Chapter V: Part 5

IN the London Chronicle, Nº. 181, published on the 25th of February 1758, in page 185, is the following article: “We hear, that about two o’clock in the morning of the 24th of last month” (which was the month of January), “an Earthquake was felt in the parishes of Worthe, and East-Grinsted, in Sussex; Lingfield, in Surrey; and Edenbridge, in Kent; and other adjacent places: which alarmed several of the inhabitants very much; but no damage ensued.”

Mr. Burrow, having some connection with these two last parishes of Lingfield and Edenbridge, immediately wrote to the Rev. Mr. Goodricke of Lingfield, to inquire into the truth of this report: and Mr. Goodricke’s answer confirmed the fact of its being felt there, and at other adjacent places; and added, “that it shook the beds and windows, and made the plates rattle; and went off with a noise, like a small gust of wind.”

However, Mr. Burrow did not then judge it to be either regular or proper to trouble the Society with this account; because Mr. Goodricke only received it from hearsay and report, he himself happening to be absent from Lingfield at that time.

But Mr. Burrow having passed some days, during the late recess of the Society, at a place called Starborough-castle, which lies nearly _between_ the two churches of Lingfield and Edenbridge (scarce four miles distant from each other), he has had an opportunity of being more particularly and circumstantially informed of the fact, as far as relates to those two parishes: and he is now assured, that it was certainly and undoubtedly felt and observed by _some_ persons in each of those two parishes; tho’ (as it happened in the dead of the night, when most people were fast asleep) it was not _generally_ perceived: nor was it much spoken of, even by those, who were sure they felt it.

The persons, from whose own mouths he can authenticate the fact, are James Martin, Adam Killick, Mrs. Jewell, and Mr. Chapman: and he has no less doubt as to Mr. Orgles and Mrs. Pigott (who was waked and much frighted by it), tho’ he did not indeed personally converse with either of the two last.

These two, and Mrs. Jewell, all inhabit quite close to Lingfield church-yard, on different sides of it: and Chapman lives within a quarter of a mile of it, to the south-west.

James Martin lives within a bow-shot of Starborough-castle, at the eastern edge of the parish of Lingfield, where it joins to that of Edenbridge; and Adam Killick’s habitation is three miles north-east of Starborough, at the north-western point of the parish of Edenbridge.

All these four, with whom Mr. Burrow personally conversed, agreed as to the _time_ of the concussion; _viz._ between one and two in the morning: and they all agreed as to the _shaking_ of their beds and windows; and all of them described the _continuance_ of the shock as not much more than instantaneous: but they did _not_ all hear the _noise_, which _some_ of them observed it to conclude with; particularly Adam Killick heard NO _noise_ at all; and yet, he says, he was broad awake when it first began: and it shook his house and bed, and made his windows rattle so much, that he was apprehensive of their being broken; and even caused one pane of glass (which was indeed loose before) actually to drop out. But James Martin, who was likewise fully awake (as was his wife too), _did hear_ the noise distinctly. He says, he felt his house and bed shake, heard his windows rattle, and some earthen ware clatter upon a chest of drawers; and also heard a noise, like the distant discharge of a cannon: whereupon he immediately said to his wife, “Lord! what is _that_?” but she happening, at that very instant, either to cough or sneeze (she cannot recollect which of the two), did not, tho’ quite awake, perceive any thing at all of the matter. However, she confirmed her husband’s asking her this question under an apparent surprize.

Mr. Burrow had a very particular conversation with these two separately: and he had also a very minute detail from Adam Killick (who works for him as a sort of gardener at Starborough); who further added, “that the shock waked and frighted his wife, tho’ she was fast asleep before.”

6th April, 1758.

James Burrow.

LXXXIII. _An Account of the Case of the First Joint of the Thumb torn off, with the Flexor Tendon in its whole Extent torn out. By_ Robert Home, _late Surgeon to the Thirtieth Regiment of Foot, and Surgeon at_ Kingston upon Hull. _In a Letter to_ John Pringle, _M. D. F.R.S._

[Read April 6, 1758.]

SIR,

I Take the liberty of inclosing to you a case in surgery, which I imagine is not very common. Marchetis indeed has an observation of the same kind; and there are several others collected together by Mons. Morand, in the second volume of the Memoires of the Royal Academy of Surgery at Paris: but as I have not heard of that volume’s being translated into English, and believe there is no observation of a similar nature in the Philosophical Transactions, I beg the favour of you to communicate it to the Royal Society, of which you are a Fellow; and at the same time to make them an offer of the joint of the thumb, with its adherent tendon, which you will receive at the same time with this; hoping they will do me the honour of accepting it, as a testimony (tho’ trifling) of my great esteem and respect for the most learned Society in Europe. Your Friend Dr. Knox saw the patient dressed oftener than once; and Mr. Thornhill, late Surgeon and Manmidwife in Bristol, saw it when near healed.

I beg you will believe me to be, with great truth,

SIR,
Your most obedient,
and most humble Servant,
Robert Home.

Hull, March 17th, 1758.

JAnuary 2d, 1758, William Taylor, 17 years of age, an apprentice to a white-smith in this place, in endeavouring to make his escape from one, who was going to correct him, opened the door of a cellar, and threw himself into it; but in his hurry so intangled his right thumb with the latch, that the whole weight of his body was suspended by it, until it gave way, and was torn off at the first articulation; the flexor tendon being at the same time pulled out in its whole length, having broke when it became muscular. I was immediately sent for, found little or no hæmorrhage, and the bone of the second phalanx safe, and covered with its cartilage, but protruding considerably, occasioned by part of the skin belonging to it being irregularly torn off with the first joint.

I was doubtful, whether or not I should be obliged, at last, to make a circular incision, and saw the bone even with the skin; but thought it proper to give him a chance for the use of the whole phalanx.

He complained only for the first day of a pretty sharp pain in the course of the tendon; to which compresses, wrung out of warm brandy, were applied: but his arm was never swelled; there was no _ecchymosis_; nor had he so much fever, as to require bleeding even once. The cure proceeded happily, no symptoms arising from the extracted tendon. At the third dressing the bone was covered; and no other application but dry lint was necessary during the whole time. No exfoliation happened; yet it was twelve weeks before it was intirely cicatrised, owing to the loss of skin: and he seems to enjoy the use of the stump as completely, as if that tendon was not lost.

LXXXIV. _An Account of the late Discoveries of Antiquities at_ Herculaneum, _and of an Earthquake there; in a Letter from_ Camillo Paderni, _Keeper of the Museum at_ Herculaneum, _and F.R.S. to_ Tho. Hollis, _Esq; F.R.S. dated_ Portici, Feb. 1. 1758.

[Read April 6, 1758.]

WE have been working continually at Herculaneum, Pompeii, and Stabiæ, since my last of Dec. 16, 1756. The most remarkable discoveries made there are these, which follow.

February 1757, was found a small and most beautiful figure of a naked Venus in bronze, the height of which is six Neapolitan inches. She has silver eyes, bracelets of gold on her arms, and chains of the same metal above her feet; and appears in the attitude of loosening one of her sandals. The base is of bronze inlaid with foliage of silver, on one side of which is placed a dolphin.

In July we met with an inscription, about twelve Neapolitan palms in length, which I have here copied.

IMP·CAESAR·VESPASIANVS·AVG·PONTIF·MAX

TRIB·POT·̅VĪĪ·IMP·X̅VĪĪ·P·P·COS·̅VĪĪ·DESIGN·̅VĪĪĪ

TEMPLVM·MATRIS·DEVM·TERRAE·MOTV·CONLAPSVM·RESTITVIT

After having found a great number of volumes of papirus in Herculaneum; many pugillaries, styles, and stands with ink in them, as formerly mentioned; at length, in the month of August, upon opening a small box, we also found, to our exceeding great joy, the instrument, with which they used to write their manuscripts. It is made of wood, of an oblong form, but petrified, and broke into two pieces. There is no slit in it, that being unnecessary, as the ancients did not join their letters in the manner we do, but wrote them separate.

In September were discovered eight marble busts, in the form of terms. One of these represents Vitellius, another Archimedes; and both are of the finest workmanship. The following characters, in a black tint, are still legible on the latter, namely, ΑΡΧΙΜΕΔ which is all the inscription that now remains.

In October was dug up a curious bust of a young person, who has a helmet on his head, adorned with a civic crown, and cheek-pieces fastened under his chin. Also another very fine bust of a philosopher, with a beard, and short thick hair, having a slight drapery on his left shoulder. Likewise two female busts; one unknown, in a veil; the other Minerva, with a helmet; both of middling workmanship.

In November we met with two busts of philosophers, of excellent workmanship, and, as may be easily perceived, of the same artist; but unfortunately, like many others, without names.

In January was found a small, but most beautiful eagle, in bronze. It hath silver eyes, perches on a _praefericulum_, and holds a fawn between its talons.

In the same month we discovered, at Stabiæ, a term six palms high, on which is a head of Plato, in the finest preservation, and performed in a very masterly manner. Also divers vases, instruments for sacrificing, scales, balances, weights, and other implements for domestic uses, all in bronze.

At length I have finished, with much labour, the examination and arrangement of the scales, balances, and weights, which are very numerous in this museum; and, what is remarkable, many of the former, with all the weights, exactly answer those now in use at Naples. At present I am considering the liquid measures; and also engaged in disposing the paintings in the new apartment allotted for them. These affairs, with my usual province of inspecting the workmen, who are busied in digging; my being obliged to keep an exact register of every thing, that is discovered; besides other daily and accidental occurrences; employ my time so intirely, that I have not a moment’s repose, but in my bed.

The square belonging to the palace, in which the museum is deposited, will be finished, and completely ornamented, by Easter. In the center of it I have placed the bronze horse, which was broken in many pieces, and restored by me, as mentioned in my last. In the walls of the colonades are affixed all the inscriptions hitherto discovered: and I shall yet adorn them with altars, curule chairs, and other antiquities proper for such places. The principal entrance into the museum hath been made to correspond with the grand stair-case. On the right side of it stands the consular statue of Marcus Nonius Balbus, the father; and on the left, that of Marcus Nonius Balbus, the son; with two inscriptions relating to, and found near them. Upon the stair-case are placed eight antique statues in bronze, on beautiful pedestals of polished marble. In an opening in the center of the right hand colonade is fixed the statue of the wife of the elder Balbus, with the antique inscription belonging to it. At the entrance of the square, a magnificent pair of iron gates, with palisades, are just put up, ornamented with many bronzes, which are gilt; and on the sides of these gates are two other consular statues of persons unknown.

The whole day and night of the 24th of last month it seemed as if Mount Vesuvius would again have swallowed up this country. On that day it suffered two internal fractures, which intirely changed its appearance within the crater, destroying the little mountain, that had been forming within it for some years, and was risen above the sides; and throwing up, by violent explosions, immense quantities of stones, lava, ashes, and fire. At night the flames burst out with greater vehemence, the explosions were more frequent and horrible, and our houses shook continually. Many fled to Naples, and the boldest persons trembled. For my own part, I resolved to abide the event here at Portici, on account of my family, consisting of eight children, and a very weak and aged mother, whose life must have been lost by a removal in such circumstances, and so rigorous a season. But it pleased God to preserve us; for the mountain having vented itself that night and the succeeding day, is since become calm, and throws out only a few ashes.

LXXXV. _A further Attempt to facilitate the Resolution of Isoperimetrical Problems. By Mr._ Thomas Simpson, _F.R.S._

[Read April 13, 1758.]

ABOUT three years ago I had the honour to lay before the Royal Society the investigation of a general rule for the resolution of isoperimetrical problems of that kind, wherein one, only, of the two indeterminate quantities enters along with the fluxions, into the equations expressing the conditions of the problem. Under which kind are included the determination of the greatest figures under given bounds, lines of the swiftest descent, solids of the least resistance, with innumerable other cases. But altho’ cases of this sort do, indeed, most frequently occur, and have therefore been chiefly attended to by mathematicians, others may nevertheless be proposed, such as actually arise in inquiries into nature, wherein _both_ the flowing quantities, together with their fluxions, are jointly concerned. The investigation of a _rule_ for the resolution of these, is what I shall in this paper attempt, by means of the following

GENERAL PROPOSITION.

_Let_ Q, R, S, T, &c. _represent any variable quantities, expressed in terms of_ x _and_ y (_with given coefficients_), _and let_ q, r, s, t, &c. _denote as many other quantities, expressed in terms of_ ẋ _and_ ẏ; _It is proposed to find an equation for the relation of_ x _and_ y, _so that the fluent of_ Qq + Rr + Ss + Tt, &c. _corresponding to a given value of_ x (_or_ y), _may be a_ maximum _or_ minimum.

Let _A E_, _A F_, and _A G_, denote any three values of the quantity _x_, having indefinitely small _equi-differences E F_, _F G_; and let _E L_, _F M_, and _G N_, (perpendicular to _A G_) be the respective values of _y_, corresponding thereto; and, supposing _EF_ (= _FG_ = _ẋ_) to be denoted by _e_, let _c M_ and _d N_ (the successive values of _ẏ_) be represented by _u_ and _w_. Moreover, supposing _P´p´_ and _P´´p´´_ to be ordinates at the middle points _P´ P´´_, between _E_, _F_ and _F_, _G_, let the former (_P´p´_) be denoted α, and the latter (_P´´p´´_) by β; putting _A P´_ = _a_ and _A P´´_ = _b_. Then, if _a_ and α (the mean values of _x_ and _y_, between the ordinates _E L_ and _F M_) be supposed to be substituted for _x_ and _y_, in the given quantity _Qq_ + _Rr_ + _Ss_ + _Tt_, _&c._ and if, instead of _ẋ_ and _ẏ_, their equals _e_ and _u_ be also substituted, and the said (given) quantity, after such substitution, be denoted by _Q´q´_ + _R´r´_ + _S´s´_ + _T´t´_, _&c._ it is then evident, that this quantity _Q´q´_ + _R´r´_ + _S´s´_ + _T´t´_, _&c._ will express so much of the whole required fluent, as is comprehended between the ordinates _E L_ and _F M_, or as answers to an increase of _E F_ in the value of _x_. And thus, if _b_ and β be conceived to be wrote for _x_ and _y_, _e_ for _ẋ_, and _w_ for _ẏ_, and the quantity resulting be denoted by _Q´´q´´_ + _R´´r´´_ + _S´´s´´_ + _T´´t´´_, _&c._ this quantity will, in like manner, express the part of the required fluent corresponding to the interval _F G_. Whence that part answering to the interval _E G_ will consequently be equal to _Q´q´_ + _R´r´ &c._ + _Q´´q´´_ + _R´´r´´ &c._ But it is manifest, that the whole required fluent cannot be a _maximum_ or _minimum_, unless this part, supposing the bounding ordinates _E L_, _G N_ to remain the same, is also a _maximum_ or _minimum_. Hence, in order to determine the fluxion of this expression (_Q´q´_ + _R´r´ &c. Q´´q´´_ + _R´´r´´ &c._) which must, of consequence, be equal to nothing, let the fluxions of _Q´_ and _q´_ (taking α and _u_ as variable) be denoted by _̅Q_̇α and _̅qu⋅_; also let _̅R_̇α and _̅ru⋅_ denote the respective fluxions of _R´_ and _r´_; and let, in like manner, the fluxions of _Q´´, q´´, R´´, r´´, &c._ be represented by _̿Q_̇β, _̿q͘w_, _̿R_͘͘β͘ _̿rẇ_, _&c._ respectively. Then, by the common rule for finding the fluxion of a rectangle, the fluxion of our whole expression (_Q´q´_ + _R´r´ &c._ + _Q´´q´´_ + _R´´r´´ &c._) will be given equal to _Q´ ̅qu⋅_ + _q´ ̅Q_̇α + _R´ ̅ru⋅_ + _r´ ̅R_̇α _&c._ + _Q´´̿qẇ_ + _q´´ ̿Q_̇͘͘͘β + _R´´ ̿r͘w_ + _r´´ ̿R_̇β _&c._ = 0.

But _u_ + _w_ being = _GN_ - _EL_, and β - α = (_GN_ - _EL_) ⁄ 2 (a constant quantity), we therefore have _ẇ_ = -_u͘_, and ̇β = ̇α: also _u_ being (= 2_rp´_) = 2α - 2_EL_, thence will _u͘_ = 2̇α: which values being substituted above, our equation, after the whole is divided by ̇α, will become

2_Q´ ̅q_ + _q´ ̅Q_ + 2_R´ ̅r_ + _r´ ̅R, &c._ - 2_Q´´ ̿q_ + _q´´
̿Q_ - 2_R´´ ̿r_ + _r´ ̿R, &c._ = 0;

or, _Q´´ ̿q_ - _Q´ ̅q_ + _R´´ ̿r_ - _R´ ̅r &c._ = (_q´ ̅Q_ + _q´´
̿Q_) ⁄ 2 + (_r´ ̅R_ + _r´´ ̿R_) ⁄ 2, _&c._

But _Q´´ ̿q_ - _Q´ ̅q_, the excess of _Q´´ ̿q_ above _Q´ ̅q_, is the increment or fluxion (answering to the increment, or fluxion, _ẋ_) arising by substituting _b_ for _a_, β for α, and _w_ for _u_. Moreover, with regard to the quantities on the other side of the equation, it is plain, seeing the difference of _q´ ̅Q_ and _q´´ ̿Q_ is indefinitely little in comparison of their sum, that _q´ ̅Q_ may be substituted in the room of (_q´ ̅Q_ + _q´´ ̿Q_) ⁄ 2, _&c._ which being done, our equation will stand thus:

_Flux. Q´ ̅q_ + _R´ ̅r &c._ = _q´ ̅Q_ + _r´ ̅R &c._

But _q´ ̅Q_ + _r´ ̅R &c._ represents (by the preceding notation) the fluxion of _q´Q´_ + _r´R´ &c._ (or of _Qq_ + _Rr &c._) arising by substituting α for _y_, making α alone variable, and casting off ̇α. If, therefore, that fluxion be denoted by ̇υ, we shall have _flux. Q´ ̅q_ + _R´ ̅r &c._ = ̇υ, and consequently _Q´ ̅q_ + _R´ ̅r &c._ = υ. But _Q´ ̅q_ + _R´ ̅r &c._ (by the same notation) appears to be the fluxion of _Q´q´_ + _R´r´ &c._ (or of _Qq_ + _Rr &c._) arising by substituting _u_ for _ẏ_, making _u_ alone variable, and casting off _̇u_. Whence the following

GENERAL RULE.

_Take the fluxion of the given expression_ (_whose fluent is required to be a_ maximum _or_ minimum) _making_ ẏ _alone variable; and, having divided by_ ÿ, _let the quotient be denoted by_ υ: _Then take, again, the fluxion of the same expression, making_ y _alone variable, which divide by_ ẏ; _and then this last quotient will be_ = ̇υ.

When _ẏ_ is not found in the quantity given, υ will then be = 0; and, consequently, the expression for ̇υ, equal to nothing also. But if _y_ be absent, then will ̇υ = 0, and consequently the value of υ = a constant quantity. It is also easy to comprehend, that, instead of _ẏ_ and _y, ẋ_ and _x_ may be made successively variable. Moreover, should the case to be resolved be confined to other restrictions, besides that of the _maximum_ or _minimum_, such as, having a certain number of other fluents, at the same time, equal to given quantities, still the same method of solution may be applied, and that with equal advantage, if from the particular expressions exhibiting all the several conditions, one general expression composed of them all, with unknown (but determinate) coefficients, be made use of.

In order to render this matter quite clear, let _A, B, C, D, &c._ be supposed to represent any quantities expressed in terms of _x, y_, and their fluxions, and let it be required to determine the relation of _x_ and _y_, so that the fluent of _Aẋ_ shall be a _maximum_, or _minimum_, when the cotemporary fluents of _Bẋ, Cẋ, Dẋ, &c._ are, all of them, equal to given quantities.

It is evident, in the first place, that the fluent of _Aẋ_ + _bBẋ_ + _cCẋ_ + _dDẋ, &c._ (_b, c, d, &c._ being any constant quantities whatever) must be a _maximum_, or _minimum_, in the proposed circumstance: and, if the relation of _x_ and _y_ be determined (_by the rule_), so as to answer this single condition (under all possible values of _b, c, d, &c._) it will also appear evident, that such relation will likewise answer and include all the other conditions propounded. For, there being in the general expression, thus derived, as many unknown quantities _b, c, d, &c._ (to be determined) as there are equations, by making the fluents of _Bẋ, Cẋ, Dẋ, &c._ equal to the values given; those quantities may be so assigned, or conceived to be such, as to answer all the conditions of the said equations. And then, to see clearly that the fluent of the first expression, _Aẋ_, cannot be greater than arises from hence (other things remaining the same) let there be supposed some other different relation of _x_ and _y_, whereby the conditions of all the other fluents of _Bẋ, Cẋ, Dẋ, &c._ can be fulfilled; and let, _if possible_, this new relation give a greater fluent of _Aẋ_ than the relation above assigned. Then, because the fluents _bBẋ, cCẋ, dDẋ, &c._ are given, and the same in both cases, it follows, according to this supposition, that this new relation must give a greater fluent of _Aẋ_ + _bBẋ_ + _cCẋ_ + _dDẋ, &c._ (under all possible values of _b, c, d, &c._) than the former relation gives: _which is impossible_; because (whatever values are assigned to _b, c, d, &c._) _that_ fluent will, it is demonstrated, be the greatest possible, when the relation of _x_ and _y_ is that above determined, by the General Rule.

To exemplify, now, by a particular case, the method of operation above pointed out, let there be proposed the fluxionary quantity (_xⁿ yᵐ ẏᵖ_) ⁄ _ẋ⁽ᵖ ⁻ ¹⁾_; wherein the relation of _x_ and _y_ is so required, that the fluent, corresponding to given values of _x_ and _y_, shall be a _maximum_, or _minimum_. Here, by taking the fluxion, making _ẏ_ alone variable (_according to the rule_) and dividing by _ÿ_, we shall have (_pxⁿ yᵐ ẏ⁽ᵖ ⁻ ¹⁾_) ⁄ _ẋ⁽ᵖ ⁻ ¹⁾_ = υ. And, by taking the fluxion a second time, making _y_ alone variable, and dividing by _ẏ_, will be had (_mxⁿ y⁽ᵐ ⁻ ¹⁾ ẏᵖ_) ⁄ _ẋ⁽ᵖ ⁻ ¹⁾_ = ̇υ. Now from these equations to exterminate υ, let the latter be divided by the former; so shall _mẏ_ ⁄ _py_ = ̇υ ⁄ υ; and therefore _ay⁽ᵐ ⁄ ᵖ⁾_ = υ (_a_ being a constant quantity). From whence _y⁽ᵐ ⁄ ᵖ⁾ẏ_ = _(a ⁄ p)⁽¹ ⁄ ⁽ᵖ ⁻ ¹⁾⁾_ × _ẋx⁽⁻⁽ⁿ ⁄ ⁽ᵖ ⁻ ¹⁾⁾⁾_; and consequently (_p_ ⁄ (_m + p_)) × _y⁽⁽ᵐ + ᵖ⁾ ⁄ ᵖ⁾_ = _(a ⁄ p)⁽¹ ⁄ ⁽ᵖ ⁻ ¹⁾⁾_ × (_p_ - 1) ⁄ (_p_ - _n_ - 1) × _x_⁽⁽_ᵖ_ ⁻ _ⁿ_ ⁻ ¹⁾ ⁄ ⁽_ᵖ_ ⁻ ¹⁾⁾.

Let there be now proposed the two fluxions _xⁿyᵐẋ_ and _xᵖy⒬ẏ_, the fluent of the former being required to be a _maximum_, or _minimum_, and that of the latter, at the same time, equal to a given quantity. Then the latter, with the general coefficient _b_ prefixed, being joined to the former, we shall here have _xⁿyᵐẋ_ + _bxᵖy⒬ẏ_. From whence, by proceeding as before, _bxᵖy⒬_ = υ, and _mxⁿy⁽ᵐ ⁻ ¹⁾ẋ_ + _qbxᵖy⁽ᵖ ⁻¹⁾ẏ_ = ̇υ. From the former of which equations, by taking the fluxions on both sides, will be had _pbx⁽ᵖ ⁻¹⁾y⒬ẋ_ + _qbxᵖy⁽⒬ ⁻ ¹⁾ẏ_ (= ̇υ) = _mxⁿy⁽ᵐ ⁻ ¹⁾ẋ_ + _qbxᵖy⁽⒬ ⁻ ¹⁾ẏ_. Whence _pbx⁽ᵖ ⁻ ¹⁾y⒬_ = _mxⁿy⁽ᵐ ⁻ ¹⁾_; and therefore _pby⁽⒬ ⁻ ᵐ ⁺ ¹⁾_ = _mx⁽ⁿ ⁻ ᵖ ⁺ ¹⁾_. And in the same manner proper equations, to express the relation of _x_ and _y_, may be derived, in any other case, and under any number of limitations.

LXXXVI. _Observations on the_ Alga Marina latifolia; _The Sea Alga with broad Leaves. By_ John Andrew Peyssonel, _M.D. F.R.S. Translated from the_ French.

[Read April 13, 1758.]

HAVING cast anchor at Verdun, the road at the entrance of the river of Bourdeaux, I was fishing with a kind of drag-net upon a bank of sand, which was very fine and muddy. We collected a number of sea-plants, and among them the great broad-leaved Alga, which I did not know: and as the root or pedicle of this plant appeared to be very particular, I observed it with attention. The following is its description, and the detail of my observations.

From a pedicle, which is sometimes flat, and sometimes round (for they vary in these plants, and might be about three lines in diameter, and an inch high, of a blackish colour, and coriaceous substance, approaching to the nature of the bodies of lithophyta), a single flat leaf arises, about an inch or an inch and half broad, thick in its middle to about three lines, ending at the sides in a kind of edge, like a two-edged sabre, almost like the common Alga, formed of longitudinal fibres interlaced with other very delicates ones, and the whole filled with a thick juice, like the _parenchyma_ of succulent plants, such as the Sedum, Aloes, and the like, of a clear yellowish green, and transparent. This first leaf is always single, and serves instead of a trunk or stem to the whole plant.

When it rises to about a foot high, more or less, it throws out at the sides other leaves formed of a continuation of the longitudinal fibres; and these second leaves are of the same thickness and substance with the first: they are two or three feet long, and the whole plant is five or six, or more (for one can hardly tell the length); and is not capable of supporting itself, but is sustained by the strength of the waters, in which it floats.

The substance of the plant is not so solid as that of the common Alga, which is capable of drying as it fades, and of being kept: whereas the leaves of this great Alga shrink and wither in the air, become of a blackish colour, and very friable, or indeed soon fall into putrifaction. I never observed, that they bore any fruit: perhaps this was not the season.

But what we find particular in this plant is its root or foot: First, this pedicle extends in ribs, like what we call the thighs of certain trees: these thighs are in right lines: perhaps they run in the same direction or situation, that is, placed north and south, or east and west; but this I could not observe. They are about three or four lines high towards the pedicle, and, ending, are lost. They flourish and spread at the bottom, forming an elliptical bladder, like an egg, flattened above and below, and rounded at the sides, being intirely empty: it is rough without, and very smooth within. This egg, or oval bladder, is exactly round at the ends of the great diameter, but varies a little in the lesser diameter, and forms itself like the body of a fiddle. The under part is a little flattened; and there is a hole, which is very considerable, in the center of the two diameters. This hole is about an inch wide, and is quite round: it gives passage to the root, or pivot, which I shall by and by mention: the edges appear to turn a little inward: and it is by this hole that the egg fills with sea-water. The whole substance of this bladder or egg is of a coriaceous matter, firm and transparent, and of a clear green; nor can there be any fibres, either longitudinal or transverse, observed upon it.

The vault at the top, surmounted by the thighs, is as it were granulated; but at the rounding of the egg it produces a kind of _mammæ_, or little elevations, very round and cylindrical, intirely full; of the same nature and substance with the egg.

In examining the under part of the egg, we found a second rank of these _mamellæ_, somewhat longer than the first, and at equal distances from one another, in a circular line; then a third yet longer; then a fourth, which at the extremities were bifurcated; and at last a fifth rank, which divided into three, and sometimes into five, branches: these last, placed round the hole, were wreathed inwards, and several were joined together, and only formed a small body; and in wreathing themselves thus they close and embrace the pivot mentioned below. None of these _mamellæ_ have any apparent opening: their substance is compact, of the same nature with the bladder or egg, that produces them.

Below the trunk and thighs the plant protrudes a pivot, of a like substance with that of the bladder. This pivot, which is large at its origin, proceeding thus from the trunk and thighs, forms something like the knot of the sea-tree: it descends perpendicularly to the trunk, diminishing as it lengthens, and as it grows round; and then divides into a number of _mamellæ_, branched and wreathed inwards so firmly, as not to be retracted; of a coriaceous nature, blackish, forming a bunch like what we call the Rose of Jericho. I cannot recollect the name of this plant or flower.

This bunch, or wreathed rose, incloses a heap of gravel, as if petrified or hardened, and ends upon a level with the hole of the egg, exactly as high as the last rank of _mamellæ_, which wreath upon, embrace, and sustain it, leaving always an empty space to let the sea-water pass in, which should fill the inside of the egg or bladder, and even to let in little fishes and shells.

I was surprised to find in one little living muscles, as they always are attached to some solid body by their beards. Now by what means could they enter into this egg? I conjectured, that they had their beginning there, by the seminal matter of muscles carried in by the sea-water. I also found some small star-fish, whose rays might be about four or five lines long.

If my stay here had been longer, I had continued my observations; and perhaps should have made some discoveries. It belongs to the academicians of Bourdeaux to push these observations further, if they think proper.

From the Entrance of the river of Bourdeaux, the 4th of August, 1756.

Peyssonel.

LXXXVII. _An Account of the distilling Water fresh from Sea-water by Wood-ashes. By Capt._ William Chapman: _In a Letter to_ John Fothergill, _M. D._

[Read April 13, 1758.]

Whitby, 10th 2d mo. Feb. 1758.

THY kind acceptance of my last emboldens me to inform thee, how, on my return from a voyage to the north part of Russia, I procured a sufficient quantity of fresh water from sea-water, without taking with me either instruments or ingredients expressly for the purpose.

Some time in September last, when I had been ten days at sea, by an accident (off the north cape of Finland) we lost the greatest part of our water. We had a hard gale of wind at south-west, which continued three weeks, and drove us into 73° lat. During this time I was very uneasy, as knowing, if our passage should hold out long, we must be reduced to great straits; for we had no rains, but frequent fogs, which yielded water in very small quantities. I now blamed myself for not having a still along with me (as I had often thought no ship should be without one). But it was now too late; and there was a necessity to contrive some means for our preservation.

I was not a stranger to Appleby’s method: I had also a pamphlet wrote by Dr. Butler, intituled, _An easy Method of procuring of fresh Water at Sea_. And I imagined, that soap might supply the place of capital lees, mentioned by him. I now set myself at work, to contrive a still; and ordered an old pitch-pot, that held about ten quarts, to be made clean: my carpenter, by my direction, fitted to it a cover of fir deal, about two inches thick, very close; so that it was easily made tight by luting it with paste. We had a hole thro’ the cover, in which was fixed a wooden pipe nearly perpendicular. This I call the still-head: it was bored with an augre of 1½ inch diameter, to within three inches of the top or extremity, where it was left solid. We made a hole in this, towards the upper part of its cavity (with a proper angle) to receive a long wooden pipe, which we fixed therein, to descend to the tub in which the worm should be placed. Here again I was at a loss; for we had no lead pipe, nor any sheet-lead, on board. I thought, if I could contrive a strait pipe to go thro’ a large cask of cold water, it might answer the end of a worm. We then cut a pewter dish, and made a pipe two feet long; and at three or four trials (for we did not let a little discourage us) we made it quite tight. We bored a hole thro’ a cask, with a proper descent, in which we fixed the pewter pipe, and made both holes in the cask tight, and filled it with sea-water: the pipe stuck without the cask three inches on each side. Having now got my apparatus in readiness, I put seven quarts of sea-water, and an ounce of soap, into my pot, and set it on the fire. The cover was kept from rising by a prop of wood to the bow. We fixed on the head, and into it the long wooden pipe above-mentioned, which was wide enough to receive the end of the pewter one into its cavity. We easily made the joint tight.

I need not tell thee with what anxiety I waited for success: but I was soon relieved; for, as soon as the pot boiled, the water began to run; and in twenty-eight minutes I got a quart of fresh water. I tried it with an hydrometer I had on board, and found it as light as river-water; but it had a rank oily taste, which I imagine was given it by the soap. This taste diminished considerably in two or three days, but not so much as to make it quite palateable. Our sheep and fowls drank this water very greedily without any ill effects. We constantly kept our still at work, and got a gallon of water every two hours; which, if there had been a necessity to drink it, would have been sufficient for our ship’s crew.

I now thought of trying to get water more palateable; and often perused the pamphlet above-mentioned, especially the quotation from Sir R. Hawkins’s voyage, who “with four billets distilled a hogshead of water wholsome and nourishing.” I concluded he had delivered this account under a veil, lest his method should be discovered: for it is plain, that by four billets he could not mean the fuel, as they would scarce _warm_ a hogshead of water. When, ruminating on this, it came into my head, that he burnt his four billets to ashes, and with the mixture of those ashes with sea-water he distilled a hogshead of fresh water wholsome and nourishing. Pleased with this discovery, I cut a billet small, and burnt it to ashes; and after cleaning my pot, I put into it a spoonful of those ashes, with the usual quantity of sea-water. The result answered my expectations: the water came off bright and transparent, with an agreeable pungent taste, which at first I thought was occasioned by the ashes, but afterwards was convinced it received it from the resin or turpentine in the pot, or pipes annexed to it. I was now relieved from my fears of being distressed thro’ want of water; yet thought it necessary to advise my people not to be too free in the use of this, whilst we had any of our old stock remaining; and told them, I would make the experiment first myself; which I did, by drinking a few glasses every day without any ill effect whatever. This water was equally light with the other, and lathered very well with soap. We had expended our old stock of water before we reached England; but had reserved a good quantity of that which we distilled. After my arrival at Shields, I invited several of my acquaintance on board to taste the water: they drank several glasses, and thought it nothing inferior to spring-water. I made them a bowl of punch of it, which was highly commended.

I have not the convenience of a still here, or should have repeated the experiment for the conviction of some of my friends: for as to myself, I am firmly persuaded, that wood-ashes mixed with sea-water will yield, when distilled, as good fresh water as can be wished for. And I think, if every ship bound a long voyage was to take a small still with Dr. Hales’s improvements, they need never want fresh water. Wood-ashes may easily be made, whilst there is any wood in the ship; and the extraordinary expence of fuel will be trifling, if they contrive so that the still may stand on the fire along with the ship’s boiler.

I shall think myself sufficiently recompensed, if any hints here may tend to the relief of my brother sailors from the dismal extremity of want of water; an extremity too little regarded by those, who have never experienced it.

_P. S._ During my passage from Russia we very rarely had any _aurora
borealis_; and those few we saw were faint, and of short continuance:
at which I was much surprised; for about ten years ago, being in a
high north latitude, we had very beautiful ones almost every night in
the month of September; which exceeded any I have seen described in
the _Philosophical Transactions_, or _Memoires de l’Academie Royale_.

Wm. Chapman.

LXXXVIII. _Observatio Eclipsis Lunaris facta_ Matriti _a Pª._ Joanne Wendlingen, _Societatis_ Jesu, _in Regali Observatorio Collegii Imperialis ejusdem Societatis, Die_ 30 Julii 1757.

_Quælibet observatio bis instituta fuit, semel interjecto oculum
inter lentemque ocularem vitri clari, cærulei, plani, ac bene tersi,
fragmento. Hæ observationes notantur hac voce_ cerul. _Telescopium,
quo usus sum, est_ Gregorianum _trium pedum_ Anglicanorum, _omnino
præclarum_.

_Communicated by_ Matthew Maty, _M. D. F.R.S._

[Read April 20, 1758.]

IMMERSIONES. |Tempus verum| Differentia
| h ´ ´´ |
PRincipium eclipsis, _clar._ | 9 47 34 |
Mare Humorum, _clar._ | -- 52 47 |
{ _cær._ | -- 54 28 | ´´
Grimaldus { _clar._| -- 55 27 | ---- 59
{_cær._ | 10 1 21 | ---- 13
Bullialdus {---- | 10 1 34 |
{---- | -- 9 35 | ---- 10
Keplerus {---- | -- 9 45 |
{---- | -- 16 15 | ---- 12
Copernicus {---- | -- 16 28 |
{---- | -- 18 14 | ---- 10
Heraclides {---- | -- 18 24 |

Manilius {_clar._ | 10 30 43 | ´´
{_cær._ | 10 30 54 | ---- 11
Menelaus {---- | -- 34 11 | ---- 9
{---- | -- 34 20 |
Promontorium {---- | -- 44 49 | ---- 9
{---- | -- 44 58 |
Mare Crisium {---- | -- 45 33 | ---- 11
{---- | -- 45 44 |
Proclus, _clar._ | -- 46 54 |
{---- | -- 54 48 | ---- 14
Plato {---- | -- 55 2 |
{---- | 11 7 3 |
Langrenus {---- | 11 7 23 | ---- 20

EMERSIONES. |Tempus verum| Differentia
| h ´ ´´ |
Plato {_clar._ | 11 40 34 | ´´
{_cær._ | 11 40 48 | ---- 14
Heraclides {---- | -- 41 27 | ---- 12
{---- | -- 41 39 |
Grimaldus {---- | -- 47 57 | ---- 7
{---- | -- 48 4 |
Keplerus {---- | -- 52 58 | ---- 10
{---- | -- 53 8 |
Copernicus {---- | 12 1 36 | ---- 12
{---- | 12 1 48 |
Menelaus {---- | -- 17 18 | ---- 10
{---- | -- 17 28 |
Finis eclipseos, _clar._ | -- 52 15 |

_Observatio Eclipsis Lunaris, facta ab eodem, eodem modo, eodem loco, iisdemque instrumentis Die_ 24 Januar. _Anni_ 1758.

_Ab hora 5ᵗᵃ usque ad finem observationis tantum commovebatur imprægnata plurimum vaporibus athmosphæra, ut tota lunæ illuminatæ portio præter morem undulare videretur. Flabat boreas, indicante thermometro Reaumuriano. 1. grandem infra aquæ congelationem._

IMMERSIONES. |Tempus verum| Differentia
| h ´ ´´ |
Principium | 4 7 42 | ´´
Grimaldus {_cær._ | -- 9 55 | ---- 38
{_clar._ | -- 10 33 |
Aristarchus {---- | -- 15 37 | ---- 34
{---- | -- 16 11 |
Mare Humorum {---- | -- 20 48 | ---- 24
{---- | -- 21 12 |
Copernicus {---- | -- 26 45 | ---- 13
{---- | -- 26 58 |
Plato {---- | -- 35 41 | ---- 41
{---- | -- 36 22 |
Tycho {---- | -- 39 31 | ---- 38
{---- | -- 40 9 |
Menelaus {---- | -- 45 43 | ---- 39
{---- | -- 46 22 |
Plinius {---- | -- 50 17 | ---- 27
{---- | -- 50 44 |
Promontorium Somni {---- | -- 58 15 | ---- 27
{---- | -- 58 42 |
Cleomedes {---- | 5 0 22 | ---- 14
{---- | 5 0 36 |

Proclus {_cær._ | 5 2 9 |
{_clar._ | 5 2 15 | ---- 6
Princip. Maris Crisii {---- | -- 3 6 | ---- 25
{---- | -- 3 31 |
Langrenus {---- | -- 7 40 | ---- 14
{---- | -- 7 54 |
Immers. tot. Maris Crisii {---- | -- 8 19 | ---- 11
{---- | -- 8 30 |
Immersio totalis Lunæ {---- | -- 12 50 | ---- 40
{---- | -- 13 30 |

In fine cœlum serenum, & athmosphæra quieta.

REFLEXIO.

Notabilis appulsus umbræ terrestris ad faculas maculasque lunares differentia, dum partim vitro colore cæruleo tincto, partim absque eo, observationes instituuntur, inventa a Dº. de Barros, & tum in observatorio Parisino tum alibi sæpius confirmata, ad me duplicem hanc lunæ eclipsim, ea qua vel licuit circumspectione, instituendam determinavit, spe fretus; me phænomeni hujus causas, si non veras, veritati saltem proximas, inventurum; unde in tempore de vitris planis bene tersis, diametri mediæ lineæ, partim colore cæruleo claro, partim flavo tinctis mihi provideram, his tamen ultimis uti non licuit ob nimiam umbræ penumbræque confusionem.

Interjecto oculum inter, lentemque ocularem vitri cærulei fragmento, sequentia observavi. 1. Umbra terrestris in immersione citius maculam aut faculam lunarem attigit, & in emersione tardius deseruit, quam dum absque eo observationem institui. 2. Claritas lunæ, alioquin offendens oculum, suavior apparebat. 3. Limites umbræ perfecte terminabantur excepta secunda eclipsi, in qua (flante borea) ab hora quinta illuminata lunæ pars undulare videbatur.

Suppositis his phænomenis, uti et athmosphæra lunari, de qua vix dubio locus, sequentia intuli: 1. Quo densior dicta athmosphæra fuerit, major radiorum portio ab hac in immersam umbræ terrestri lunæ portionem, limitibus saltem proximam, reflectetur, eosque reddet dubios, quod quidem contingit, dum absque adminiculo per nudum telescopium observatio instituitur, secus vero dum oculum inter, lentemque ocularem, vitrum cæruleo colore tinctum interjicitur. Addito secundo, ac tertio phænomeno, nempe per vitrum cæruleum lumen multum apparere suavius, infertur, si color cæruleus sufficit ad mitigandam tantopere eam lunæ illuminatæ portionem, quæ extra omnem umbram conspicitur, quanto magis sufficit, ad tollendam omnem claritatem, quæ ab athmosphæra lunari in hoc corpus reflectitur? & ecce tibi secundam illationem, nempe limites umbræ facilius determinari. 3. Diametrum umbræ majorem videri debere, & vel ideo immersiones macularum aut facularum lunarium citius, emersiones vero tardius succedere debere; quæ quidem omnia cum observationibus congruunt.

Dixi in prima illatione, reflecti aliquam luminis portionem a lunæ athmosphæra in ipsam eclipsatam corporis hujus portionem, non secus, ac in globo hoc terraqeno accidit, qui post solis occasum aliquo adhuc tempore illuminatur. Hæc lucis reflexio tanto erit major, quanto athmosphæra fuerit densior, & quia supponere licat, hanc in luna non semper esse æqualem, infertur, differentiam temporis appulsus umbræ non in omni eclipsi lunari posse esse æqualem, quod demum convenire videtur duplici meæ observationi, ut ex adnotatis temporum differentiis liquet. Hæc mea est circa propositum phænomenon opinandi ratio.

LXXXIX. _Observations upon a slight Earthquake, tho’ very particular, which may lead to the Knowlege of the Cause of great and violent ones, that ravage whole Countries, and overturn Cities. By_ John Andrew Peyssonel, _M. D. F.R.S. Translated from the_ French.

[Read April. 20, 1758.]

I Went to make my observations upon the natural history of the sea; and when I arrived at a place called the Cauldrons of Lance Caraibe, near Lancebertrand, a part of the island of Grande Terre Guadaloupe, in which place the coast runs north-east and south-west, the sea being much agitated that day flowed from the north-west. There the coast is furnished with hollow rocks, and vaults underneath, with chinks and crevices: and the sea, pushed into these deep caverns by the force and agitation of the waves, compresses the air, which, recovering its spring, forces the water back in the form of the most magnificent fountains; which cease, and begin again at every great pressure. This phænomenon is common to many places in this island. The explanation of it is easy; but the following is what I particularly observed.

As I walked within about forty paces from the brink of the sea, where the waves broke, I perceived, in one place, the plants were much agitated by some cause, that was not yet apparent. I drew near, and discovered a hole about six feet deep, and half a foot diameter; and stopping to consider it, I perceived the earth tremble under my feet. This increased my attention; and I heard a dull kind of noise underground, like that which precedes common earthquakes; which I have observed many a time. It was followed by a quivering of the earth; and after this a wind issued out of the hole, which agitated the plants round about. I watched to see whether the motion extended to any distance; but was sensible it did not reach above three or four paces from the hole, and that no motion was perceived farther off.

I further observed, that this phænomenon never happens till after the seventh wave rolls in; for it is a common thing in this country to find the sea appear calm for some time, and then to produce seven waves, which break upon the coast one after another: the first is not very considerable; the second is somewhat stronger; and thus they go on increasing to the seventh, after which the sea grows calm again, and retires. This phænomenon of the seven waves is observed by navigators with great attention, especially at low water, in order to be the better able to go in or come out at the very time that the sea grows quiet. These seven waves successively fill the caverns, which are all along the coast; and when the seventh comes to open itself, the air at the bottom of the caverns being greatly compressed, acted by its elasticity, and immediately made those fountains and gushings I have mentioned; and the waters continuing in the caverns, up to the very place of the hole, began to produce that dull noise, caused the emotion or earthquake, and finished with the violent wind forced up thro’ the hole; after which the water retired into the sea, and having no further impelling cause, on account of the waves, rendered every thing quiet again.

I observed, that this phænomenon happened at no limited time, but according to the approach of the waves, being strongly put in motion after the seventh. I remained near half an hour to observe it; and nearly followed the course of the cavern to its entrance, directed by the disposition of the coast. I made my negroes go down where the water broke; for they doubted the report of the greatness of these caverns; and when the sea was calm one of them ventured in, but returned very quickly, or he must have perished. Therefore I conclude, that these small earthquakes round the hole, about forty paces from the wave, were only caused by the compressed air in some great vault about this place, and that by its force was driven up the hole that appeared: that this air in the caverns, compressed to a certain degree, first caused the dull noise, by the rolling of the waters, which resisted in the cavern; then acting more violently, caused the small earthquake, which ceased when the wind passed out of the hole, and that the sea retired, and gave liberty to the air, which was contained and compressed.

Such are the observations I have made; from which the learned, who are endeavouring to find the cause of earthquakes, since that dreadful one, which destroyed the city of Lisbon, may make such conclusions as they shall think proper.

At Guadaloupe, Jan. 6. 1757.

Peyssonel.

XC. _A Catalogue of the_ Fifty Plants _from_ Chelsea Garden, _presented to the_ Royal Society _by the worshipful Company of Apothecaries, for the Year 1757, pursuant to the Direction of Sir_ Hans Sloane, _Baronet, Med. Reg. & Soc. Reg. nuper Præses, by_ John Wilmer, _M. D. clariss. Societatis Pharmaceut._ Lond. _Socius, Hort._ Chelsean. _Præfectus & Prælector Botanic._

[Read April 20, 1758.]