Page:Elementary Text-book of Physics (Anthony, 1897).djvu/19

§4] accessory piece, fitted to slide on the principal scale of the instrument to which it is applied. A portion of the accessory piece, equal to $$n$$ minus one or $$n$$ plus one divisions of the principal scale, is divided into $$n$$ divisions. In the former case, the divisions are numbered in the same sense as those of the principal scale; in the latter, they are numbered in the opposite sense. In either case we can measure a quantity accurately to the one nth part of one of the primary divisions of the principal scale. Fig. 1 will make the construction and use of the vernier plain.

In Fig. 1, let 0, 1, 2, 3 ... 10 be the divisions on the vernier; let 0, 1, 2, 3. . . 10 be any set of consecutive divisions on the principal scale.

If we suppose the of the vernier to be in coincidence with the limiting point of the magnitude to be measured, it is clear that, from the position shown in the figure, we have 29.7, expressing that magnitude to the nearest tenth; and since the sixth division of the vernier coincides with a whole division of the principal scale, we have $$\tfrac{6}{10}$$ of $$\tfrac{1}{10}$$, or $$\tfrac{6}{100}$$ of a principal division to be added: hence the whole value is 29.76.

The micrometer screw is also much employed. It consists of a carefully cut screw, accurately fitting in a nut. The head of the screw carries a graduated circle, which can turn past a fixed line. This is frequently the straight edge of a scale with divisions equal in magnitude to the pitch of the screw. These divisions will then show through how many revolutions the screw is turned in any given trial; while the divisions on the graduated circle will show the fractional part of a revolution, and consequently the fractional part of the pitch that must be added. If the screw be turned through $$n$$ revolutions, as shown by the scale, and through an additional fraction, as shown by the divided circle, it will pass through $$n$$ times the pitch of the screw, and an additional fraction of the pitch determined by the ratio of the number of divisions read