In the year 1631 Pierre Vernier, Capitaino et Chutenein pour as Majeet6 au Chasteau Dornana, &c., published at Bruxelles 'La Con struction, l'Usage, et lea Proprietez do Quadrant nouveau do alathe. niatiquc,' which he dedicated to the Princess Isabella. Ile supposes quadrant divided into half-degrees on the limb, the surface of which rises above the plane of the instrument (this ho calls tho 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 act off on the sector, which is subdivided into thirty equal parts. He directs two lines of eight 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 tho zero end of the quadrant to be directed to any object :—If the division 30' on the sector (we will now call this the rosier) which answers to the line of 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 are of IV 30' is divided ou the vernier into 30 equal parts, each part is equal to 31'; and therefore that wheu 0' is placed opposite a division of the quad rant, the division 1' of the vernier overshoots the next division of the quadrant in tho 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 in 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 liedneus published at Leyden his 'Nova et Accurate Astrolabii Ooometrici, uco non Quadrantis Aatronomici 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 inner division and the centre of tho quadrant, and dividing that portion which is included between the inner and outer circles into ten parts, when the subdivision will be true. I:fedi-zees has adopted the vernier, but without naming the inventor : his astrolabe and quadrant are well contrived.
lievelius applied to his instruments the transversal divisiou of Tycho as well as the vernier. He seems 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. (' alachina C,celestis,' 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 Hevelius's book, Hooke pub lished at London his Animadversione on the first part of the Machina Cock:leis of the honourable, learned, and deservedly famous astronomer Johannes Ifevelius,' a tract distinguished by its acuteness and origin ality. It is remarkable that be did not see the merit of Vernier's irvention,t 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 scale, 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 WM carried into execution in flamsteed's sextant, and turned out so ill that the diagonal division was applied as an after-thought. See his prolegomeua (' Historia Crelestis,' vol. iii. p.106, and Baily's Flamsteed.) Hooke'e advice was afterwards followed in making a quadrant for the Greenwich Observatory, which was also found to be useless. In the mural arc which Flarnsteed erected at his own expense and under his own direction, ho drew diagonals after having divided the inner and outer area to 5'. Tho subdivision was performed by dividing the fiducial edge of the index, not into five equal parte but into such parte as would give the minutes exactly, and each of these was divided into six equal parts; so that the instrument read off to 10", and by estimation to 5". The outer edge was also racked after Hooke's method, but rather, we think, as a check against erroneous reading, than as a means for exact measurement.
Romer proceeded in a totally different manner. The limb of the circle was divided to 10', and a magnified image of each division was formed in the focus of a microscope, so as exactly to fill the space between eleven threads at equal intervals. Thus the arc was read off to minutes by the threads and the seconds estimated, which they easily might be to 5", according to Horrebow.
The vernier appears to have come into general use after Flamsteed's time, and in the larger quadrants there were usually two sets of divisions, one into 90° and the other into 96 parts, each with their peculiar vernier : the approximate divisions were brought into exact coincidence and the quantity measured by the revolutions and parts of the tangent-screw, after Hevelius's method. Such were the mural quadrants at Greenwich and elsewhere, erected by Bird, Ramsden, in the last century; and the portable astronomical quadrant had the same or similar contrivances for subdivision. In the sector employed in the French survey, and described in ` La Mdridienne de Paris verifiee; Paris, 1744, the arc was divided by fine points to every 10'. In making the observation the plumb line was first brought directly over one of these dots, and the star afterwards bisected by a micrometer-screw carrying a wire in the focus of the telescope. The degrees and tens of minutes being read off on the limb, the revolutions and parts of the screw furnished the remaining minutes and seconds. This method of subdivision was applied by La Caille to the sextant with which he observed at the Cape of Good Hope and at Paris. The invention is due to the Chevalier de Louville, whose memoir is to be found in the Ete l'Academie' for 1714.