VERNIER. We shall give under this head a short account of the different methods employed to measure the parts of the divisions of astronomical and geodesical instruments. This and the article GRADUATION may be considered as a sort of introduction as well as supplement to the description of each particular instrument. It ie necessarily both meagre and imperfect, but the references will point out the principal authorities to be consulted. We shall conclude with a brief account of the vernier in its simplest form.
We are not aware that the Greeks or their successors the Arabs had any contrivance for subdivision. They seem to have simply divided their circles as accurately as possible, and into small convenient por tions. Ptolemy's catalogue does not profess to distinguish less quantities than 10'; or rather, the parts of degrees are marked frac tionally with no larger denominator than G. Ulug Beigh used instru ments of greater dimensions, and seems from his catalogue to have noted minutes. At the revival of astronomy in Europe the instru. 'Tecate were very rude, and the simple division, aided by estimation, was probably considered sufficiently accurate without any artificial contrivance.
Peter Nonius, in the third proposition of his treatise 'De Crepus culis Olyssipone,' 1542, proposed the following graduation for astrouo mind instruments :—Forty-five concentric circles are to be inscribed on the limb, and separated into quadrants by diameters intersecting at right angles. The quadrants are then to he sub-divided as follows : the outermost into 90 equal parts, each of which consequently equals 1' ; the next into 89, that following into 88, and so on to the inner most, which is to he divided into 46 equal parts. Each circumference is marked at a convenient place with the number of its subdivisions. The fiducial edge of the bar carrying the sights passes, when produced, through the centre, and the author assumes that whatever be tho direction of the line of sight, the fiducial edge will cut some ono of these circles at a division without sensible error. Tho corresponding angle in degrees, minutes, seconds, &c., is readily computed from the number of parts intercepted and the order of the circle. Thus if the
exact coincidence takes place at division 29 of that quadrantal arc which is divided into 77 parts, the corresponding arc in degrees is of 90', which is, when reduced to ,its ordinary denomination, 77 33' 53' 46" very nearly.
Tycho applied tho graduation of Nonius, or a modification of it, to some of his caner instruments, but " quia hrec subtilitae, cum ad praehn deventum eat, plus habeat laboria quam fructus, neque id in receasu prrestet, quad prima fronts, pollicetur," he abandoned it, and adopted the method of trainrersals, which is well known to most of our readers as the diagonal scale in the case of drawing.instruments. This Hooke says (' Animadversions; &c.) "was first made use of in England by the most skilful mathcinetician Richard Cantzler." Tycho describes this mode of subdivision in the supplement to his 'afeclumica; Norimbergem, 1602. Two concentric circles are drawn upon the limb at about of the radius from each other, and divided into equal parts of ]0'. The space from the zero of the inner circle to the 10' division of the outer circle is divided into 10 equal parte by 9 fine dote; and in like manner the space between the 10 of the outer circle and the 20' of the inner, and so on. These rows of points form a sharp zigzag with the angles in the two circles. The index, which may be either a fiducial edge or a fine hair, will pars over or near one of these dots in every position, and the angle to be read off is the number of degrees and tens of minutes which is taken from the circles, inner or outer, + the number of minutes and parts of a minute (the latter by estimation) reckoned by counting the points from the preceding angle. Tycho become acquainted with this divi sion by diagonals as applied to straight lines when a student at Leip zig, and in the place above referred to he proves that this subdivision, though not theoretically exact when applied to curved lines, was yet sufficiently true for his purpose. Instead of dote, other astronomers struck nine concentric circles at equal distances, and then drew straight lines where 'Tycho placed his dots.