The following outline will explain how a line may be so divided. Suppose the line AB ([Fig. 40]) is to be divided into nine equal parts. Adjust a hinged rule so that the points A and B coincide with the inside edges of the limbs, one of them, A, being at the ninth division (e.g. the ninth inch) of CE. Then if lines parallel to ED be drawn from each division of the scale to meet AB, AB will be divided into nine equal parts.

A very convenient and simple arrangement on this principle for dividing a line into any number of equal parts with considerable accuracy, is described by Miss S. Marks in the Proceedings of the Physical Society, July 1885.[20] One limb of a hinged rule D is made to slide upon a plain rule fixed to it; the plain rule carries needles on its under surface which hold the paper in position. The position of the divided rule and line to be divided being adjusted, the hinged rule is gently pushed forwards, as indicated by the arrow in [Fig. 40], till division eight coincides with the line AB. A mark is made at the point of coincidence, and division seven on the scale is similarly brought to the line AB, and so on. The inner edge of EC should have the divisions marked upon it, that their coincidence with AB maybe more accurately noted. The joint E must be a very stiff one.

A line drawn of given length or a piece of paper may be divided into any given number of equal parts, and will then serve as the scale A of [Fig. 39], [p. 74], the thermometer or other object to be graduated taking the place of B.

Scales carefully divided according to any of the methods described will be fairly accurate if trustworthy instruments have been employed as standards.

It will be found possible when observing the volume of a gas over mercury, or the height of a column of mercury in a tube, to measure differences of one-sixth to one-eighth of a millimetre with a considerable degree of accuracy. To obtain more delicate measurements a vernier[21] must be employed.

To Calibrate Apparatus.—The glass tubes of which graduated apparatus is made are, as already stated, very rarely truly cylindrical throughout their entire lengths. It follows that the capacities of equal lengths of a tube will usually be unequal, and therefore it is necessary to ascertain by experiment the true values of equal linear divisions of a tube at various parts of it.

A burette may be calibrated by filling it with distilled water, drawing off portions, say of 5 c.c. in succession, into a weighing bottle of known weight, and weighing them.

Great care must be taken in reading the level of the liquid at each observation. The best plan is to hold a piece of white paper behind the burette, and to read from the lower edge of the black line that will be seen. Each operation should be repeated two or three times, and the mean of the results, which should differ but slightly, may be taken as the value of the portion of the tube under examination.

If the weights of water delivered from equal divisions of the tube are found to be equal, the burette is an accurate one, but if, as is more likely, different values are obtained, a table of results should be drawn up in the laboratory book showing the volume of liquid delivered from each portion of the tube examined. And subsequently when the burette is used, the volumes read from the scale on the burette must be corrected. Suppose, for example, that a burette delivered the following weights of water from each division of 5 c.c. respectively:—

C.C.Grams.
0to5gave4·90
5„10„4·91
10„15„4·92
15„20„4·93
20„25„4·94
25„30„4·95
30„35„4·96
35„40„4·97
40„45„4·98
45„50„4·99