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The Calipers

The calipers consist of a straight rectangular bar of brass, D E (fig. 1), on which is engraved a finely-divided scale.

From this bar two steel jaws project. These jaws are at right angles to the bar; the one, D F, is fixed, the other, C G, can slide along the bar, moving accurately parallel to itself. The faces of these jaws, which are opposite to each other, are planed flat and parallel, and can be brought into contact On the sliding piece C will be observed two short scales called verniers, and when the two jaws are in contact, one end of each vernier, marked by an arrowhead in the figure, coincides with the end of the scale on the bar.(1) If then, in any other case, we determine the position of this end of the vernier with reference to the scale, we find the distance between these two flat faces, and hence the length of any object which, fits exactly between the jaws.(2)

It will be observed that the two verniers are marked 'out-sides' and 'insides' respectively. The distance between the jaws will be given by the outsides vernier. The other pair of faces of these two jaws, opposite to the two plane parallel ones, are not plane, but cylindrical, the axes of the cylinders being also perpendicular to the length of the brass bar, so that the cross section through any point of the two jaws, when pushed up close together, will be of the shape of two U's placed opposite to each other, the total width of the two being exactly one inch. When they are in contact, it will be found that the arrowhead of the vernier attached to the scale marked insides reads exactly one inch, and if the jaws of the calipers be fitted inside an object to be measured - e.g., the internal dimensions of a box - the reading of the vernier marked insides gives the distance required.

Suppose it is required to measure the length of a cylinder with flat ends. The cylinder is placed with its axis parallel to the length of the calipers. The screw A (fig. 1) is then turned so that the piece attached to it can slide freely along the scale, and the jaws of the calipers are adjusted so as nearly to fit the cylinder (which is shown by dotted lines in the diagram). The screw A is then made to bite, so that the attached piece is 'clamped' to the scale. Another screw, B, on the under side of the scale, will, if now turned, cause a slow motion of the jaw c G, and by means of this the fit is made as accurate as possible. This is considered to be attained when the cylinder is just held firm. This screw B is called the 'tangent screw', and the adjustment is known as the 'fine adjustment'

It now remains to read upon the scale the length of the cylinder. On the piece c will be seen two short scales - the 'outsides' and 'insides' already spoken of. These short scales are called 'verniers'. Their use is to increase the accuracy of the reading, and may be explained as follows: suppose that they did not exist, but that the only mark on the piece c was the arrowhead, this arrowhead would in all probability lie between two divisions on the large scale. The length of the cylinder would then be less than that corresponding to one division, but greater than that corresponding to the other. For example, let the scale be actually divided into inches, these again into tenths of an inch, and the tenths into five parts each; the small divisions will then be 1/50 inch or 0.02 inch in length. Suppose that the arrowhead lies between 3 and 4 inches, between the third and fourth tenth beyond the 3, and between the first and second of the five small divisions, then the length of the cylinder is greater than 3+3/10+1/50, i.e. >3.32 inches, but less than 3+3/10+2/50, i-e. <3.34 inches. The vernier enables us to judge very accurately what fraction of one small division the distance between the arrowhead and the next lower division on the scale is. Observe that there are twenty divisions on the vernier,(3) and that on careful examination one of these divisions coincides more nearly than any other with a division on the large scale. Count which division of the vernier this is - say the thirteenth. Then, as we shall show, the distance between the arrowhead and the next lower division is 13/20 of a small division, that 13/1000 = 0.013 inch, and the length of the cylinder is therefore

We have now only to see why the number representing the division of the vernier coincident with the division of the scale gives in thousandths of an inch the distance between the arrowhead and the next lower division.

Turn the screw-head B till the arrowhead is as nearly coincident with a division on the large scale as you can make it. Now observe that the twentieth division on the vernier is coincident with another division on the large scale, and that the distance between this division and the first is nineteen small divisions. Observe also that no other divisions on the two scales are coincident. Both are evenly divided; hence it follows that twenty divisions of the vernier are equal to nineteen of the scale - that is, one division on the vernier is 19/20ths of a scale division, or that one division on the vernier is less than one on the scale by 1/20th of a scale division, and this is 1/1000th of an inch.(4)

Now in measuring the cylinder we found that the thirteenth division of the vernier coincided with a scale division. Suppose the unknown distance between the arrowhead and next lower division is x. The arrowhead is marked o on the vernier. The division marked i will be nearer the next lower scale-division by 1/1000th of an inch, for a vernier division is less than a scale division by this amount. Hence the distance in inches between these two divisions, the one on the vernier and the other on the scale, will be

The distance between the thirteenth division of the vernier and the next lower scale division will similarly be

But these divisions are coincident, and the distance between them is therefore zero; that is x = 13/1000. Hence the rule which we have already used.

The measurement of the cylinder should be repeated four times, and the arithmetic mean taken as the final value. The closeness of agreement of the results is of course a test of the accuracy of the measurements.

The calipers may also be used to find the diameter of the cylinder. Although we cannot here measure surfaces which are strictly speaking flat and parallel, still the portions of the surface which are touched by the jaws of the calipers are very nearly so, being small and at opposite ends of a diameter.

Put the calipers on two low supports, such as a pair of glass rods of the same diameter, and place the cylinder on end upon the table. Then slide it between the jaws of the calipers, adjusting the instrument as before by means of the tangent screw, until the cylinder is just clamped. Repeat this twice, reading the vernier on each occasion, and taking care each time to make the measurement across the same diameter of the cylinder.

Now take a similar set of readings across a diameter at right angles to the former.

Take the arithmetic mean of the different readings, as the result.

Having now found the diameter, you can calculate the area of the cross section of the cylinder. For this area is πd2/4, d being the diameter.

The volume of the cylinder can also be found by multiplying the area just calculated by the length of the cylinder.

Experiments.

Determine the dimensions (1) of the given cylinder, (2) of the given sphere.

Enter results thus:

1. Readings of length of cylinder, of diameter.

2. Readings of diameter of sphere.



(1) If with the instrument employed this is found not to be the case, a correction must be made to the observed length, as described in §3. A similar remark applies to §2.
(2) See frontispiece, fig. 3.
(3) Various forms of vernier are figured in the frontispiece
(4) Generally, if n divisions of the vernier are equal to n-1 of the scale, then the vernier reads to 1/nth of a division of the scale


Last Update: 2011-03-27