Q^U A

Q^U A

OUADRANT (Cyel.)— Davis's Quddrant. When the horizon is obfcured by hazy weather, Davis's Qjiu- drant is of no ufe ; and this often occafions melan- choly confcquences. Means have therefore been fought after to remedy this defect. Mr. Leigh propofes a water-level to be fixed to the Quadrant ; and he likewife has given the defcription and ufe of an apparatus to be added to this inftrument, confiding of a mercurial level, which he prefers, no doubt juftly, to a water-level. See Phil. Tranf. N»43i. Sea. I and 2. ■Hadley's Quadrant, the common name for the juftly efteemed Quadrant, invented by the late John Hadley, Efq; This Qtiadrant, which at firft had the fate of all other inge- nious inventions, to be neglected by ignorant and obftinatc men, even though highly ufeful to them in their profeffion, feems at laft to have made its way, in fpite of habit and pre- judice.

We cannot here infert a full defcription and draught of this inftrument ; but we muft obferve, that though the late Mr. Hadley was undoubtedly the inventor of it, yet the principle upon which his invention turns, had not efcaped the fagacity of Sir Ifaac Newton, long before, as appears from a paper in his hand-writing found among the papers of the late Dr. Halley. But this was totally unknown to Mr. Hadley, and fcemed to have been forgot by Dr. Halley himfelf. The account of Sir Ifaac's invention is inferted in the Philofophical Tranfaflions, N° 465, and in Dr. Martyn's Abridgment, vol. 8. p. 129. and is as follows :

P Q_R S denotes a plate of brafs accurately divided in the limb D Q, into { degrees, { minutes, and T 'j minutes, by a diagonal Icale ; and the \ degrees, J minutes, and T ' Y minutes, counted for degrees, minutes, and ^ minutes. A B is a telcf- cope, three or four feet long, fixed on the edge of the brafs plate. G is a fpeculum, fixed on the faid brafs plate per- pendicularly, as near as may be to the objefl glafs of the telefcope, fo as to be inclined 45 degrees to the axis of the telefcope, and intercept half the light which would otherwife come through the telefcope to the eye. C D is a moveable index, turning about the center C, and, with its fiducial edge, mewing the degrees, minutes, and £ minutes, on the limb of the brafs plate P Qj the center C, muft be over- againft the middle of the fpeculum G. H is another fpecu- lum, parallel to the former, when the fiducial edge of the index falls on oo d 00' 00"; fo that the fame ftar may then ap- pear through the telefcope, in one and the fame place, both by the dirca rays and by the refkaed ones ; but if the index be turned, the ftar will appear in two places, whofe diftance is fnewed, on the brafs limb, by the index. ■ By this inftrument the diftance of the moon from any fixed ftar is thus obferved : view the ftar through the perfpicil by the direS light, and the moon by the refleaed (or, on the contrary) and turn the index till the ftar touch the limb of the moon, and the index mall (new upon the brafs limb of the inftrument, the diftance of the ftar from the limb of the moon ; and though the inftrument fhake, by the motion of your ftup at fca, yet the moon and ftar will move together as if they did really touch one another in the heavens ; fo

that an obfervation may be made as exaaiy at Tea as at land. And, by the fame inftrument may be obferved, exaaiy, the altitudes of the moon and ftars, by bringing them to the hori- zon ; and thereby the latitude, and times of obfervations, may be determined more exaaiy than by ways formerly prac- tifed. In the time of obfervation, if the inftrument move an- gularly about the axis of the telefcope, the ftar will move in a tangent of the moon's limb, or of the horizon ; but the ob- fervation may notwithftanding be made exaaiy, by noting ' when the line, defcribed by the ftar, is a tangent to the moon's limb, or to the horizon. To make this inftrument ufeful, the telefcope ought to take in a large angle : And to make the obfervation true, let the ftar touch the moon's limb, not on the outfide of the limb, but on the infide. Vid. Philofoph Tranfaa. N° 465. p. 155, 156.

For the common ufes at fea a telefcope is not neceflary ; Mr. Hadley's Quadrants are therefore generally made without one, which renders the ufe of them much more ready. He has alio added fome contrivances to facilitate their ufe ; which are def- cribed in the printed papers ufually fold with the inftrument: Other Quadrants have been contrived fince, by fome ingenious artifts, all of which have their merit, but the particulars of their conftruaions are too many for this place ; and perhaps on the whole nothing preferable to Mr. Hadley's invention has yet been found.

Mural Quadrant. Mr. Gerften has lately given us a de- fcription of a new aftronomical mural Quadrant, which he fays is free from many of the ufual inconveni'encies attending the ufe of fuch inftruments. Sec Phil. Tranf. N° 483. Sea. 18.

QUADRIGA, infurgery, otherwife called Cataphracta, is a ftrong bandage made ufe of in fraflures of the Sternum. It is compofed of a double headed roller about fix Paris ells long, and. three or four fingers broad. See Heifer's Surgery, P. III. Ch. 4. §. 14.

QUADRILLE, a well known game at cards ; and which has been, in feveral cafes, the objea of mathematical computa- tions. See Mr. De Moivre's Doarine of Chances, 2d' edit p- 83 to 90.

QUAKING-oro/i, in botany. See the article Grass, Append.

QUANTITY (Cyd.) - The note in the Cyclopaedia, from Mr. Machm's paper in the Phil. Tranf. N" 447. fhould have been extended, as it ferves to render the notions of mathema- tical Quantity more diftina and adequate than any thing that is commonly to be met with in authors on this fubjea. Not to give the reader the trouble of turning to the Cyclopaedia for the fake of a few lines, we (hall infert the whole. Mr. Ma- chin, in the poftfeript to the folulion of Kepler's problem, in- ferted in the before cited number of the Phil. Tranf. fays, That he takes a mathematical Qjiantity, and that for which any fymbol is put, to be nothing clfe but number with regard to fome mcafure which is confidered as one. For we cannot know precifely and determinately, that is, mathematically, how much any thing is but by means of number. The notion of continued Quantity , without regard to any meafure, is indiftina and confufed ; and although fome fpecics of fuch Quantity, confidered phyfically, may be defcribed by motion, as lines by' points, and furfaces by lines, and lb on ; yet the magnitudes or mathematical Quantities are not made by that motion, but by numbering according to a meafure. Accordingly, all the feveral notations that are found neceflary to exprefs the formations of Quantities, do refer to fome office or property of number or meafure ; but none can be inter- preted to fignify continued Qjiantity as fuch. Thus fome notations are found requifite to exprefs number in its ordinal capacity, or the Humerus numerans, as when one follows or precedes another, in the firft, fecond, or thiid place^ from that upon which it depends ; as the Quantities x\ x\ x, x', x", referring to the principal one x . So, in many cafes, a notation is found neceflary to be given to a meafure as a meafure ; as for inftance, Sir Ifaac Newton's fymbol for a fluxion i ; for this ftands for a meafure of fome kind, and accordingly he ufually puts an unit for it, if it be the principal one upon which the reft depend. So fome notations are exprefly to fhew a number in the form of its compofition, as the index to the geometrical power x", de- noting the number of equal h&crs which go to the compofi- tion of it, or what is analogous to fuch. But that there is no fymbol or notation hut what refers to dif- creet Quantity, is manifeft from the operations, which are all arithmetical.

And hence it is, there are fo many fpecles of mathematical Quantity as there are forms bf compofite numbers, or ways in the compofition of them ; among which there are two more eminent for their fimplicity and univerfality than the reft ; one is the geometrical power, formed from a conftant root; and the other, though well known, yet wanting a name, as

well