Chapter XIV: Part 14

All seeds and the stones of fruits, having a firm texture, are also capable of being strongly impregnated with stony and pyritical matter; and I make no doubt but that the smaller seeds, if carefully looked for, might be found fossil, as well as these before you; such, I mean, as have a firmness in the covering; but being small, and mixt with the dirt, sand, and the like, probably is the reason of their being overlooked. Fruits of various kinds are found petrified; but this is only in their green state, when they are hard enough to endure till they are impregnated with stony or mineral particles. The rudiments of fruits, when once well formed, and a little advanced, are firm and acid: and the more remote they are from maturity, the more secure from putrifaction; and their acid juice is no small help to their preservation from growing soon rotten. But indeed, when the fruit advances in growth, the texture grows gradually more lax; the acid juices are now beginning to be replaced by saccharine or others more soft; the fibres are driven farther asunder, and they now arrive at their most ripe state: and the utmost maturity of fruits is the next step to putrifaction. Hence they are destroyed before stony or other particles can have time enough to impregnate them: and this is exactly the case with the flesh of animals of every kind. The husks and hard calyces of fruits, as well as their stones, are also susceptible of petrifaction.

If these fruits, which I have the honour to lay before you, are antediluvian, one would be apt to imagine they, in some measure, point out, with Dr. Woodward, the time of year in which the deluge began; which he thinks was in May: and yet this very opinion is liable to some objections; because altho’ fruits capable of being petrified, from their green state, may be pretty well formed in May here, as well as in the same latitude elsewhere, in favour of this opinion; yet there are the stones of fruits, found fossil, so perfect, as to make one imagine they were very ripe, when deposited in the places where they are discovered; which would induce one to think the deluge happened nearer Autumn, unless we could think them the productions of more southern latitudes, where perhaps their fruits are brought to perfection before ours are well formed.

What follows is a catalogue of these fossil fruits &c. before you: and I should be glad, if any of the gentlemen would take the trouble of examining them, in order to assist in our conjectures about such of them, as appear doubtful: but first beg leave to insert the following remark:

I cannot omit an observation of Doctor Mason, Woodwardian professor, in this place; which is well worth notice, and indeed which I never attended to. It regards the impressions of fishes upon slate. Now there are several kinds of slate, which have such impressions upon them: in some there remains only the bare impression, without any part of the fish; in others the scales only, but retaining the intire form of the animal; and in others no part adheres to the slate, but the skeleton, or part of it, most commonly the spine. He says that he always observed, that the bones are never seen but upon the grey or blue slate, or their impressions; and that the scales or skin are to be found only upon the black stone or slate; which makes him conjecture, that something erosive in the grey slate destroys every part but the bony system; but that the black, being of a more soft and unctuous nature, preserves the scales, and often the very skin. This, however, must be referred to further observation.

IP MD. _delin._ _J. Mynde sc._]

TAB. XV.

_Fig._ 1, 3. These two bodies seem to be figs, petrified when hard and green; being, as I have just observed, then capable of receiving the pyritical particles, with which they are manifestly impregnated. One is more perfect in its form than the other; and they are now shooting their salts, and will soon fall to pieces.

_Fig._ 2. appears to be a Myrobalan, distinguished from the other species of that name by its round figure; and is called the belleric Myrobalan. It is nearly destroyed by the pyritical matter, and will not long remain whole.

_Fig._ 4. seems to be a species of Phaseolus, one of those especially distinguished by the fruits. _Fructibus splendentibus nigris._

_Fig._ 5. Another Phaseolus.

_Fig._ 7. Another. See _Fig. 4._

_Fig._ 8. Semen Cucurbitæ, a large species of American gourd.

_Fig._ 9. Coffee-berries.

_Fig._ 10, 11. Two species of Beans, very apparent.

_Fig._ 12. Unknown. This, however, appears to be a fruit, with the calyx running up, and embracing it, in its hard green state; being somewhat compressed on the upper part, as it lay confined in the earth.

_Fig._ 13. _An Staphilodendri species?_ The learned and reverend Dr. Hales gave me, some years ago, a handful of the recent fruits, one or two of which are sent with this fossil one, for your consideration. He had them from Bengal, and called them, in the Indian name, Neermelis; and said the natives used them to fine down liquors.

_Fig._ 14. A compressed pod of the Arachidna, or Underground-Pea. The full-grown pods are much larger, but of various sizes, as are other kinds. This, however, seems to have been, when deposited where it was found, not so far advanced. It has the reticulated surface, the apex on one side, and every other character of that fruit or seed-pod, but somewhat compressed.

_Fig._ 15. is evidently an Acorn. We have of this species here, and in America also.

_Fig._ 16. An exotic fruit, like a small melon; but uncertain. It is somewhat deformed by compression.

_Fig._ 17. This I took at first for a fruit; but now I rather believe it a Fungoides of a very pretty kind. _Fig._ 18. _An Anguria?_ I take it for a seed of a species of water-melon.

_Fig._ 19. seems a small plumb-stone.

_Fig._ 20. Unknown. The calyx seems to run up and embrace this fruit towards the apex.

_Fig._ 21. Unknown. This resembles an American seed, which I have in my collection, but do not know its name. Its apex is inclining to one side; and it appears to have had a strong pedicle.

_Fig._ 22. _An Lachryma Jobi?_

_Fig._ 23. A Cherry-stone.

IP _MD. delin._ _J. Mynde sc._]

TAB. XVI.

_Fig._ 1. _An Euonymi species?_ If this be an Euonymus, it is not so far advanced as to form the seeds: and is therefore to be considered only in its progress from the flower towards seeding: which is the case in several of these, whose calyces appear still upon them, and hinder us from absolutely determining what they are.

_Fig._ 2. A berry of the Sapindus, or Soap-tree, of America, being not at all deformed, only having a little lump of pyrites upon it: but there is another quite free.

_Fig._ 3. _Huræ Germen._ This is undoubtedly the young Sand-box, or fruit of the Hura, so well known for its beautiful form to the curious, who collect specimens of natural history; and seems to shew the time of the deluge.

_Fig._ 4. This, I think, is certainly the stone of an eastern Mango; such as comes over to us pickled, and, the stone being opened on one side, is generally stuffed with spices.

_Fig._ 5. _Euonymi latifolii species._ This is a large species of Euonymus, perhaps of Clusius.

_Fig._ 6. This body seems to be a Milleped, or Wood-louse. It is turned round, the two extremities meeting; which is the attitude assumed by these animals, upon being in any-wise obstructed in their passage, or handled.

_Fig._ 7. A small long Bean, like our horse-bean; but longer than any we have in England.

_Fig._ 8. Unknown to me.

_Fig._ 9. A species of Horse-chesnut from America.

_Fig._ 10. The external husk of the fruit of the Sapindus, or Soap-tree.

_Fig._ 11. I cannot determine whether this be an Olive, or the yellow Myrobalan; but believe it the Myrobalan.

_Fig._ 12. _A Palmæ species?_ It seems a small Palma-coco.

_Fig._ 13, 14. unknown, as well as _fig._ 15.

_Fig._ 16. Unknown. The reason of the four last being not to be distinguished is, that they seem to be the buds of their several species, before they were perfectly formed. So that while some of the antediluvian productions are mature, others appear to be premature; and consequently one would be inclined to think them the inhabitants of places of different latitudes.

_Fig._ 17. A species of foreign Walnut, injured and compressed.

_Fig._ 18. A Plumb-stone.

_Fig._ 19. The claw of an American Crab; which, being on the opposite side of the mass containing the body, could not come in view with it at the same time.

_Fig._ 20. The body of the crab, with other parts, appearing thro’ the stony matter that invelopes it, which appears to be an induration of yellow clay.

_Fig._ 21. seems a long American Phaseolus. Part of the petrified husk is upon it.

_Fig._ 22. An American Echinite of the flat kind, much resembling that species which Rumphius calls _Echinus sulcatus primus_.

_Fig._ 23. _Arista cujusdam Graminis._ This body has all the characteristics of an ear of corn, or some species of grass, of which there are many.

This has been taken for a spine of an Echinus: but, as we are to consider its nearest resemblance to whatsoever body, we must conclude it as we have said. I never saw any spine in the least like it; but an ear of corn, ripe and dry, is as susceptible of being petrified, as a crustaceous animal, in every respect. Indeed the spiculæ of the ear, each arising from the grain, being very slender, are of course destroyed during the petrifaction; but the form of the ear is actually preserved, as much as the nature and circumstances of the thing will allow.

_Fig. a._ A manifest species of Pediculus Marinus crumped up.

_b._ A Seed-vessel, given me by Mr. Da Costa, found in a clay-pit in Staffordshire.

_c._ Cocculus Indicus.

LII. _Observations upon the Comet that appeared in the Months of_ September _and_ October _1757, made at the Royal Observatory by_ Ja. Bradley, _D.D. Astronomer Royal, F.R.S. and Member of the Royal Academy of Sciences at_ Paris.

[Read Dec. 22, 1757.]

I Deferred to give an account of my observations upon the Comet that hath lately appeared, till I could settle the places of the stars with which it had been compared; several of them not being inserted in the British catalogue, and those which are, requiring some small corrections, which I have since made from my own observations.

When I first discovered this Comet, it appeared to the naked eye like a dull star of the 5th or 6th magnitude; but viewing it thro’ a seven-foot Telescope, I could perceive a small Nucleus (surrounded, as usual, with a nebulous atmosphere), and a short tail extended in a direction opposite to the sun.

Some small stars then appearing in the field of the telescope with the Comet, I measured its distance from them with a Micrometer; and on September 12ᵈ at 16ʰ 2’ mean time, I found it to be 1° 13’ 5" distant from a small star, whose right ascension was afterwards found to be 89° 49’ 40" and declination 36° 11’ 30" north: and near the same time the Comet was observed to be 43’ 10" from another star, whose right ascension was 90° 20’ 0" and declination 35° 12’ 0" north.

Hence I collected, that the Comet’s right ascension was 89° 29’ 10“ and its declination 35° 0’ 20" north.

September 13ᵈ 12ʰ 37’ mean time (which is likewise made use of in the following observations), the Comet had the same right ascension with a small star, whose right ascension was 93° 5’ 30" and declination 34° 36’ 40" north; and it was about two minutes more northerly than the star. Hence the Comet’s right ascension was 93° 5’ 30" and its declination 34° 38’ 40" north.

September 14ᵈ 14ʰ 0’ the Comet preceded θ Geminorum 1° 31’ 35“ in right ascension, and was 11’ 35" more southerly. The apparent right ascension of θ Geminorum was then 99° 11’ 40“ and its declination 34° 13’ 25" north. Hence the right ascension of the Comet was 97° 40’ 5" and its declination 34° 1’ 50" north.

Sept. 17ᵈ 13ʰ 0’ a small star (whose right ascension was 109° 55’ 20“ and declination 31° 27’ 40") preceded the Comet 47’ 10" in right ascension, and was 12’ 30" more northerly. Hence the Comet’s right ascension was 110° 42’ 40" and its declination 31° 15’ 10" north.

Sept. 19ᵈ 15ʰ 17’ a star (whose right ascension was 118° 29’ 40" and declination 28° 9’ 45") preceded the Comet 1° 14’ 0" in right ascension, and was more southerly 15’ 45“. Hence the Comet’s right ascension was 119° 43’ 40" and declination 28° 25’ 30" north.

Sept. 23ᵈ 15ʰ 57’ a star (whose right ascension was 134° 55’ 45" and declination 22° 15’ 55" north) preceded the Comet 12’ 30" in right ascension, and was 29’ 0" more northerly. Hence the Comet’s right ascension was 135° 8’ 15" and its declination 21° 46’ 55" north.

Sept. 24ᵈ 15ʰ 21’ the Comet had the same declination with a small star that preceded it 10’ 15“ in right ascension. This star’s right ascension was afterwards found to be 138° 13’ 45" and its declination 20° 5’ 20". Hence the Comet’s right ascension was 138° 24’ 0" and its declination 20° 5’ 20" north.

Sept. 28ᵈ 16ʰ 22’ the Comet followed Regulus 1° 7’ 12" in right ascension, and was 14’ 45" more northerly. The right ascension of Regulus being then 148° 51’ 13" and its declination 13° 8’ 35" north; the Comet’s right ascension was 149° 58’ 25" and its declination 13° 23’ 20" north.

Sept. 30ᵈ 16ʰ 24’ ρ Leonis (whose right ascension was 155° 0’ 10" and declination 10° 32’ 53" north) followed the Comet 18’ 45" in right ascension, and was 7’ 53" more northerly. Hence the Comet’s right ascension was 154° 41’ 25" and its declination 10° 25’ 0" north.

October 2ᵈ 16ʰ 48’ the 37th star Sextantis. Hevel. in the British Catalogue (whose right ascension was 158° 21’ 25" and declination 7° 38’ 40" north) preceded the Comet 32’ 50" in right ascension, and was 3’ 20" more southerly. Hence the Comet’s right ascension was 158° 54’ 15" and its declination 7° 42’ 0" north.

October 3ᵈ 16ʰ 45’ _c_ Leonis (whose right ascension was 162° 2’ 15’ and declination 7° 24’ 0" north) followed the Comet 1° 12’ 55" in right ascension, and was 56’ 40" more northerly. Hence the Comet’s right ascension was 160° 49’ 20" and its declination 6° 27’ 20" north.

October 4ᵈ 17ʰ 0’ _d_ Leonis (whose right ascension was 162° 0’ 15" and declination 4° 54’ 57" north) preceded the Comet 40’ 15” in right ascension, and was more southerly 20’ 53". Hence the Comet’s right ascension was 162° 40’ 30" and its declination 5° 15’ 50" north.

October 7ᵈ 16ʰ 54’ the 79th Leonis in the British Catalogue (whose right ascension was 167° 53’ 37" and declination 2° 44’ 15" north) followed the Comet 13’ 0" in right ascension, and was more northerly 38’ 35". Hence the Comet’s right ascension was 167° 40’ 37" and its declination 2° 5’ 40" north.

October 8ᵈ 16ʰ 53’ the Comet preceded _v_ Leonis 1° 53’ 30" in right ascension, and was 37’ 20" more northerly. The right ascension of this star was 171° 7’ 45" and its declination 0° 30’ 55" north; therefore the Comet’s right ascension was 169° 14’ 15" and its declination 1° 8’ 15" north.

October 11ᵈ 16ʰ 52’ the Comet followed _v_ Leonis 2° 33’ 30" in right ascension, and appeared 1° 55’ 5" more southerly; but it being near the horizon, the difference of right ascension must have been contracted by refraction about 1’ 5", and the difference of declination about 1’ 30": so that the corrected right ascension of the Comet was 173° 42’ 20" and its declination 1° 25’ 40" south.

Immediately after this observation a fog arose, which prevented me from repeating it; and several mornings following proving hazy or cloudy, I could not see the Comet again till October 18th, about an hour and a quarter before sun-rising; when the twilight being strong, and the Comet low, it appeared very faint. However, I was unwilling to omit the opportunity of determining its place, as near as I could, by a single observation, in the following manner.

At 6ʰ 59’ 54" ½ sidereal time, I observed the passage of the Comet over the perpendicular wire of my equatorial Sector; then leaving the instrument in the same position till the next evening, I observed, that at 22ʰ 8’ 15" sidereal time, the 17th star of Eridanus in the British Catalogue passed over the same wire (or horary circle) 9’ 30" more southerly than the Comet. And at 23ʰ 45’ 36" sidereal time the star marked _b_ in Eridanus passed, 19’ 55" more northerly than the Comet.

I found that the situation of my instrument was not sensibly altered between the 18th and 19th of October; for the transits and the difference of declination of the same stars being observed with it again on the 19th of October, they agreed very well with those that were taken the preceding night. It may therefore be supposed, that the position of the instrument continued the same likewise during the time of the foregoing observations.

The right ascension of the 17th star of Eridanus being 49° 39’ 10" and its declination 5° 55’ 25" south; and the right ascension of _b_ of Eridanus being 73° 59’ 15" and its declination 5° 25’ 10" south; I collected, that when the Comet passed the wire (or horary circle) which was October 17ᵈ 17ʰ 12’ mean time, its right ascension was 182° 34’ 0" and its declination 5° 45’ 35" south.

The last time that I saw the Comet was on the 19th of October in the morning; but it then appeared so faint, that I could not observe its place. Its elongation from the sun was then but about 20 degrees; and from that day to the present it hath always been less; which is the principal reason why it was invisible to us at the time when it was in its perihelion, and hath remained so ever since. The elongation will indeed soon become greater, and yet it is probable that we shall not be able to see the Comet again; because its real distance from the sun will be greater than it was when I first saw it, and it will be also four times further from us than it was at that time.

The Comet kept nearly at the same distance from the earth for ten or twelve days together after I first saw it; but its brightness gradually increased then, because it was going nearer to the sun. Afterwards, when its distance from the earth increased, altho’ it continued to approach the sun, yet its lustre never much exceeded that of stars of the second magnitude, and the tail was scarce to be discerned by the naked eye.

All the forementioned observations were made with a Micrometer in a seven-foot Tube, excepting those of the 3d, 11th, and 17th days of October, which were taken with a curious Sector constructed for such purposes by the late ingenious Mr. George Graham; of which Dr. Smith has given a very exact description in his third book of Optics.

Supposing the Trajectory of this Comet to be parabolic, I collected from the foregoing observations, that its motion round the sun is _direct_, and that it was in its _perihelion_ October the 21st, at 7ʰ 55’ mean (or equated) time at Greenwich. That the inclination of the plane of its Trajectory to the ecliptic is 12° 50’ 20"; the place of the descending Node ♉ 4° 12’ 50"; the place of the Perihelion ♄ 2° 58’ 0"; the distance of the Perihelion from the descending Node 88° 45’ 10"; the Logarithm of the Perihelion distance 9.528328; the Logarithm of the diurnal motion 0.667636.

From these Elements (which are adapted to Dr. Halley’s general Table for the Motion of Comets in parabolic Orbits), I computed the places of this Comet for the respective times of the foregoing observations, as in the following table; which contains likewise the longitudes and latitudes deduced from the observed right ascensions and declinations, and also the differences between the computed and observed places. These differences (no-where exceeding 40") shew, that the elements here set down will be sufficient to enable future astronomers to distinguish this Comet upon another return; but as they do not correspond with the elements of the orbit of any other Comet hitherto taken notice of, we cannot determine at present the period thereof.

Greenwich, 1757.| Comet. Long.|
Mean Time. | Observ. | Latit. Observ.
----------------+--------------+-----------------+
_d._ _h._ '| S. ° ’ " | ° ’ "
----------------+--------------+-----------------+
Sept. 12 16 2 | ♊ 29 34 13 | 11 32 16 No.
13 12 37 | ♋ 2 35 34 | 11 12 13
14 14 0 | 6 27 45 | 10 44 3
----------------+-------------+-----------------+
17 13 0 | 17 49 40 | 9 3 31
19 15 17 | 26 6 8 | 7 36 49
23 15 57 | ♌ 11 19 18 | 4 33 38
----------------+-------------+-----------------+
24 15 21 | 14 44 19 | 3 49 37
28 16 22 | 27 23 43 | 1 3 44 No.
30 16 24 | ♍ 2 45 43 | 0 5 30 So.
----------------+-------------+-----------------+
Octob. 2 16 48 | 7 37 43 | 1 5 50
3 16 45 | 9 51 36 | 1 32 22
4 17 0 | 12 1 4 | 1 56 42
----------------+-------------+-----------------+
7 16 54 | 17 51 3 | 2 56 48
8 16 53 | 19 39 45 | 3 13 7
11 16 52 | 24 47 22 | 3 48 49
17 17 12 | ♎ 4 38 58 | 4 15 42 So.

Greenwich, 1757.| | | Diff. | Diff.
Mean Time. | Long. Comp. | Latit. Comput. | Long. | Latit.
----------------+----------------+---------------+-------+--------
_d._ _h._ '| S. ° ’ " | ° ’ " | " | "
----------------+----------------+----------------+-------+-------
Sept. 12 16 2 | ♊ 29 34 11 | 11 32 20 No. | -2 | +4
13 12 37 | ♋ 2 35 47 | 11 12 11 | +13 | -2
14 14 0 | 6 27 42 | 10 43 43 | -3 | -20
----------------+----------------+----------------+-------+-------
17 13 0 | 17 50 16 | 9 3 11 |+36 |-20
19 15 17 | 26 5 50 | 7 36 30 |-18 |-19
23 15 57 | ♌ 11 19 4 | 4 33 32 |-14 | -6
----------------+----------------+----------------+-------+-------
24 15 21 | 14 44 3 | 3 49 39 |-16 | +2
28 16 22 | 27 23 32 | 1 3 52 No. |-11 | +8
30 16 24 | ♍ 2 45 39 | 0 5 17 So. | -4 |-13
----------------+----------------+----------------+-------+-------
Octob. 2 16 48 | 7 37 42 | 1 5 32 | -1 |-18
3 16 45 | 9 51 29 | 1 31 55 | -7 |-27
4 17 0 | 12 0 25 | 1 56 23 | -39 | -19
----------------+----------------+----------------+-------+------
7 16 54 | 17 51 6 | 2 56 24 | +3 | -24
8 16 53 | 19 39 33 | 3 12 28 | -12 | -39
11 16 52 | 24 47 47 | 3 49 29 | +25 | +40
17 17 12 | ♎ 4 38 36 | 4 15 2 So. | -22 | -40

LIII. _The Resolution of a General Proposition for Determining the_ horary _Alteration of the Position of the Terrestrial Equator, from the Attraction of the Sun and Moon: With some Remarks on the Solutions given by other Authors to that difficult and important Problem. By Mr._ Tho. Simpson, _F.R.S._

[Read Dec. 22, 1757.]

SINCE the time, that that excellent Astronomer, my much honoured friend Dr. Bradley, published his observations and discoveries concerning the inequalities of the precession of the equinox, and of the obliquity of the ecliptic, depending on the position of the lunar nodes, mathematicians, in different parts of Europe, have set themselves diligently to compute, from physical principles, the effects produced by the sun and moon, in the position of the terrestrial equator; and to examine whether these effects do really correspond with the observations.

Two papers on this subject have already appeared in the Philosophical Transactions; in which the authors have shewn evident marks of skill and penetration. There is, nevertheless, one part of the subject, that seems to have been passed over without a due degree of attention, as well by both those gentlemen, as by Sir Isaac Newton himself.

This part, which, upon account of physical difficulties, is indeed somewhat slippery and perplexing, I shall make the principal subject of this essay.

GENERAL PROPOSITION.

_Supposing an homogeneous sphere_ OABCD (Fig. 1.) _revolving uniformly about its centre, to be acted on at the extremity_ A _of the radius_ OA, _in a direction_ AL _perpendicular to the plane of the equator_ ABCD, _and parallel to the axis of rotation_ Pp, _by a given force, tending to generate a new motion of rotation at right angles to the former; It is proposed to determine the change, that will arise in the direction of the rotation in consequence of the said force._

Let _F_ denote the given force, whereby the motion about the axis P_p_ is disturbed, supposing _f_ to represent the centrifugal force of a small particle of matter in the circumference of the equator, arising from the sphere’s rotation; and let the whole number of such particles, or the content of the sphere, be denoted by _c_: let also the momentum of rotation of the whole sphere, or of all the particles, be supposed, in proportion to the momentum of an equal number of particles, revolving at the distance OA of the remotest point A, as _n_ is to _unity_.

It is well known, that the centripetal force, whereby any body is made to revolve in the circumference of a circle, is such, as is sufficient to generate all the motion in the body, in a time equal to _that_, wherein the body describes an arch of the circumference, equal in length to the radius. Therefore, if we here take the arch AR = OA, and assume _m_ to express the time, in which that arch would be uniformly described by the point A, the _motion_ of a particle of matter at A (whose central force is represented by _f_) will be equal to _that_, which might be uniformly generated by the force _f_, in the time _m_; and the motion of as many particles (revolving, all, at the same distance) as are expressed by _cn_ (which, by hypothesis, is equal to the momentum of the whole body), will, consequently, be equal to the momentum, that might be generated by the force _f_ × _cn_, in the same time _m_. Whence it appears, that the momentum of the whole body about its axe P_p_ is in proportion to the momentum generated in a given particle of time _m’_, by the given force _F_ in the direction AL, as _ncf_ × _m_ is to _F_ × _m’_, or, as _unity_ to (_F_/_ncf_) × (_m’_/_m_) (because the quantities of motion produced by unequal forces, in unequal times, are in the ratio of the forces and of the times, conjunctly). Let, therefore, AL be taken in proportion to AM, as (_F_/_ncf_) × (_m’_/_m_) is to _unity_ (supposing AM to be a tangent to the circle ABCD in A), and let the parallelogram AMNL be compleated; drawing also the diagonal AN; then, by the composition of forces, the angle NAM (whose tangent, to the radius OA, is expressed by OA × (_F_/_ncf_) × (_m’_/_m_)) will be the change of the direction of the rotation, at the end of the aforesaid time (_m’_). But, this angle being exceeding small, the tangent may be taken to represent the measure of the angle itself; and, if Z be assumed to represent the arch described by A, in the same time (_m’_) about the center O, we shall also have (_m’_/_m_) = (Z/AR) = (Z/AO), and consequently OA × (_F_/_ncf_) x (_m_/_m’_) = Z × (_F_/_ncf_). From whence it appears, that the angle expressing the change of the direction of the rotation, during any small particle of time, will be in proportion to the angle described about the axe of rotation in the same time, as _F_/_ncf_ is to _unity_. _Q.E.I._

Altho’, in the preceding proposition, the body is supposed to be a perfect sphere, the solution, nevertheless, holds equally true in every other species of figures, as is manifest from the investigation. It is true, indeed, that the value of _n_ will not be the same in these cases, even supposing those of _c_, _f_ and _F_ to remain unchanged; except in the spheroid only, where, as well as in the sphere, _n_ will be = ⅖; the momentum of any spheroid about its axis being 2-5ths of the momentum of an equal quantity of matter placed in the circumference of the equator, as is very easy to demonstrate.

But to shew now the use and application of the general proportion here derived, in determining the regress of the equinoctial points of the terrestrial spheroid, let AE_a_F (_Fig. 2._) be the equator, and P_p_ the axis of the spheroid: also let HECF represent the plane of the ecliptic, S the place of the sun, and HAPNH the plane of the sun’s declination, making right-angles with the plane of the equator AE_a_F: then, if AK be supposed parallel, and OKM perpendicular, to OS, and there be assumed _T_ and _t_ to express the respective times of the annual and diurnal revolutions of the earth, it will appear (from the _Principia_, B. III. prop. xxv.) that the force, with which a particle of matter at A tends to recede from the line OM in consequence of the sun’s attraction, will be expressed by (_3tt_/_TT_) × (AK/OA) × _f_; _f_ denoting the centrifugal force of the same particle, arising from the diurnal rotation. Hence, by the resolution of forces, (_3tt_/_TT_) × (AK/OA) × (OK/OA) × _f_ will be the effect of that particle, in a direction perpendicular to OA, to turn the earth about its center O.

But it is demonstrated by Sir Isaac Newton, and by other authors, that the force of all the particles, or of all the matter in the whole spheroid AP _ap_, to turn _it_ about its center, is equal to ⅕th of the force of a quantity of matter, placed at A, equal to the excess of the matter in the whole spheroid above _that_ in the inscribed sphere, whose axis is P_p_. Now this excess (assuming the ratio of π to 1, to express _that_ of the area of a circle to the square of the radius) will be truly represented by (4π/3) × OP × (OA² - OP²); and, consequently, the force of all the matter in the whole earth, by (_3tt_/_TT_) × (AK/OA) × (OK/OA) × (4π/15) × OP × (OA²- OP²). Let, therefore, this quantity be now substituted for _F_, in the general formula _F_/_ncf_, writing, at the same time, (4π/3) × OA² × OP, and ⅖, in the place of their equals _c_ and _n_; by which means we have (here) (_F_/_ncf_) = (_3tt_/_2TT_) × ((OA² - OP²)/OA²) × ((AK × OK)/OA²). Put the given quantity (_3tt_/_2TT_) × ((OA² - OP²)/OA²) = _k_; and let the angle EA_e_ represent the horary alteration of the position of the terrestrial equator, arising from the force _F_ (here determined), and let the arch E_e_ be the regress of the equinoctial point E, corresponding thereto: then, in the triangle EA_e_ (considered as spherical) it will be sin. _e_ ∶ sin. AE (∷ sin. EA_e_: sin. E_e_) ∷ EA_e_ ∶ E_e_ (= (sin. AE x EA_e_)/sin. E) = _k_ × (sin. AE/sin. E) × ((AK × OK)/OA²) = _k_ × ((sin. AE × cos. AH × sin. AH)/sin. E). But in the triangle EHA, right-angled at A (where HA is supposed to represent the sun’s declination, AE his right ascension, and HE his distance from the equinoctial point E[207]) we have (_per spherics_)

sin. AE ∶ 1 (rad.) ∷ co-t. E ∶ co-t. AH,
(sin. AH)² ∶ (sin. EH)² ∷ (sin. E)² ∶ 1² (rad.²)

From whence we get, sin. AE × co-t. AH × (sin. AH)² = (sin. EH)² × co-t. E × (sin. E)². But co-t. AH × sin. AH = co-s. AH × 1 (rad.), and co-t. E × sin. E = co-s. E × 1 (rad.): therefore sin. AE × co-s. AH × sin. AH = (sin. EH)² × co-s. E × sin. E; and, consequently, _k_ × (sin. AE × co-s. AH × sin. AH)/sin. E = _k_ × co-s. E × (sin. EH)² (= E_e_).

Let, now, the sun’s longitude EH be denoted by Z (considered as a flowing quantity); then, (sin. Z)² being = ½-½ co-s. 2 Z, we shall have _k_ × co-s. E × (sin. EH)² = ½_k_ × co-s. E × 1-co-s. 2 Z. But the angle described about the axe of rotation P_p_, in the time that the sun’s longitude is augmented by the particle Ż, will be = (_T/t_) × Ż. Therefore (by the general proposition) we have, as 1: ½_k_ × co-s. E × 1-co-s. 2 Z ∷ (_T/t_) × Ż : ½_k_ × (_T/t_) × co-s. E × Ż - Ż co-s. 2 Z, the true regress of the equinoctial point E, during that time: whose fluent, ½_k_ × (_T_/_t_) × co-s. E × (Z- ½ sin. 2 Z), will consequently be the total regress of the point E, in the time that the sun, by his apparent motion, describes the arch HE or Z; which, on the sun’s arrival at the solstice, becomes barely = ½_k_ × (_T_/_t_) × co-s. E × an arch of 90°: the quadruple whereof, or ½_k_ × (_T_/_t_) × co-s. E × 360° (= (3_t_/4_T_) × ((OA²-OP²)/OA²) × co-s. E × 360°) is therefore the whole annual precession of the equinox caused by the sun. This, in numbers (taking OP/OA = 229/230) comes out (3/(4 × 366¼)) × (2/230½) × 0.917176 × 360° = 21´´ 6´´´.

The very ingenious M. Silvabelle, in his essay on this subject, inserted in the 48th volume of the Philosophical Transactions, makes the quantity of the annual precession of the equinox, caused by the sun, to be the half, only, of what is here determined. But this gentleman appears to have fallen into a twofold mistake. First, in finding the _momenta of rotation_ of the terrestrial spheroid, and of a very slender ring, at the equator thereof; which _momenta_ he refers to an axis perpendicular to the plane of the sun’s declination, instead of the proper axe of rotation, standing at right angles to the plane of the equator. The difference, indeed, arising from thence, with respect to the spheroid (by reason of its near approach to a sphere) will be inconsiderable; but, in the ring, the case will be quite otherwise; the equinoctial points thereof being made to recede just twice as fast as they ought to do. This may seem the more strange, if regard be had to the conclusions, relating to the nodes of a satellite, derived from this very assumption. But, that these conclusions are true, is owing to a second, or subsequent mistake, at Art. 27; where the measure of the sun’s force is taken the half, only, of the true value; by means whereof the motion of the equinoctial points of the ring is reduced to its proper quantity, and the motion of the equinoctial points of the terrestrial spheroid, to the half of what it ought to be.

That expert geometrician M. Cha. Walmsley, in his Essay on the Precession of the Equinox, printed in the last volume of the Philosophical Transactions, has judiciously avoided all mistakes of this last kind, respecting the sun’s force, by pursuing the method, pointed out by Sir Isaac Newton; but, in determining the effect of that force, has fallen into others, not less considerable than those above adverted to.

In his third Lemma, the momentum of the whole Earth, about its diameter, is computed on a supposition, that the momentum or force of each particle is proportional to its distance from the axis of motion, or barely as the quantity of motion in such particle, considered abstractedly. No regard is, therefore, had to the lengths of the unequal levers, whereby the particles are supposed to receive and communicate their motion: which, without doubt, ought to have been included in the consideration.

In his first proposition, he determines, in a very ingenious and concise manner, the true annual motion of the nodes of a ring (or of a single satellite) at the earth’s equator, revolving with the earth itself, about its center, in the time of one siderial day. This motion he finds to be = (3co-s. 23° 29´/4 rad.) × (⅟366¼) × 360°. Then, in order to infer from thence, the motion of the equinoctial points of the earth itself, he, first, diminishes that quantity, in the ratio of 2 to 5: Because (as is demonstrated by Sir Isaac Newton in his 2d Lemma) the whole force of all the particles situated without the surface of a sphere, inscribed in the spheroid, to turn the body about its center, will be only 2-5ths of the force of an equal number of particles uniformly disposed round the whole circumference of the equator, in the fashion of a ring. The quantity ((3co-s. 23° 29´/4 rad.) × ⅖ × (⅟366¼) × 360°) thus arising, will, therefore, express the true motion of the equinoctial points of a ring, equal in quantity of matter to the excess of the whole earth above the inscribed sphere, when the force whereby the ring tends to turn about its diameter is supposed equal to the force whereby the earth itself tends to turn about the same diameter, in consequence of the sun’s attraction. Thus far our author agrees with Sir Isaac Newton; but, in deriving from hence the motion of the equinoctial points of the earth itself, he differs from him; and, in the corollary to his third Lemma, assigns the reasons, why he thinks Sir Isaac Newton, in this particular, has _wandered a little from the truth_. Instead of diminishing the quantity above exhibited (as Sir Isaac has done) in the ratio of all the motion in the ring to the motion in the whole earth, he diminishes it in the ratio of the motion of all the matter above the surface of the inscribed sphere to the motion of the whole earth: which matter, tho’ equal to that of the ring, has nevertheless a different momentum, arising from the different situation of the particles in respect to the axis of motion.

But since the aforesaid quantity, from whence the motion of the earth’s equinox is derived, as well by this gentleman, as by Sir Isaac Newton, expresses truly the annual regress of the equinoctial points of the ring (and not of the hollow figure formed by the said matter, which is greater, in the ratio of 5 to 4) it seems, at least, as reasonable to suppose, that the said quantity, to obtain from thence the true regress of the equinoctial points of the earth, ought to be diminished in the former of the two ratios above specified, as that it should be diminished in the latter. But, indeed, both these ways are defective, even supposing the momenta to have been truly computed; the ratio, that ought to be used here, being that of the momenta of the ring and earth about the proper axe of rotation of the two figures, standing at right-angles to the plane of the ring and of the equator. Now this ratio, by a very easy computation, is found to be as 230²-229² to ⅖ of 230²; whence the quantity sought comes out = (3co-s. 23° 29´/4 rad.) × (⅟366¼) × (230²-229²)/230² × 360° = 21´´ 6´´´: which is the same that we before found it to be, and the double of what this author makes it.

What has been said hitherto, relates to that part of the motion only, arising from the force of the sun. It will be but justice to observe here, that the effect of the moon, and the inequalities depending on the position of her nodes, are truly assigned by both the gentlemen above-named; the ratio of the diameters of the earth, and the density of the moon being so assumed, as to give the maxima of those inequalities, such as the observations require: in consequence whereof, and from the law of the increase and decrease (which is rightly determined by theory, tho’ the absolute quantity is not) a true solution, in every other circumstance, is obtained.

The freedom, with which I have expressed myself, and the liberty I have here taken, to animadvert on the works of men, who, in many places, have given incontestible proofs of skill and genius, may, I fear, stand in need of some apology. ’Tis possible I may be thought too peremptory. Indeed, I might have delivered my sentiments with more caution and address: but, had not I imagined myself quite clear in what has been advanced, from a multitude of concurrent reasons, I should have thought it too great a presumption to have said any thing at all here, on this subject. The great regard I have for this Society, of which I have the honour to be a member, will, I hope, be considered as the motive for my having attempted to rectify some oversights, that have occurred in the works of this learned body.

LIV. _Remarks upon the Heat of the Air in_ July 1757. _in an Extract of a Letter from_ John Huxham, _M.D. F.R.S. to_ William Watson, _M.D. F.R.S. dated at_ Plymouth _19th of that Month. With additional Remarks by Dr._ Watson.

[Read Dec. 22, 1757.]

“FROM the beginning of June last we have had a very dry season, generally very warm, and sometimes excessively hot. From the 7th to the 14th of this month the heat was violent; greater, indeed, than has been known here in the memory of man. I have talked with several persons, who have lived a considerable time in Jamaica, Gibraltar, and Minorca; and they severally assert, that they never felt such intense heat in any of those places. Upon the 11th, 12th, and 13th of this month, Fahrenheit’s thermometer, in the shade, about three o’clock in the afternoon, was at 87; nay, upon the 12th it was even above 88.

Abundance of people have suffered very severely from these excessive heats: putrid, bilious, petechial, nervous fevers, are exceedingly common every-where. Dysenteries, hæmorrhages, most profuse sweats, affect not only those in fevers, but a vast many others. The days and nights were so intolerably hot, that little or no sleep was to be gotten day or night. The wind we had, like the Campsin, actually blew hot, tho’ strong.

Upon the 15th, about seven at night, at Falmouth, Penryn, Truro, and thereabouts, a pretty smart shock of an earthquake was felt, attended with a hollow rumbling noise, throwing down pewter, china-ware, and such-like. The tinners felt it eighty fathom under ground. No great damage however was done. The day before we had, about eleven o’clock before noon, a most violent hurricane, which lasted five or six minutes, attended with a heavy shower.”

Thus far Dr. Huxham.

The heat of the air at London, during the period above-mentioned, was much greater than has been usually observed in these high latitudes; tho’ it was never quite so severe here as at Plymouth. The following table exhibits the degrees of the heat, taken here upon the respective days, about four o’clock in the afternoon, by a Fahrenheit’s thermometer. The instrument was placed in the shade; and the accuracy of the observer, who favoured me with his minutes, is not to be questioned.

1757. July 5 75
6 78
7 75½
8 78
10 80¼
11 83¼
12 80¼
13 80
14 85
15 81
16 73

From hence it appears, that the air at London was, upon several days, hotter than it had been observed at Madeira for ten years together: for, by Dr. Thomas Heberden’s observations, mentioned in the Philosophical Transactions, the heat of the air at Madeira, during that period, was never but once at 80.

William Watson.

LV. _Remarks upon the Letter of Mr._ John Ellis, _F.R.S. to_ Philip Carteret Webb, _Esq; F.R.S. printed in the_ Philosophical Transactions, _Vol._ xlix. _Part_ ii. _p._ 806. _By Mr._ Philip Miller, _F.R.S._

[Read Dec. 15, 1757.]

THE paper of mine, which was read before the Royal Society on the 8th of May 1755, and afterward printed in the xlixth volume of the Philosophical Transactions[208], was written at the request of Mr. Watson; who informed me, that a letter from the Abbé Mazeas to the reverend Dr. Hales had been communicated to the Royal Society, in which it was mentioned, that the Abbé Sauvages had made a discovery of the juice of the Carolina Toxicodendron staining linen of a permanent black. But Mr. Watson said, that the letter, he thought, required a careful perusal before it was printed; and he wished I would confirm it. I told him, if the letter was put into my hands, I would look it over, and deliver my opinion of it.

Accordingly Dr. Birch delivered the letter to me; and, upon reading it, I found, that tho’ this might be a discovery to those two gentlemen; yet, as it had been mentioned in several printed books long before, I thought it might not be for the reputation of the Royal Society to have it printed as such in their Transactions.

This was my motive for writing that paper: in which I have not endeavoured to depreciate the discovery of the Abbé Sauvages, but have only mentioned what had occurred to me in those books of botany, where that shrub is taken notice of. And as the knowlege of it, and the method of collecting the varnish, might be of service to the inhabitants of the British colonies in America, I took the liberty of adding the account given of it by Dr. Kœmpfer.

Mr. Ellis, in his letter to Mr. Webb, asserts, that the American _Toxicodendron_ is not the same with Kœmpfer’s _Arbor vernicifera legitima_. This assertion of his makes it necessary to lay before the Society the authorities, upon which I have grounded my belief, that they are the same. But it may not be amiss first to take notice, that the shrub mentioned by the Abbé Sauvages is the same with that, which the gardeners about London call the Poison-ash. The title of it, mentioned by the Abbé Sauvages, was given by myself to that shrub, in a catalogue of trees and shrubs, which was printed in the year 1730; before which it had no generical title applied to it. And about the same time I sent several of the plants to Paris and Holland with that title, which I had raised a few years before from seeds, which were sent by Mr. Catesby from Carolina.

And altho’ this shrub had not been reduced to any genus before, yet it had been some years growing in the gardens of the Bishop of London at Fulham, at Mr. Reynardson’s at Hillenden, Mr. Darby’s at Hoxton, and in the Chelsea garden, which were raised from seeds sent by Mr. Banister from Virginia; two of which were growing at Chelsea in the year 1722, when the care of that Garden was intrusted to me.

The first intimation I had of the American shrub being the same with Dr. Kœmpfer’s true varnish-tree, was from the late Dr. William Sherard, in the year 1726, when that gentleman desired me to bring him a specimen of the American Toxicodendron from the Chelsea garden; which I accordingly did: and then the Doctor, and Dr. Dillenius, compared it with a dried specimen in the collection of the former, which was gathered in Japan, and which, if I remember right, he told me he received from Dr. Kœmpfer some years before. It appeared to those two gentlemen, that they were the same; and their skill in the science of botany was never doubted.

About a year after this, I carried a specimen of the American Toxicodendron to an annual meeting of some botanists at Sir Hans Sloane’s in Bloomsbury; where there were present Mr. Dale of Braintree, Mr. Joseph Miller, Mr. Rand, and some others; which was then compared with Dr. Kœmpfer’s specimen, whose collection Sir Hans Sloane had purchased: and it was the opinion of every one present, that they were the same. Nor has any one doubted of their being so, who has compared the American shrub with Kœmpfer’s figure and description of his true varnish-tree, but Mr. Ellis.

And now give me leave to examine his reasons for differing in opinion from every late botanist, who has mentioned this shrub.

He says, that the midrib, which supports the lobe leaves, is quite smooth in the poison-ash, as is also the under side of the leaves; whereas Dr. Kœmpfer, in his description of the midrib of the true varnish-tree, calls it _læviter lanuginoso_; and in his description of the lobes or _pinnæ_ he says, they are _basi inequaliter rotunda_; whereas those of the poison-ash come to a point at their footstalks nearly equal to that at the top. These characters, Mr. Ellis thinks, are sufficient to prove, that they are different plants: and he blames Dr. Dillenius for having omitted these necessary characters in his description of it; and supposes this must have misled the accurate Linnæus, who quotes his synonyma.

But as Dr. Linnæus is possessed of Kœmpfer’s book, he would little have deserved the appellation of accurate in this particular, had he not consulted the original, but trusted to a copy. But this I know he has done, and is as well assured, that the plants in question are the same, as Mr. Ellis can be of the contrary.

But here I must observe, that the branch, from which Dr. Kœmpfer’s figure is taken, is produced from the lower part of a stem, which seems to have been cut down, and not from a flowering branch; and it is not improbable, that his description may have been taken from the same branch: and if this be the case, it is easy to account for the minute differences mentioned by Mr. Ellis; for it would not be difficult to produce instances of hundreds of different trees and shrubs, whose lower and upper branches differ much more in the particulars mentioned by Mr. Ellis, than the figure and description given by Kœmpfer do from the American Toxicodendron. I will only mention two of the most obvious: the first is the white poplar, whose shoots from the lower part of the stem, and the suckers from the root, are garnished with leaves very different in form and size from those on the upper branches, and are covered on both sides in the spring with a woolly down. The next is the willow with smooth leaves, which, if a standard, and the head lopped off, as is usual, the young shoots are garnished with leaves much broader, and of different forms from those on the older branches; and these have frequently a hairy down on their under surface, which does not appear on those of the older. So that a person unacquainted with these differences in the same tree would suppose they were different. And the American Toxicodendron has varied in these particulars much more, in different seasons, than what Mr. Ellis has mentioned.

Mr. Ellis next says, that the Toxicodendron mentioned by Mr. Catesby, in his Natural History of Carolina, is not the same with that, which is now called by the gardeners poison-ash: but I am very positive of the contrary; for most of the plants in the nursery-gardens about London were first raised from the seeds, which were sent by Mr. Catesby from Carolina; part of which were sent to the late Dr. Sherard, as is mentioned by him in the Philosophical Transactions, Nº. 367; and another part came to my hands, from which I raised a great many of the plants, which were distributed, and some of them are now growing in the Chelsea garden.

And that this shrub grows naturally in Carolina, I can have no doubt, having received the seeds of it two or three times from the late Dr. Dale, who gathered them in the woods of that country.