Q. 



QUADRANT. 



s:e 



Q 



Qis a superfluous letter of the alphabet, having the same sound as t, 

 though limited to words where a u follows. This letter furnishes 

 evidence that the alphabetical characters were originally of syllabic 

 power. Thus the Hebrew koph and the Greek koppa. appear to have 

 been used only in those words where the sound of o follows, as in Cos, 

 Corinth, and Syracoeii, &c. Indeed the name of the letter implies as 

 much. The Greek alphabet probably stopped at one period like the 

 Hebrew, at T, BO an to have no ti. On the other hand, the Etruscan 

 alphabet had a u, but no o. Hence in Italy, the q, which, by position 

 in the alphabet, corresponds to the Greek koppa, was limited to words 

 where a u followed. In the same way the kaph of the Hebrew and 

 kappa of the Greek were probably at first limited to those words where 

 an a follows, as we know was the case in Latin ; and as the modern 

 name of the letter, to, denotes, for it would otherwise have been called 

 lee or ft. This view becomes more complete if it be called to mind 

 that the name of x connects it with the vowel t ; and that the ij or H 

 of the Greek alphabet was originally a guttural aspirate, sounded 

 perhaps as xn, and thus was adopted to denote either a guttural con- 

 sonant or a long e. For the various forms of the symbol q see 

 ALPHABET, and for the changes to which the letter is liable see C 

 andK. 



QUADI, an ancient people of Germany, who inhabited the country 

 north of the Danube, between that river, the mountains of Bohemia, 

 and the river March. Towards the north they bordered on the 

 Marcomanni, in connection with whom they are frequently mentioned 

 by the Roman writers as allies. Tacitus (' German.,' 42) mentions the 

 Quadi, the Marcomanni, and the Narisci as being in the foremost rank 

 among the German nations towards the borders of the Roman empire, 

 the Danube forming the line of demarcation between the power of 

 Rome and German independence. At a later period the Quadi joined 

 a great confederacy of German nations against Rome, which occasioned 

 much alarm to the empire, and which twice obliged the emperor 

 Marcus Aurelius Antoninus to repair to Germany at the head of his 

 legions. They are afterwards mentioned by Eutropius as having 

 invaded Paunonia in the reign of Gallienus. 



QUADRANGLE and QUADRILATERAL (four-angled and four 

 sided). These terms are indiscriminately used to denote a figure with 

 four sides in the same plane. [PARALLELOGRAM ; RECTANGLE ; SQUARE ; 

 TRAPEZIUM; RHOMBUS.] 



QUADRANT. [SEXTAST.] 



QUADRANT. As an astronomical instrument, the quadrant has 

 within a few years been so completely superseded by the entire circle, 

 that it will not be worth while to describe particularly its construction 

 or adjustments. Still BO much of the very groundwork of modern 

 astronomy depends on data furnished by the quadrant, that it cannot 

 be properly passed over without some notice. 



We have already said [CIRCLE] that the earliest form of instrument 

 for measuring celestial altitudes was also the best, namely, the solstitial 

 or meridian circle described by Ptolemy. After showing how the 

 proportion which the arc between the tropics bears to the whole 

 circumference was to be determined by this instrument, Ptolemy 

 proceeds to lay (' Amalgest,' book i., chap. 10), " We have made this 

 sort of observation more conveniently by using, instead of circles, a 

 stout quadrangular block of wood or stone, having one side plane aud 

 smooth. Upon this side we described a fourth part of a circle from a 

 centre near one of the angles, and having drawn from the centre two 

 radii including a right angle, we divided the circumference into ninety 

 degrees with subdivisions. We then inserted two perfectly equal 

 cylinders at the extremities of the vertical radius, so as to be exactly 

 concentric with the centre and extreme point, and set the block 

 vertical by A plumb-line passing over the cylinders, and also hi the 

 plane of the meridian by a north and south line described on the 

 horizontal plane. We observed at noon the shadow of the central 

 cylinder, having applied something to the divided arc to show the 

 place more clearly, and, marking the middle point, we took the 

 corresponding division of the quadrant as showing the elevation of the 

 sun on the meridian." It would seem that on the revival of learning, 

 when Ptolemy was thought infallible, the quadrant came into use on 

 thin authority, to the exclusion of the circle. In the ' Astronomias 

 Inntauratfc Mechanica ' of Tycho Brah<S, figures and descriptions will 

 be found of quadrants and sextants of various forms and sizes. We do 

 not think justice ix done at the present day to the merits of Tycho, 

 who is better known as the perplexer of the Copemican hypothesis, 

 than as the first great practical astronomer after Hipparchus. Among 

 his numerous instruments Tycho had a large quadrant fixed on a wall, 

 which he calls a mural quadrant, with which he observed meridian 

 altitudes, noting the time of transit by a clock. There are several 

 other quadrants figured and described, which revolve on a vertical 

 axis, and some have a horizontal circle by which the azimuth was 

 observed at the same time with the altitude. These may be considered 



ARTS AND 8CL WV. VOL. VI. 



as the precursors of the modern astronomical quadrant, and still more 

 perfect altitude and azimuth instrument, just as his mural quadrant 

 led to the mural arc of Flamsteed, the mural quadrants of Bird and 

 Ramsden, and finally to the mural circle of Troughton. The imper- 

 fection of his clocks (for the pendulum was not applied till nearly a 

 century later) compelled Tycho to adopt an instrument which has long 

 been out of vise. This was his astronomical sextant, which was 

 stronger, more convenient, and lighter than the quadrant. It was 

 supported at the centre of gravity on a ball and hemispherical cup, 

 and could consequently be easily placed in the plane passing through 

 two stars, and so used for measuring their distance from each other. 

 To verify the value of the arc, and to test the powers of his sextants 

 and quadrants, the distances of a chain of stars near the equator were 

 taken, and their declinations also observed, when it was found that the 

 sum of the angles at the pole which resulted from observation was 360 

 very nearly. (Tycho Brane^ ' Astronomiue Instauratce Progymnasmata,' 

 pp. 138, 145.) 



Hevelius has described his quadrants and sextants in the first volume 

 of his ' Machina Coclestis,' a work which is not uncommon ; the second 

 volume, containing his observations, was burnt soon after it was 

 printed, with the exception of a few copies, and is one of the scarcest 

 and dearest astronomical books in existence. In the convenience of his 

 instruments, and perhaps in the accuracy of their graduation, he 

 surpassed Tycho, but he never could understand the advantage of 

 telescopic over plain sights, though one of the best practical opticians 

 and industrious star-gazers of his time. This unfortunate prejudice 

 not only rendered the labour of his long life labour in vain, but 

 embittered his latter years to a painful degree by involving him in a 

 dispute with Hooke. 



Picart, aided, as it is said, by Auzout, first applied telescopic sights 

 to graduated instruments. In his meisure of the earth, executed in 

 1669 and 1670, he used a quadrant for his terrestrial angles. This he has 

 described, with figures, in a special work, printed at the Louvre, which 

 became so rare that the ' Acade'mie Royale des Sciences ' reprinted it 

 in then- Memoirs (vol. vii,, part i., p. 133).. The quadrant was of 

 38 inches radius, with one telescope fixed in the direction of one 

 radius, aud the other moveable about the centre ; the arc of the 

 instrument was divided by transversals, and the angle read off by the 

 index of the moveable telescope was equal to the angle subtended at 

 the quadrant by the objects bisected by the cross-wires of the two 

 telescopes. The instrument could be fixed on its stand with the plane 

 vertical when used for altitudes, and by an additional piece, a geaou, 

 was moveable into any other plane, when it was wanted for surveying. 

 The whole turned on a vertical axis, like Tycho's azimuthal quadrants, 

 but without an azimuthal circle. Quadrants like Picart's continued to 

 be made by the French artists and used by their astronomers (with 

 some improvements, of course) up to the latter end of the last century, 

 when they were superseded by the repeating circle of Borda. The 

 verification of the arc and of the graduation was performed in Tycho's 

 manner, only employing well defined objects in the horizon instead 



>1 .-tar.-. 



For a fixed observatory Picart and Roemer recommended a large 

 quadrant permanently fixed, that is, a copy of Tycho's mural quadrant, 

 with the changes which telescopic sights required. Lemonnier, in the 

 preface to his ' Histoire Cdleste,' says that La Hire had one erected in 

 the Royal Observatory at Paris, in 1683, and that it was described in 

 the first edition of La Hire's tables. This description he repeats at 

 page xlii. of his work. 



Flamsteed made his earlier observations at Greenwich with a sector, 

 the plan of which may be understood by conceiving one of Tycho's 

 sextants with telescopes, instead of plain sights, to be mounted on a 

 polar axis. (' Historia Ccclestis,' vol. iii., p. 103.) This instrument was 

 designed for measuring the distances of stars from each other. But in 

 pursuing his primary object, that of settling the places of the fixed 

 stars with accuracy, Flamsteed found that he required a meridian 

 instrument. Some unlucky trials at constructing a quadrant were 

 made by the person employed by the Royal Society, and Flamsteed 

 finally constructed, at his own expense, and by Abraham Sharp's 

 hands, the mural arc with which he observed from 1689 to his death.* 

 (See the description and figure, ' Historia Ccelestis,' vol. iii., p. 108.) 

 This differed from other mural arcs chiefly in this, that it contained 

 140* or 150, so that all stars were observable with it, from Polaris, 

 below the pole, to the south horizon. The arc was placed as nearly 

 in the meridian as might be, and the errors in its plane detected by 

 comparing the observed time of the sun's passage over the middle wire 

 of the instrument, with the true time of his meridian passage, as 



* Among the real injuries which Flamsteed received, we consider the trans- 

 lation of his preface into indifferent Latin one of the greatest, though committed 

 with a friendly intention. 



3 K 



