was when the Comet was descending towards the Sun. The tails of some Comets have been observed to be of a very considerable length; the tail of the Comet of 1618 appeared under an angle of 104°; that of 1680, subtended an angle of 70°; and, according to Mr. Maclaurin, the tail extended from the head to a distance scarcely inferior to the vast distance of the Sun from the earth.

Dr. Halley was the first who predicted the return of a Comet. By comparing the elements of the orbits of the Comets of 1456, 1531, 1607, and 1682, he supposed them to be the same Comet, and that it would return about the end of the year 1758, or the beginning of 1759, which prediction was accordingly verified.

The number of Comets belonging to the solar system is very uncer tain. Riccioli enumerated 154 previous to the year 1618. Lubienietzki states the number to be 415 in the year 1665; and some late writers have increased the number to upwards of 700.

In order to calculate the place of a Comet, the elements of its orbit must be previously ascertained; these are, the time when the Comet was in its perihelion, the place of its perihelion, the perihelion distance, the place of its ascending node, and the inclination of its orbit to the ecliptic. From these data the place of a Comet may be easily found by tables computed expressly for that purpose; as those by Dr. Halley, M. Bockhart de Saron, M. du Séjour, M. de Lambre. *

Mr. Whiston supposed that the deluge was occasioned by the tail of the Comet of 1680 in its descent towards the Sun; and he also suggested that the general conflagration will arise from the tail of the same Comet in its ascent from the the Sun. The interval between two successive periods is supposed to be 12,000 years, if the periodic time of the above-mentioned Comet is 575 years, there will be 21 revolutions in 12,075 years.

Dr. Halley observes, that in the late descent of the Comet of 1680, its true path left the orbits of Saturn and Jupiter below itself a little towards the south: it approached much nearer to the paths of Venus and Mercury, and much nearer still to that of Mars. But as it was passing thro' the plane of the ecliptic, viz. to the southern node, it came so near the path of the Earth, that had it come towards the Sun 31 days later than it did, it had scarce left our globe one semidiameter of the Sun towards the north; and, without doubt, by its centripetal force (which, with the great Newton, I suppose proportional to the bulk, or quantity of matter in the Comet), it would have produced some change in in the situation and species of the Earth's orbit, and in the length of the year. But may the great good GoD avert a shock or contact of such great bodies moving with such forces (which, however, is by no means impossible), lest this most beautiful order of things be entirely destroyed, and reduced into its ancient chaos: and Mr. Maclaurin, speaking of the same Comet, says; "it is not to be doubted but that, while so many Comets pass among the orbits of the planets, and carry

In M. de La Lande's Astronomie, vol. iii. page 251, there is a table of the elements of the orbits of 78 Comets, and in Dr. Rees's Dictionary, one of 97 Comets.

such

such immense tails with them, we should have been called by very extraordinary consequences, to attend these bodies long ago, if their motions in the universe had not been at first designed and produced by a Being of sufficient skill to foresee their distant consequences. M. du Séjour observes, that it is very improper to instill terror into the minds of men without any just reason. The Comet of 1770 approached nearer to the earth than any hitherto observed, and produced no sensible effect either upon the motion of the Earth, or upon its inhabitants.

Dr. Halley mentions, in his Synopsis of Comets, printed in 1705, and also in his Astronomical Tables, that as it is more than probable, that the rest of the Comets described in his Catalogue, will return after having finished their periods, whence their periodic times being given, the axes, and from thence the species of their elliptic orbits will be also given; in order, therefore, to render the tediousness of these operose calculations as easy as possible to future astronomers, he calculated a general table of the motions of Comets, according to the parabolic hypothesis, wherein are contained the double areas of the segments, the logarithms of the right and versed sines, with their differences, and the versed sines themselves to every fifth part of the degrees of the excentric anomaly.

The reason of taking notice of Comets, is that of corresponding observations which may be made on them at different places, their relative situation in longitude may be accurately determined, if their velocity is considerable, which has been the case with many: The Comet of 1472, observed by Regiomontanus, described an arch of 40° in one day, in the circum-polar parts of the northern hemisphere; the remarkable Comet that appeared in 1664 and 1665, moved over a space of 20° in one day, and described almost six signs before it disappeared; and the motion of the Comet, in longitude, of 1760, from the 7th to the 8th of January, was 41°. See upon this subject Sir Isaac Newton's Principia; Maupertuis' Essays on Comets; M. de la Lande's Astronomie, tome iii. p. 221; Traité Analytique des Mouvemens Apparens des Corps Celestes, par M. Dionis du Séjour, tome ii. p. 416; Sir Henry Englefield, Bart. M. Pingre, &c.

Riccioli Almagest.

BOOK

воок II.

CONTAINING

An Account of the Instruments for observing Altitudes and angular Distances at Sea, and of the Corrections to be applied to Olservations made with those Instruments.

CHAP. I.

Of HADLEY'S QUADRANT.

THE first account we have of an instrument for measuring angles by reflection, is in Sprat's History of the Royal Society, page 246, which is as follows: "A new instrument for taking angles by reflection, by which means the eye at the same time sees the two objects, both as touching in the same point, though distant almost a semicircle; which is of great use for making exact observations at sea." The inventor of this instrument is supposed to be Dr. Hook. Other instruments of a similar nature were invented by Sir Isaac Newton, Dr. Halley, and Mr. Street.* We are, however, indebted to John Hadley, Esq. for the first account of this admirable instrument, which he communicated to the Royal Society, May 13, 1731.

This ac

count was published in the Transactions of that Society, No. 420. In the same paper he describes another instrument, having a third speculum, and the positions of the specula and telescope altered, whose use is to observe the Sun's altitude by means of the opposite part of the horizon. An instrument of a similar kind was invented by Mr. Godfrey of Pennsylvania; and Mr. Logan, Chief Justice of that province, transmitted a description of it to England, before or about the time Mr. Hadley's account was published in the Philosophical Transactions.

The instruments in use for measuring altitudes at sea, previous to the invention of Hadley's Quadrant, were, the Cross Staff and Davis'

In Mr. Edward Harrison's Idea Longitudinis, printed at I ondon in the year 1696, page 50, he says, "Mr. Street's way," (of finding the Longitude) is unknown to me, but we suppose his way by the Moon's motion also, by his contriving an Instrument for taking Angles by Reflection: I have seen the Instrument.

Quadrant.

Quadrant. The advantages possessed by the latter for observations of the Sun's altitude, brought it into more general use, especially among the British navigators. Observations, however, made with that instrument, though in the hands of a good observer, were found liable to error, when the sea was agitated; and it was found impossible to observe the Sun's altitude, when the motion of the ship was very considerable. Hence, appears the superior excellence of Hadley's Quadrant, which is designed to be of use, where the motion of the observer, or any circumstance occasioning an unsteadiness in the common instruments, render the observations difficult or uncertain.

The form of this instrument, according to the present mode of construction, is an octagonal sector of a circle, and, therefore, the arch contains 45°; but because of the double reflection, the limb is divided into 90°; and, therefore, this instrument is usually called a Quadrant -of which the following are the principal parts:

1. An Octant, consisting of an arch or limb, connected with two radii.

2. An Index, moveable round a center, and accompanied with a dividing scale, to show the observed altitude, or angular distance. 3. A Speculum, or Index Glass, placed on the Index in such a manner, that its plane is over the center of motion of the Index.

4. Two Horizon Glasses, with their adjusters; H (fig. 6.) being the fore-horizon glass, and G the back-horizon glass.

5. A set of coloured Glasses, to prevent the effect of the solar rays on the eye of the observer.

6. Two sight Vanes.

Of the OCTANT.

The Octant consists of two radii, a limb, and two braces, which last are intended to strengthen the instrument, and prevent it from warping. The arch or limb, although only an eighth part of a circle, is divided into 90°, on account of the double reflection. These degrees are numbered from right to left, and each is commonly divided into three equal parts. Hence, one of these intervals contains twenty minutes; and by means of a scale at the end of the index, divided into twenty equal parts, an observation may be easily read off to the nearest minute. The graduation on the limb is continued a few degrees to the right of O; this portion is usually called the arch of excess, and is found very convenient for several purposes.

Of the INDEX.

The Index is a flat bar, commonly made of brass, moveable round the center of the intrument, and broader towards the axis of motion; at the other end of the index, a piece of brass turns up, behind the limb, having a spring to make the dividing scale lie close to the limb,

and

and a screw to fasten it in any position. Some quadrants have an adjusting screw affixed to the lower part of the index, by which means the index is made to move gently along the limb, without those sudden startings to which it is liable when moved by hand, and which may render the observation uncertain to two or three minutes. It may be observed, that when the index is moved by hand, it should be taken hold of by the lower part, and not by the middle, as is sometimes the practice.

That part of the index, which moves along the limb, has a small scale attached to one side of a rectangular aperture, called a Dividing Scale, but most commonly a Vernier or Nonius, from the names of

*

the

This method of division was first clearly explained by Clavius, in Lemma 1st of his Treatise on Astrolabes, printed at Mayence in 1611; it was afterwards published by Pierre Vernier, who claimed it as his own, in a small tract, intitled, " La Construction, l'Usage, & les Proprietés du Quadrant Nouveau de Mathematique," &c. printed at Brussels, 1631. This method of division may be thus illustrated:

Let two equal lines or circular arcs be so divided, that the number of equal divisions in the one, is one more than the number of equal divisions in the other; that is, let the one be divided inton, and the other into n+1 parts, and let a part of the former be called unity. n+1 Then, : :: n+1: a part of the other.

Or, let the one be divided into 2, and the other into n-1 parts;

Now since in common quadrants, the Vernier is divided into 20 equal parts, whereof the limb contains either 19 or 21, the absolute length of both being the same, it is hence evident, that each division on the dividing scale must answer to 1 minute; for in the present case n represents 20, and, therefore,- of a division on the limb: but each divison 20 on the limb is 20 minutes, and of 20 minutes is 1 minute.

1 20

1

1

n

Let a degree on the limb be divided into four equal parts, and let the dividing scale contain a space equal to 7 degrees, or 29 of these parts, but divided into 30 equal parts, 1 60' then will the dividing scale show half minutes, for of 30

min. or 30". And lastly,

if a degree is divided into six equal parts, and the dividing scale contains 59, or 61 of these parts but is divided into 60 equal divisions, then will each division shown by the dividing scale be 10"; for

1 60 60 6

1

of a minute = 10".

6

This method of division has been unjustly ascribed to Petrus Nonius; for Nonius' method is very different from Vernier's, as may be seen in his Treatise," De Crepusculis," printed at Lisbon, 1522, and also in his Treatise, "De Arte atque Ratione Navigandi.' Nonius' method consists in describing within the same quadrant 45 concentric arches, dividing the outermost into 90 equal parts, the next within into 89, the next into 88, and so on till the innermost was divided into 46 equal parts only: by which means, in most observations, the plumb line or index must cross one or other of these circles very near a point of division-whence, by computation, the degrees and minutes of the intercepted arch might be easily inferred. However, this method of division gave way to that of diagonals, published by Thomas Diggs in his Treatise, "Alæ seu Scala Mathematicæ," printed at London in 1573, who says it was invented by a Richard Chanseler, a famous H 2 mathematical