IS 



VERMILION. 



VERNIER. 



of maccaroni, vermicelli, or fedelini, baring been thoroughly dried, are 

 rwujr for use. 



Toe Italians manufacture the pute into many other forms ; into thin 

 Oat (trip* like ribbon*, into thin sheet* like paper, into round balls, and 

 into beam and peas. The Neapolitans, who UM great quantities of 

 macaroni as their favourite food, use nothing but the pure paste of 

 wheat and water, but the Genoese mix nffron with it, which gives it a 

 yellow tinge. The French, who also manufacture a good deal of it, 

 frequently season the paste with various condiment*. 



VERMILION. rCoLOCRWo MATTKBS ; M.RCUBT.] 



\ KUNAI., VERNAL EQUINOX. The word vernal is the ad- 

 jective derived from rrr, the spring ; and the vernal equinox is that 

 point of the equator which the sun crosses when it passes into the 

 iirmixphere of the observer, and when his days begin to be longer than 

 the nights. Consequently that point of the ecliptic which is called the 

 first point of Aries is the vernal equinox to those in the northern 

 hemisphere, while the first point of Libra is the same to those in the 

 southern. If there were any decidedly astronomical nations south of 

 the equator, some confusion might perhaps have arisen ; but as all the 

 science will be carried from the north, it is probable that the terms 

 and modes of measurement peculiar to the north will be universally 

 retained. 



VKKXIER. 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 is 

 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 6. 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- 

 ments 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,' 1642, proposed the following graduation for astrono- 

 mical 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 be 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 be 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 the 

 direction of the line of sight, the fiducial edge will cut some one of 

 these circles at a division without sensible error. The corresponding 

 angle in degrees, minutes, seconds, ic., 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 



L- of 90*, which is, when reduced to .its ordinary denomination, 



33 53' 46" very nearly. 



Tycho applied the graduation of Nonius, or a modification of it, to 

 some of his earier instruments, but " quia haec subtilitas, cum ad 

 praxim deventum cat, plus habeat laboris quam fructus, neque id in 

 recessu pncstet, quod prima fronte pollicetur," he abandoned it, and 

 adopted the method of traiurenab, which is well known to most of 

 oar readers as the diagonal scale in the case of drawing-instruments. 

 This Hooke says ('Animadversions,' Ac.) "was first made use of in 

 England by the most skilful mathematician Richard Cantzler." Tycho 

 describes this mode of subdivision in the supplement to his 

 'Mechanica,' Norimbergjo, 1602. Two concentric circles an drawn 

 upon the limb at about /, of the radius from each other, and divided 

 into equal parts of Iff. The space from the zero of the inner circle to 

 the 1(X division of the outer circle is divided into 10 equal parts by 

 9 fine dots ; and in like manner the space between the lo'of the outer 

 circle and the 2tf of the inner, and so on. These rows of point* form 

 a sharp zigzag with the angle* in the two circles. The index, which 

 may be either a fiducial edge or a fine hair, will pass over or near one 

 of these dots in every position, and the angle to be read off is the 

 number of degree* 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 became acquainted with this divi- 

 sion by diagonals as applied to straight lines when a student at Leip- 

 rjg, and in the place above referred to he proves that this subdivision, 

 though not theoretically exact when applied to curved lines, was yet 

 sufficiently tme for hi* purpose. Instead of dot*, other astronomers 



struck nine concentric circles at equal distance*, and then drew 

 straight line* where Tycho placed hi* dot*. 



In the year 1631 Pierre Vernier, Capitaine et Chastellain pour sa 

 MajeiU au Chastoau Domans, Ac., published at Bruxelle* ' La Con- 

 struction, 1'Usage, et les Proprieter du Quadrant nouveau de Mathe- 

 matique,' which he dedicated to the Princes* Isabella. He suppose* a 

 quadrant divided into half-degrees on the limb, the surface of which 

 rises above the plane of the instrument ithis he calls the base), and a 

 moveable plate of the form and figure of a sector (and so named by 

 him), which is concentric with and exactly fitted within the limb, the 

 surfaces of the two forming one plane. An arc of 15 30' is then set 

 off on the sector, which is subdivided into thirty equal part*. He 

 directs two lines of sight to be fixed on the extreme radii of the sector, 

 which therefore include an angle of 15* 30', and orders the division 

 to degrees and half-degrees to be numbered one way on the limb from 

 left to right, and the divisions of the sector to be numbered up to 30" 

 from right to left. Suppose the line of sight towards the zero end of 

 the quadrant to be directed to any object : If the division 3d' on the 

 sector (we will now call this the vernier) which answers to the 1: 

 sight, seems to be a continuation of a division of the quadrant, the 

 angle read off will be that degree or half-degree of the quadrant, and 

 the 0' of the vernier will exactly correspond to another division of the 

 quadrant. No other division of the vernier will so correspond if the 

 division be exact. Now it will easily be seen that as the arc of 15 30' 

 is divided on the vernier into 30 equal parts, each part is equal to 31'; 

 and therefore that when 0' is placed opposite a division of the quad- 

 rant, the division 1' of the vernier overshoots the next division of the 

 quadrant 1' in the direction of the vernier, and contrary to the 

 numbering of the limb. If the line of sight were pushed forward 1', 

 the vernier division of 1' would therefore agree with a division iu the 

 quadrant, and so on ; so that in fact, whatever be the position of the 

 line of sight, the true angle is to be read off, first as to degrees 

 and half-degrees from the quadrant, and then for the minutes from 

 the vernier.* 



In 1643 Benedictus Hedncus published at Leyden his 'Novaet 

 Accurata Astrolabii Geometric!, iiec non Quadrantis Astronomic! 

 Structure,' dedicated to his sovereign, Queen Christina of Sweden. 

 In his preface he objects to the inaccuracy of Tycho's method of 

 transversals, and gives himself a correct construction, namely, by de- 

 scribing a circular arc through 10' of the outer division, 0' of the 



ler division and the centre of the quadrant, and dividing that 

 portion which is included between the inner and outer circles into ten 

 parts, when the subdivision will be true. Hedncus has adopted the 

 vernier, but without naming the inventor : his astrolabe and quadrant 

 are well contrived. 



Hevelius applied to his instruments the transversal division of 

 Tycho as well as the vernier. He seeins to claim the invention of the 

 tangent-screw for giving a slow motion to his line of sight, and dwells 

 at great length on the subdivision of the larger divisions by the 

 revolution and parts of the tangent-screw. (' Machina Coeleetis,' Pars 

 Prior, cap. xv. Gedani, 1673.) So far as we can judge from his asser- 

 tions and description, he arrived at great excellence in this part of 

 mechanical construction, which however his unaccountable rejection of 

 telescopic sights rendered of little value. 



The next year after the appearance of Hovclius's book, Hooke pub- 

 lished at London his ' Animadversions on the first part of the Machina 

 Coolestis of the honourable, learned, and deservedly famous astronomer 

 Johannes Hevelius,' a tract distinguished by its acuteness and origin- 

 ality. It is remarkable that he did not see the merit of Vernier's 

 invention/)- nor, as it would seem, of Hevelius's application of the 

 revolutions of the tangent-screw to measuring very minute quantities. 

 He suggests a very elegant application of the diagonal scaK-, with rules 

 for its accurate division when applied to circular arcs, but recommends 

 racking the outer edge of the quadrant and measuring the angle by the 

 revolutions and parts of the screw which carries the telescope by 

 working in the racked limb. 



Hooke's unlucky idea was carried into execution in Flamsteed's 

 sextant, and turned out so ill that the diagonal division was applied as 

 an after-thought. See his prolegomena (' Historia Coelestis,' vol. iii. 

 p. 106, and Baily's Flamsteed.) Hooke's advice was afterwards followed 

 in making a quadrant for the Greenwich Observatory, which was also 

 found to be useless. In the mural arc which Flamsteed erected at his 

 own expense and under his own direction, he drew diagonals after 

 having divided the inner and outer arcs to 5'. The subdivision was 

 performed by dividing the fiducial edge of the index, not into five 

 equal parts but into such parts as would give the minutes exactly, and 

 each of these was divided into six equal parts ; so that the instrument 



Vernler'i tract i very cree, >nd the injustice of those writer! who per. 

 ninlcd In Riving the name or Nonius to his Invention has induced us to enter 

 Into a more particular exposition of both principles. The second line of sibt 

 i merely to enable the observer lo extend the angle to 90" without carrying 

 the sector beyond the quadrant. He gives * very prolix account of the 

 graduation proper for quadrants and astrolabes of different sines, and how 

 angles exceeding 80' arc to be measured, but of this no further notice is 

 required here. 



t llooke conjectures that Tycho had Invented Vernier's contrivance and 

 rejected it, but without any probability. Tycho'i word! and figure refer 

 clearly to some change of Nonius's diritors. 



