313.—It may be useful to the surveyor, far from aid of the optician, to know that divisions on silver which are much oxidised may be brought up to sharp lines by the use of a piece of fine-grained charcoal, sharpened by a clean file to a chisel point. This should be frequently dipped in water, and rubbed lightly with the flat of its end surface, Fig. 118, keeping the motion of the hand in the direction of the circumference of the circle. The piece of charcoal before being used should be first tried upon a piece of plain, smooth metal—an old coin which is worn smooth will do—to see that it is not scratchy. No kind of polishing powder should in any case be used for cleaning limbs or verniers, as this is sure to rub down the edges of the cuts and thereby ruin the divisions of the instrument.
314.—It must be understood that the above directions are not intended for the ordinary cleaning of the circle for an instrument in general use, as such would be injurious to it. In the ordinary daily use of the circle, if it is not in any case touched by the hand, and is kept carefully brushed with a large, soft camel-hair brush when taken from the case, and the same when returned to it, it will keep a long time in an excellent state. If the circle is slightly tarnished, this tarnish may be removed by a piece of quite clean wash leather; but the brush is always the safest if sufficient. If the vernier gets grubby against the circle, a piece of clean thin writing-paper may be passed between these parts, which will clear out any dirt or grit there may be between sufficiently.
315.—The Vernier Reading Index.—This is one of the most important inventions ever applied to instruments of precision for measuring upon the circumference of the circle. It was invented or brought into practical use by Pierre Vernier, a native of Ornans, near Besançon, in Burgundy. The first publication of the invention appears in a pamphlet published in Brussels in 1631, Construction, Usage, et Proprietes du Quadrant Nouveau de Mathematique. This invention was possibly foreshadowed, as it is mentioned by Cristopher Clavius in his Opera Mathematica, 1612, vol. ii. p. 5, and vol. iii. p. 10; but he did not propose to attach it permanently to read into an arc, that is, to place it in its practical form.
316.—The value of the vernier as a means of reading small quantities depends upon the fact that the eye cannot separate lines, drawn at equal distance apart, of above a certain degree of closeness, there being a point for all vision where such lines appear to mix with the ground upon which they are drawn and form a tint; therefore, an index reading into such close lines would be, unless under extreme magnification, most indefinite; whereas the eye can see a single separate line clearly and detect any break in it. The vernier for reading subdivisions depends upon the functions of the eye having power to detect any break in an otherwise straight line, so that a line that appears without a break may be taken as the index of reading from among others that appear broken or separated. It is found in practice that a line as fine as it can be clearly seen will appear broken in its continuity with another equally fine line, if at the meeting the rectilinear displacement is as much as ·25 to ·2 part of the width of the line. It therefore follows that we may read closer by displacement of parts of a single line than by any possible series of lines that can be drawn in spaces apart upon a surface; so that if we can arrange lines in such a manner that they open out or separate into distinct lines to admit of this principle, we obtain the full value of the unbroken single line reading, and this is the principal aim of the vernier.
317.—On the same principle that we can find the straight or most direct line of a series of lines to take as our index, we can also estimate the amount of the displacement of our selected line, if this does not read perfectly straight from the vernier division to the circle division. This small difference is detected in practice by many experienced surveyors, so that a vernier reading nominally to minutes only is recorded n′ + 15″, 30″ or 45″, that is to 15″. There is no doubt that this will be approximate, but it may be much nearer than the even minutes, say to the 30″ on a 5-inch, or the 15″ on a 6-inch sharply divided circle.
Fig. 119.—Origin of vernier scale.
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318.—The Vernier Scale, as employed by Vernier, was divided to read minutes upon a circle or limb divided to half degrees, by taking thirty-one divisions of the scale and dividing these in thirty equal parts for a separate scale to read against it. This plan is now termed an inverse reading, the reading being the reverse to the direction of that of the arc. In modern practice the vernier to read minutes is divided to the length of 29 half degrees, and this length is subdivided into thirty equal parts: consequently, where the vernier and scale are placed edge to edge or reading to reading, every division of the vernier advances consecutively on the scale one-thirtieth of the half degree, that is = 1′ of arc on the scale divided to half degrees. In the above diagram, Fig. 119 represents the scale and vernier at the position from which the description is taken, wherein the vernier is shown to cover 29 half degrees or 14° 30′, and this length is divided into thirty parts. The consecutive advance of the vernier on the scale is shown + 1′ for each half degree. In this position of the vernier, or at a similar position in relation to any other half degree of the circle the arrow placed at the zero of the vernier reads direct into the degree or half degree, so that this reading must be n° or n° 30′ at any equivalent position in relation to any line on the limb.
