VERNIER

, is a scale, or a division, well adapted for the graduation of mathematical instruments, so called from its inventor Peter Vernier, a gentleman of Franche Comté, who communicated the discovery to the world in a small tract, entitled La Construction, l'Usage, et les Proprietez du Quadrant Nouveau de Mathen a<*>ique &c, printed at Brussels in 1631. This | was an improvement on the method of division proposed by Jacobus Curtius, printed by Tycho in Clavius's Astrolabe, in 1593. Vernier's method of division, or dividing plate, has been very commonly, though erroneously, called by the name of Nonius; the method of Nonius being very different from that of Vernier, and much less convenient.

When the relative unit of any line is so divided into many small equal parts, those parts may be too numerous to be introduced, or if introduced, they may be too close to one another to be readily counted or estimated; for which reason there have been various methods contrived for estimating the aliquot parts of the small divisions, into which the relative unit of a line may be commodiously divided; and among those methods, Vernier's has been most justly preferred to all others. For the history of this, and other inventions of a similar nature, see Robins's Math. Tracts, vol. 2, p. 265, &c.

Vernier's scale is a small moveable arch, or scale, sliding along the limb of a quadrant, or any other graduated scale, and divided into equal parts, that are one less in number than the divisions of the portion of the limb corresponding to it. So, if we want to subdivide the graduations on any scale into for ex. 10 equal parts; we must make the Vernier equal in length to 11 of those graduations of the scale, but dividing the same length of the Vernier itself only into 10 equal parts; for then it is evident that each division on the Vernier will be 1/10th part longer than the gradations on the instrument, or that the division of the former is equal to 11/10 of the degree on the latter, as that gains 1 in 10 upon this.

Thus let AB be a part of the upper end of a barometer tube, the quicksilver standing at the point C; from 28 to 31 is a part of the scale of inches, viz, from 28 inches to 31 inches, divided into 10ths of inches; and the middle piece, from 1 to 10, is the Vernier, that slides up and down in a groove, and having 10 of its divisions equal to 11 tenths of the inches, for the purpose of subdividing every 10th of the inch into 10 parts, or, the inches into centesms or 100th parts. In practice, the method of counting is by observing (when the Vernier is set with its index at top pointing exactly against the upper surface of the mercury in the tube) which division of the Vernier it is that exactly, or nearest, coincides with a division in the scale of 10ths of inches, for that will shew the number of 100ths, over the 10ths of inches next below the index at top. So, in the annexed figure, the top of the Vernier is between 2 and 3 tenths above the 30 inches of the barometer; and because the 8th division of the Vernier is seen to coincide with a division of the scale, this shews that it is 8 centesms more: so that the height of the quicksilver altogether, is 30.28, that is, 30 inches, and 28 hundredths, or 2 tenths and 8 hundredths.

If the scale were not inches and 10ths, but degrees of a quadrant, &c, then the 8 would be 8/10 of a degree, or 48′; or if every division on the scale be 10 minutes, then the Vernier will subdivide it into single minutes, and the 8 will then be 8 minutes. And so for any other case.

By altering the number of divisions, either in the degrees or in the Vernier, or in both, an angle can be observed to many different degrees of accuracy. Thus, if a degree on a quadrant be divided into 12 parts, each being 5 minutes, and the length of the Vernier be 21 such parts, or 1° 3/4, and divided into 20 parts, then 1/12 X 1/20 = 1°/240 = 1′/4 = 15″, is the smallest division the Vernier will measure to: Or, if the length of the Vernier he 2° 7/12, and divided into 30 parts, then 1/12 X 1/30 = 1°/360 = 1′/6 = 10″, is the smallest part in this case: Also 1/12 X 1/50 = 1°/600 = 1′/10 = 6″, is the smallest part when the Vernier extends 4° 1/4. See Robertson's Navigation, book 5, p. 279.

For the method of applying the Vernier to a quadrant, see Hadley's Quadrant. And for the application of it to a telescope, and the principles of its construction, see Smith's Optics, book 3, sect. 861.

VERSED-Sine, of an arch, is the part of the diameter intercepted between the sine and the commencement of the arc; and it is equal to the difference between the radius and the cosine. See Versed-Sine. And for coversed sine, see Coversed-Sine.

VERTEX of an Angle, is the angular point, or the point where the legs or sides of the angle meet.

Vertex of a Figure, is the uppermost point, or the vertex of the angle opposite to the base.

Vertex of a Curve, is the extremity of the axis or diameter, or it is the point where the diameter meets the curve; which is also the vertex of the diameter.

Vertex of a Glass, in Optics, the same as its pole.

Vertex is also used, in Astronomy, for the point of the heavens vertically or perpendicularly over our heads, also called the zenith.

, Path of the. See Path.