As soon as it is published I will send it you. The above is all the conjectures I can learn of the mathematicians; however, I will now beg leave to mention some difficulties that occur to me, & which probably your better judgement will set me right in. The idea Sir Isaac Newton had of the planets being kept in their

Dr. Halley observed the comet on November 20. Its R.A. 301° 59′ 50′′; and Decl. 5° 48′ 55′′, N. On December 3, Bradley looked for the comet before the moon rose, and found it among the telescopic stars, but did not feel quite sure about it. However, on December 7, he saw it, R.A. 303° 42′ 35′′; Decl. 7° 46′ 30" N. He then gives a table of observations and computations relating to it.

Bradley supposed the comet to describe a parabola, the inclination of the plane of which to the ecliptic was 49° 59′; the place of ascending node ❤ 14° 16′; the place of perihelion × 12° 52′ 20′′; distance of perihelion from node 28° 36′ 20′′; logarithm of perihelion distance 9-999414; logarithm of diurnal motion 9-961007; time of perihelion passage September 16, 16h. 10m.; motion retrograde. Bradley had not heard that this comet had been seen before Oct. 6, although it was in a proper place to be observed in the morning throughout most of September, especially from its perihelion till near the end of the month. About that time it crossed the Milky Way between the Mast of the Ship and the Head of the Great Dog, towards the Head of the Dove, where it was about September 29, and then approached the South Pole, or did not rise above our horizon. From thence it passed under the Tail of Xiphias within about 15° of the South Pole of the ecliptic, and moving on between the Head of Hydrus, and the bright star of Eridanus called Acharnar, it went by the stars in the body and neck of the Crane, about October 5, when it came again above our horizon. Hence passing under the Tail of the Southern Fish, and between stars in the shoulder of Capricorn, it crossed the ecliptic October 8. in about 81° of Aquarius, and thence by the Hands of Aquarius and Antinous towards the Head of the Eagle, according to its course before described.

proper orbits was that of attraction & gravitation. If this be true, as I think there is no reason to doubt, yet if a new body, such as a comet, should be placed between the earth & the sun, (which will be the case of the present), the motion of the earth, according to the principle of gravitation & attraction, should be disturbed, just as we know the case to be in respect to Jupiter & Saturn. Therefore I have always imagined that at the first creation of this system, that the motion of the planets was in circular orbits," & that probably by new bodies intervening, the

The comet was in opposition to the sun on October 1, when it had near 74° south latitude, and altered its longitude 2 signs in a day. About October 3, in perigee, being about 1-10 of the sun's mean distance, its apparent motion was then about 20° a day, and when Bradley last saw it, it was about twice as far off as the sun. J. R. Hind," On Comets," p. 129, Catalogue of Orbits, has the following: 1723, September 27, 15h. 4m., Greenwich mean time of perihelion passage. 42° 52′ 35′′ longitude of perihelion; 14° 14′ 17′′ ascending node; 50° 0′ 18′′ inclination; 0-99879 perihelion distance. Motion retrograde. Calculated by Spörer, p. 146. Observed in England by Hadley, Bradley, and Pound.

4 This of course would happen; but it must be remembered that the earth would also attract the comet, and affect its orbit. The amount of attraction would vary as the quantity of matter in the attracting body, and if the comet were of extreme tenuity, its effect on the earth's motion would be imperceptible. As a matter of fact, comets have not disturbed the planets, whereas Jupiter and his satellites very seriously altered a comet's orbit in 1779. "Stars of the smallest magnitude," says Herschel (Astron. Art. 558), “remain distinctly visible though covered by what appears to be the densest portion of their (comets') substance, Whenever powerful telescopes have been turned on these bodies, they have not failed to dispel the illusion which attributes solidity to that more condensed part of the head, which appears to the naked eye as a nucleus, though it is true that in some, a very minute stellar point has been seen, indicating the existence of a solid body." Jupiter is of about the same density as water, whereas the earth is about five times as heavy; the weight of Jupiter is nearly 400 times that of the earth. From these and other considerations it is inferred that comets are of very small weight indeed, aud therefore produce no sensible effect on the planetary motions.

This is a very natural supposition for any one to have made at that time, for all the planetary orbits are ellipses of small eccentricity. It is a necessary consequence of the doctrine of universal gravitation that the planets should affect each other's orbits, although but slightly. La Place discovered an “inequality of long period" (requiring about 900 years to go through all its changes) produced by the attractions of Jupiter and Saturn on each other; and Sir George Airey discovered a similar one on the earth and Venus, with a period of 240 years. So with regard to Uranus and Neptune, which has 6805 years for its period. Indeed it was from the disturbances of Uranus, which could not be otherwise accounted for, that the supposition was adopted that

orbits are now elliptical, & if more should intervene they may be changed into other curves, or more oblong ellipses, for this seems to be a consequence of gravitation & attraction. Query, whether a planet may not become a comet."

there was another exterior planet, and from these observed disturbances, the elements of this unknown planet were calculated. The result was the discovery of Neptune by Professor Adams and M. Leverrier.

One of the most remarkable theorems in the Planetary Theory was proved by Lagrange, at the end of the 18th century. It unfortunately disproves this supposition of P. Wyche's, and is as follows:

If m, m', m", &c., represent the masses of the several planets,

e, e', e", &c., the eccentricities of their elliptic orbits,

a, a', a", &c., their mean distances from the sun,

n, n'. n". &c., their mean motions in their orbits,

Now, n, n', n", &c.. are all positive, because the planets all move in the same direction, therefore all the terms in the above equation are positive; and as e, e', e", &c., are at present small, and so are m, m', m”, &c., and a, a', a′, &c., are not small, the above terms are all small, and therefore the sum of them is at present small; therefore being constant it is always small; therefore the several terms are always small; therefore the planets always will move in ellipses of small eccentricity; i.e. the planetary system is stable, or the planets will not fall into the sun. If, however, the planets were originally started in circular orbits. e, e', e", &c., would be O at the creation; and therefore the constant would then be O; therefore it would be O now; and since the terms are all positive, e, e', e′, &c., would always be O, i.e. the planets would always move in circles.-See Herschel's Astron.; Airey's Ipswich Lectures; Airey's Tracts ( Planetary Theory); Rutt's Mechanics.

2μ

г

r

• The question is rather vague. Theoretically there is nothing to prevent this happening. (1) Considered with regard to its orbit. In planetary motion, 1 = where v = the velocity of the planet at the point of its orbit under consideration, r = its distance from the sun, a = its mean distance, and μ = the absolute acceleration produced by the sun's attraction. It is quite possible that another orbit might coincide with this at the point in question, for which 2 = - if by any external impulse ▾ could be changed to ▼, and if v7 = 2 then a' would be infinite, and this would give a parabolic orbit; if v' exceeded this quantity, a' would be negative, which would give a hyperbolic orbit. If a planet were to explode, the centre of gravity of the fragments would move just as before, and it would either be impossible for one of the fragments to move in a parabolic orbit, unless indeed there were two that would do so. (2) Considered with regard to the mass of the planet, it would be impossible for it to become a comet; in the case of an explosion, a small portion of it might possibly become one.

The learned Derham' thinks that comets are the place for the damned, that there they may be sensible of the extremities of cold & heat. It is true were we to have the same bodys after death we now have, the torment we should feel by being in a comet would be very great, but this cannot be. Therefore I should incline to what Sir Isaac says, that they are designed for fuel to the sun, or to give moisture to some of the planets.

I was last night with the Bishop of Lincoln, who is so well recovered of his accident, that he proposes to be down stairs in a day or two. I told him that I had been favoured with a letter from you. He begged to hear what I could say in answer, which I gave him nearly as I have wrote above. He said it amused him so much that he was determined to look into Sir Isaac, & would have what Bradley publishes. If anything occurs here, whereby I could be serviceable to you, I should be glad at all times to shew you how much I am,

Your most obliged servant,

PETER WYCHE.

CLXVII. R. MEAD "TO DOCTOR STUKELEY, AT GRANTHAM, LINCOLNSHIRE."-H. F. ST. J.

Dear Sir,

Ormond Street, Apr. 4, 1727.

I have the favour of yours of the 24th last past. Our great freind Sir Isaac Newton dyed of an inflammation & excoriation of the neck of the bladder, which threw him, after about 7 days illness, into convulsions; he never complained, but suffered great fits of pain with a philosophical patience; neither do I hear that he sayd anything about a future state. Thus much I think I know of his opinions, that he was a christian, believed revelation, though not all the doctrines which our orthodox divines have made articles of faith. His chronology he has left written in his own hand, fitted for the press, & Mr. Conduit designs to

See page 257 n.

This was Richard Reynolds, consecrated to Bangor in 1721, at Lambeth ; translated to Lincoln in 1723; died in 1744. The usual residence of the Bishops of Lincoln was at Buckden, near Huntingdon.

9

publish it, with some account of his life. If therefore you will be so kind to transmit to him or to me any material circumstances you can gather concerning him or his family, they will be very acceptable.

Dr. Pemberton's book will not be out these 4 or 5 months, I will take care you shall have one in lieu of Bishop Parker's History.

I

My family

I am glad you are settled so much to your satisfaction. most heartily wish you all manner of happiness. joyns in most sincere respects to you. I am, dear Sir,

Your most obedient humble servant,

R. MEAD.

CLXVIII. JOHN CATLIN "TO THE REV. DR. STUKELey, at STAMFORD, IN LINCOLNSHIRE."-H. F. ST. J.

Lambeth, April 29, 1731.

Reverend Sir,

Having lately had a little leisure time I thought I could not spend it better than in the service of my friend. When I had the honour lately to wait on you at Mr. Sisson's, you made it a question whether the Asterisms were not formed when the first Star of Aries was in the very beginning thereof, & whether that was not the time also when Astronomy began. I then made myself so free as to dissent from you in both those things, & because I could not then readily recollect the reasons that induced me thereto, I have therefore since more strictly examined the matter, & find that my opinion was not altogether ill grounded,

· The title of the work here alluded to is "Chronology of Ancient Kingdoms Amended;" it was published in London in 1728, editor John Conduitt. Mr. Conduitt married Catherine Barton, the favourite niece of Sir Isaac, and succeeded him in his office as Master of the Mint. Their daughter married John, Viscount Lymington. (See page 53.) The memoir of Sir Isaac, prepared by Dr. Stukeley, thus became the property of the Earls of Portsmouth, of Hurstbourne.-See Athenæum. Ap. 1, 1882. The body of Sir Isaac lay in state in the Jerusalem chamber, and was interred in Westminster Abbey.