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 ⁄ ẋp ⁻ 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 ẏp⁻ ¹ ⁄ ẋp ⁻ ¹ = υ. And, by taking the fluxion a second time, making y alone variable, and dividing by ẏ, will be had mxⁿ ym ⁻ ¹ ẏp ⁄ ẋp ⁻ 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 aym ⁄ p = υ (a being a constant quantity). From whence ym ⁄ pẏ = (a ⁄ p)¹ ⁄ p ⁻ ¹ × ẋx⁻ⁿ ⁄ p ⁻ ¹; and consequently p ⁄ m + p × ym ⁺ p ⁄ p = (a ⁄ p) ¹ ⁄ p ⁻ ¹ × p - 1 ⁄ p - n - 1 × xp ⁻ ⁿ ⁻ ¹ ⁄ p ⁻ ¹.

Let there be now proposed the two fluxions xⁿymẋ and xpyqẏ, 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 + bxpyqẏ. From whence, by proceeding as before, bxpyq = υ, and mxⁿ ym ⁻ ¹ ẋ + qbxpyp ⁻¹ ẏ = ̇υ. From the former of which equations, by taking the fluxions on both sides, will be had pbxp ⁻¹ yqẋ + qbx py q ⁻ ¹ ẏ (= ̇υ) = mxⁿ ym ⁻ ¹ ẋ + qbxp yq ⁻ ¹ ẏ. Whence pbx p ⁻ ¹ yq = mxⁿ ym ⁻ ¹; and therefore pbyq ⁻ m ⁺ ¹ = mxⁿ ⁻ 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. 947 34
Mare Humorum, clar.—5247
Grimaldus cær.—5428´´
clar.—5527 —— 59
Bullialdus cær.10 121 —— 13
—— 10 1 34
Keplerus —— — 9 35 —— 10
—— — 9 45
Copernicus —— — 16 15 —— 12
—— — 16 28
Heraclides —— — 18 14 —— 10
—— — 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
Plato ——— 54 48 —— 14
—— — 55 2
Langrenus ——1173—— 20
——11723
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 ´ ´´
Principium4742´´
Grimaldus cær.—955 —— 38
clar.—1033
Aristarchus ———1537—— 34
———1611
Mare Humorum ———2048—— 24
———2112
Copernicus ———2645 —— 13
———2658
Plato ———3541—— 41
———3622
Tycho ———3931—— 38
———409
Menelaus ———4543—— 39
———4622
Plinius ———5017—— 27
——— 5044
Promontorium Somni ———5815—— 27
———5842
Cleomedes ——5022—— 14
——5036
Proclus cær. 529´´
clar.5215—— 6
Princip. Maris Crisii ———36—— 25
———331
Langrenus ———740—— 14
———754
Immers. tot. Maris Crisii ———819 —— 11
———830
Immersio totalis Lunæ ———1250—— 40
———1330

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.

Peyssonel.

At Guadaloupe, Jan. 6. 1757.

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.

1751ALlium sylvestre latifolium. C. B. P. 74.
Allium ursin. bifolium vernum sylvatic. J. B. 2. 565.
1752Anacampseros flavo flore Amman. Ruth. 96.
1753Anchusa strigosa, foliis linearibus dentatis, pedicellis bractea minoribus, calycibus fructiferis inflatis. Lefl. Linn. Sp. Plant. 133.
1754Asplenium sive Ceterach. J. B. 3. 749. Offic. 121.
1755Bidens calyce oblongo squamoso, feminibus radii corolla non decidua coronatis, Miller. Icon.
1756Cactus repens decemangularis Lin. Sp. Pl. 467.
1757Cerasus pumila Canadensis, oblongo angusto folio, fructu parvo, Du Hamel. Mill. Icons.
1758Ceratocarpus Amæn. Acad. 1. p. 412. Hort. Ups. 281.
1759Cotula flore luteo, radiato. Tourn. 495. Buphthalmum Cotulæ folio C. B. P. 134.
1760Cracca minor Rivini. Vicia segetum cum filiquis plurimis hirsutis C. B. P. 345.
1761Cucubalus calycibus subglobosis glabris reticulato-venosis, capsulis trilocularibus, corollis subnudis, Flor. suec. 360.
1762Cucubalus calycibus subglobosis, caule ramoso patulo, foliis linearibus acutis, Mill. Dict.
Lychnis sylvestris quæ Been album vulgo, foliis angustioribus et acutioribus C. B. P. 205.
1763Cunonia floribus sessilibus, spathis maximis. Butner Cunonia, tab. 1.
1764Cupressus foliis imbricatis frondibus ancipitibus. Linn. Spec. Plant. 1003.
Cupressus nana Mariana fructu cæruleo parvo. Pluk. Mantiss. 61.
1765Cyclamen Hederæ folio C. B. P. 308. Offic. 162.
1766Diosma foliis lineari-lanceolatis subtus convexis, bifariam imbricatis. Linn. Sp. Plant. 198.
1767Euonymoides Canadensis Saraz. Boerh. Ind. Alt. 237.
1768Filipendula foliis ternatis Hort. Cliff. 191.
1769Filipendula vulgaris, an Molon Plinii C. B. 163. Offic. 197.
1770Heliotropium foliis ovato-lanceolatis, spicis plurimis confertis, caule fruticoso. Miller’s Icons.
1771 Hieracium fruticosum latifolium hirsutum C. B. P. 129.
1772Hyoscyamus rubello flore. C. B. P. 169. Hyoscyamus Syriacus. Cam. Icon. 21. J. B. 3. 628.
1773 Hypericum floribus monogynis staminibus corolla longioribus, calycibus coloratis caule fruticoso. Miller’s Icons.
1774Hypericum floribus trigynis, calycibus acutis, staminibus corolla brevioribus, caule fruticoso. Linn. Hort. Cliff. 380. Miller’s Icons.
1775 Iris corollis barbatis, germinibus trigonis, foliis ensiformibus longissimis, caule foliis longiore bifloro. Miller’s Icons.
1776Isatis sativa, sive latifolia. C. B. P. 113. Glastum sativum. J. B. 2. 909.
1777Juniperus vulgaris fruticosa C. B. 488. Off. 252.
1778Ixia foliis gladiolatis linearibus caule bulbifero. Miller’s Icons.
1779Ixia foliis gladiolatis glabris, floribus corymbosis terminalibus. Miller’s Icons.
1780Larix C. B. 493. Officin. 264.
1781 Laserpitium foliis amplioribus, semine crispo. Tourn. 324.
1782Linum calycibus capsulisque obtusis. Sibirian Flax. Miller’s Icons.
1783Liriodendrum. Hort. Cliff. 223. Tulipifera arbor Virginiana. Hort. Lugd. Bat. 612.
1784Oenanthe Apii folio C. B. P. 162.
1785Passerina foliis linearibus. Hort. Cliff. 146. Sp. 1.
1786Platanus Orientalis verus. Park. 1427.
1787Platanus Occidentalis aut Virginiensis. Park. 1427.
1788Platanus Orientalis Aceris folio. T. Cor. 41.
1789Prenanthes foliis integris serratis scabris, radice repente, flore purpureo cæruleo. Mill. Dict.
1790 Ruta sylvestris linifolia; Hispanica Boccon. Barrel Icon. 1186 H. Mus. p. 2. 82. tab. 73.
1791Saxifraga muscosa; trifido folio. Tourn.
1792Scabiosa Virgæ Pastoris folio. C. B. P. 270. Scabiosa latifolia peregrina. Tabern. Icon. 160.
1793Thalictrum majus, siliqua angulosa aut striata, C. B. P. 336.
1794Thalictrum majus non striatum. C. B. P. 336.
1795Thalictrum Canadense majus caulibus viridantibus. Boerhaav.
1796Thalictrum Alpinum Aquilegiæ foliis. Tourn.
1797Thalictrum minus Asphodeli radice magno flore. Tourn. 271.
1798Thuya strobilis squarrosis squamis acuminatis reflexis. Hort. Upsal. 289.
1799Tordylium Narbonense minus. Tourn. 320.
1800Tridax. Hort. Cliff. 418. After American. procumbens, foliis laciniatis et hirsutis. Houston.

XCI. An Historical Memoir concerning a Genus of Plants called Lichen, by Micheli, Haller, and Linnæus; and comprehended by Dillenius under the Terms Usnea, Coralloides, and Lichenoides: Tending principally to illustrate their several Uses. Communicated by Wm. Watson, M. D. F.R.S.

——Natura nihil frustra creaverit, posteros tamen tot inventuros utilitates ex Muscis auguror, quot ex reliquis vegetabilibus.

Cui bono? Amæn. Acad. III. p. 241.

Read Apr. 27 & May 4, 1758.

THE whole class of mosses were taken but very little notice of by the revivers of botany in the sixteenth century: they indeed took some pains to distinguish the particular species that the ancients had mentioned, but disregarded almost all the rest. Modern botanists however suppose, that they were but little successful in general in their application of the ancient names to plants: nor is a failure in such attempts to be wondered at, considering the too great conciseness, and frequent obscurity, of their descriptions. In the class of mosses, as in many others, the accounts transmitted to us are little more than a scene of uncertainty and confusion.

It is to the moderns we are indebted for the discovery of the far greater number of the plants of this class. In this branch of botany our own countrymen Mr. Ray, Buddle, Dale, Doody, Petiver, and Dr. Morison, Sherard, Richardson, and others, have distinguished themselves: and amongst foreigners M. Vaillant, Sig. Micheli, and the very eminent Dr. Haller: but, beyond all, the late learned and indefatigable professor at Oxford, Dr. Dillenius, has herein made the most ample discoveries and improvements, of which his elaborate history will ever remain a standing proof.

The word lichen occurs in the writings of Dioscorides and Pliny; and tho’ it may be doubtful, there is nevertheless good reason to apprehend, that Dioscorides meant to describe under that name the very plant, or at least one of the same genus, to which the commentators agreed to affix his description. Since then the name has been variously applied by different authors; on which account it is necessary to premise, that the lichen sive hepatica Off. or liverwort of the shops, does not fall under this generical term, as it is now formed by the three above-named authors. They comprehend under the term Lichen, and Dillenius under those of Usnea, Coralloides, and Lichenoides, the hairy tree-moss or usnea of the shops; the muscus pulmonarius, tree-lungwort, or oak-lungs; the lichen terrestris cinereus, or ash-coloured ground liverwort; the coralline-mosses; the cup-mosses; horned mosses; the orchel, or Canary-weed; the muscus islandicus of Bartholine; and a multitude of others found upon trees, walls, rocks, and stones, in all parts of the world, and in many parts thereof in very great abundance.

Caspar Bauhine in his Pinax, John Bauhine, and countrymen Gerard and Parkinson, and their cotemporaries, as they wrote before the time that generical characters in botany were in use, included these lichens among the other herbaceous mosses, under the general name of muscus; adding to the name in general some epithet descriptive of its form, place of growth, or supposed virtue.

Mr. Ray, both in his History of Plants, and in the Supplement, as he was usually averse to the forming of new names, has interspersed them among other mosses, under the character of musci steriles seu aspermi, retaining the synonyms of the two Bauhines, Gerard, and Parkinson, to the general species.

Dr. Morison seems to have been the first, who separated them intirely from the herbaceous mosses; and, from the analogy he supposed they had with the fungus tribe, formed them into a genus, under the name of musco-fungus. He enumerates fifty species and upwards under this term in the Historia Oxoniensis, and has divided them into five orders, according to their different appearances, as follows:

Table the 7th of his 15th section exhibits several good figures of some of these lichens.

Tournefort was the first, who adapted the generical term lichen to them; but it was in consequence of his joining them to the lichen of the shops. He has however excluded the coralline-mosses, and forms them into a genus, by the name of coralloides; to which he has connected some plants, properly of the fungus tribe. In this distinction he is followed by Dr. Boerhaave in his Index alter Plantarum.

Dr. Dillenius first called them lichenoides, in the catalogue of plants growing about Giessen, chusing to retain the word lichen to the liverwort of the shops. Under this name however, in this work, he does not comprehend the usneæ, or hairy tree-mosses, but refers them to the conservæ, adding the epithet arborea to each species, to distinguish them from the water kinds. He enumerates upwards of sixty species of lichenoides, but has applied few or no synonyms to them.

Under the same generic term he has introduced them into the third edition of Ray’s Synopsis of British Plants, taking in the usneæ, and recounting upwards of ninety species, all found spontaneously growing in England. Many of these are undoubtedly only varieties. They are in this work very naturally divided into several orders and subdivisions, for the greater ease of distinguishing them, as follows:

Lichenoides }
caulifera }1. Capillacea et non tubulosa scutellata.
2. Coralliformia tuberculosa plerumque. }a. Solida et non tubulosa.
b. Tubulosa.
3. Pyxidata.
4. Fungiformia.
cauliculis destituta }1. Mere crustacea.
2. Crusta foliosa scutellata seu foliis scutellatis arcte adnascentibus - }a. Substantiæ gelatinosæ.
b. Substantiæ durioris.
3. Foliis magis liberis nec tam arcte adnascentibus }a. Scutellatis et tuberculatis.
b. Peltatis.

M. Vaillant, in the Botanicon Parisiense, retains Tournefort’s names. Many of these lichens, as well as other mosses, are accurately represented in the elegant tables, which adorn that work. Dr. Haller tells us he learnt to distinguish almost all the mosses solely by the help of these tables, so well are they expressed. The lovers of botanic science are greatly indebted to Boerhaave for his publication of that work.

Micheli, after Tournefort, adopts the term lichen, and comprehends all the species under it, except one or two, which he calls lichenoides. This author however does not take into this genus the liverwort of the materia medica; he describes the species of that genus under the name of marchantiæ. Near twenty of the plates in his Nova Plantarum Genera are taken up in representing various species of this genus. In this work they are divided into thirty-eight orders or subdivisions; a circumstance very necessary indeed, considering how greatly he has multiplied the number of the species. It is to be regretted, that so indefatigable an author, one whose genius particularly led him to scrutinize the minuter subjects of the science, should have been so solicitous to increase the number of species under all his genera: an error this, which tends to great confusion and embarassment, and must retard the progress and real improvement of the botanic science.

Dr. Haller retains Micheli’s term, and enumerates 160 kinds in his Enumeratio Stirpium Helvetiæ: he divides them into seven orders, according to the following titles:

The extensive number of the species, and the difficulty of distinguishing them with a tolerable degree of certainty, has deterred Dr. Haller from adding so full and complete a list of synonyms to the plants of this genus as he has elsewhere done in that splendid work. Plate the 2d exhibits several elegant sorts of these lichens.

Linnæus, and the followers of his method, who seem to have established their generical character from Micheli’s discoveries, retain also his generical title. Micheli’s passion for the multiplication of species is no-where more conspicuous than in the plants of this genus, which he has most enormously augmented to the number of 298 species. The Swedish professor cannot be charged with this foible: it is one of the excellencies of his writings, that they inculcate the reverse. He has so far retrenched this genus, that in his general enumeration of plants he recounts only eighty species belonging to it. They are in this work divided into eight orders, according to the difference of appearance which they form by their facies externa, little or no regard being had to what are usually called the parts of fructification.

Dr. Dillenius, in his most elaborate work, intituled, Historia Muscorum, has divided this Michelian genus into three, under the names of usnea, coralloides, and lichenoides. Under the word usnea he comprehends the hairy tree-mosses, among which are the usnea of the shops, and the true usnea of the Arabians. Of these he describes sixteen species. Under coralloides he describes thirty-nine species, among which are the cup-mosses, and many others, disposed according to the following scheme:

Ordo I. Fungiformia, non tubulosa, nec ramosa. 5.

Ordo II. Scyphiformia, tubulosa, simplicia et prolifera.

Series 1. Scyphis perfectioribus. 13. Cup-mosses.

Series 2. Scyphis imperfectis. 20. Horned mosses.

Ordo III. Ramosa fruticuli specie summitatibus acutis multifariam divisis.

Series 1. Species tubulosæ. 30. Tubulous coralline mosses.

Series 2. Species solidæ. 39. Solid coralline mosses; among which is the orchel.

The genus of lichenoides contains 135 species, disposed according to the following scheme:

Ordo I. Species aphyllæ mere crustaceæ. } 1. Tuberculosæ. 8.
2. Scutellatæ. 18.
Ordo II. Species foliosæ. }1. Gelatinosæ tuberculosæ et scutellatæ. 35.
2. Aridiores et exsuccæ, scutellatæ. 100.
3. Aridiores peltatæ et clypeatæ. 121.

These plants are not only largely described, and accompanied with the most perfect assemblage of synonyms; but every species is accurately figured, and many of them in various views, and at different ages of their growth; by which this laborious work, notwithstanding it is conversant upon the minutest, and consequently the most abstruse parts of botany, may nevertheless be justly esteemed, without any exaggeration, one of the most complete works extant of the kind.

Dr. Hill, in his History of Plants, has disposed them into five genera, under the following names: 1. Usnea, comprehending the hairy tree-mosses; 2. Platysma, flat-branched tree-mosses, the lungwort, and others; 3. Cladonia, containing the orchel and coralline-mosses; 4. Pyxidium, the cup-mosses; 5. Placodium, the crustaceous mosses.

The plants of this extensive genus are very different in their form, manner of growing, and general appearance: on which account those authors, who preserve them under the same name, saw the propriety and necessity of arranging them into different orders and subdivisions, that the species might be distinguished with greater facility. Upon the same principle Dr. Dillenius and Dr. Hill have formed them into several genera.

So far as the parts of fructification are distinguishable in these plants, they appear in different forms upon different species: on some, in the form of tubercles; on others, in the form of little concave dishes, called scutellæ; on others, of oblong flat shields or pelts. All these are conceived by Micheli and Linnæus to be receptacles of male flowers. The female flowers and seeds are suspected by the same authors to be dispersed in the form of farina or dust upon the same plants, and in some instances on separate ones. Dillenius has not dared to determine any thing positively with regard to the real parts of fructification in these lichens: time will hereafter, it is to be hoped, throw more light upon the subject.

In order to convey a more distinct idea of the several plants of this genus, which enter into œconomical or medical uses in the various parts of the world, we shall distribute them into several orders, according to the custom of former writers: and as is not consistent with our plan to describe each of these species, we shall refer to the page of the more modern authors, where they may be found.