thermométrie.

419

48

Fig. 13.

BOOK II.

MECHANICS AND GENERAL PHYSICS.

SECTION VI.

THE BALANCE.

Apparatus required: Delicate balance, centigram rider, two 500 gram weights.

B

The Balance, in its simplest form, consists of a straight beam AB (Fig. 14) provided at its centre with a knife edge C on which it is supported, and carrying at its ends the pans P and Q, on which the masses to be compared are placed. If the two halves of the beam are alike in every respect, so that the centre of gravity of the beam is at the point of support C, and if the pans have equal mass, the balance will be in neutral equilibrium, whether unloaded or loaded with equal masses. If unequal masses are placed in the pans, the equilibrium will be unstable, however small the inequality may be.

Fig. 14.

It would be inconvenient to have a delicate balance constructed according to this principle, for as two masses are never exactly equal, the balance would never be in equilibrium. A delicate balance, to be useful, should allow us to determine the difference between two

nearly equal masses, and it is proved in treatises on Mechanics that this can be done by constructing the beam AB of the balance so that its centre

A

Ρ

Fig. 15.

B