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tions to exterminate v, let the latter be divided by the former; so shall

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and therefore ay”” = v (a being a constant quantity.) Hence y = (F×


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; and consequently P Xyp = Let there now be proposed the two fluxions "y" and x'y'y, 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 prefixed, being joined to the former, we shall here have xy + bx'y'y. Hence, by proceeding as before, bx'y' = v, and mx*y”-1 à + qbx*y'→ y. From the former of which equations, by taking the fluxions on both sides, will be had pbay' + qbx*y'—'ÿ (= i) = mx"y"1x + qbx*y?—1ÿ. Whence play = mx"y"; and therefore pby+ = mx”→+ '. 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. On the Alga Marina Latifolia; the Sea Alga with Broad Leaves. By J. A. Peyssonel, M. D., F. R. S. Dated Aug. 4, 1758. p. 631. From the French.

Having cast anchor at Verdun, the road at the entrance of the river of Bourdeaux, Dr. P. was fishing with a kind of drag-net on a bank of sand, which was very fine and muddy. He collected a number of sea-plants, and among them the great broad-leaved alga, which he did not know; and as the root or pedicle of this plant appeared to be very particular, he observed it with attention. The following is its description, and the detail of his observations.

From a pedicle, which is sometimes flat, and sometimes round (for they vary in these plants, and might be about 3 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 3 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 delicate 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 2d leaves are of the same thickness and substance with the first: they are 2 or 3 feet long, and the whole plant is 5 or 6, or more, for one can hardly tell the length; and is not capable

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of supporting itself, but is sustained by the strength of the waters, in which it floats.

They are about 3 or 4 They flourish and spread egg, flattened above and

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 putrefaction. 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. lines high towards the pedicle, and, ending, are lost. at the bottom, forming an elliptical bladder, like an below, and rounded at the sides, being entirely 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 less 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 centre of the two diameters. This hole is about an inch wide, and is quite round; it gives passage to the root, or pivot; 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 on 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, entirely full, of the same nature and substance with the egg. In examining the under part of the egg were found a 2d rank of these mamellæ, somewhat longer than the first, and at equal distances from each other, in a circular line: then a 3d yet longer: then a 4th, which at the extremities were bifurcated; and at last a 5th rank, which divided into 3, and sometimes into 5 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 mamella 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. This bunch, or wreathed rose, incloses a heap of gravel, as if petrified or hardened, and ends on a level with the hole of the egg, ex

actly as high as the last rank of mamella, 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. He found 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? probably they had their beginning there, by the seminal matter of muscles carried in by the sea-water. He also found some small star-fish, whose rays might be about 4 or 5 lines long.

LXXXVII. Of the Distilling Water Fresh from Sea-water by Wood-ashes. By Capt. William Chapman. p. 635.

Some time in September 1757, when Capt. C. had been 10 days at sea, by an accident (off the north cape of Finland) they lost the greatest part of their water. They had a hard gale of wind at s. w. which continued 3 weeks, and drove them into 73° lat. During this time he was very uneasy, as knowing if their passage should hold out long, they must be reduced to great straits; for they had no rains, but frequent fogs, which yielded water in very small quantities He now blamed himself for not having a still along with him, as he 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 their preservation.

He was not a stranger to Appleby's method: he had also a pamphlet written by Dr. Butler, intitled, An easy Method of procuring Fresh Water at Sea. And he imagined, that soap might supply the place of capital lees, mentioned by him. He now set himself at work, to contrive a still; and ordered an old pitch-pot, that held about 10 quarts, to be made clean: the carpenter, by his direction, fitted to it a cover of fir-deal, about 2 inches thick, very close; so that it was easily made tight by luting it with paste. They had a hole through the cover, in which was fixed a wooden pipe nearly perpendicular. This he should call the still-head; it was bored with an augre of 14 inch diameter, to within 3 inches of the top or extremity, where it was left solid. They made a hole in this, towards the upper part of its cavity, with a proper angle, to receive a long wooden pipe, which they fixed in it, to descend to the tub in which the worm should be placed. Here again he was at a loss, for they had no lead pipe, nor any sheet lead, on board. He thought, if he could contrive a straight pipe to go through a large cask of cold water, it might answer the end of a worm. They then cut a pewter dish, and made a pipe 2 feet long: and at 3 or 4 trials, for they did not let a little discourage them, they made it quite tight. They bored a hole through a cask, with a proper descent, in which they fixed the pewter pipe, and made both holes in the cask tight, and filled it with sea-water: the pipe stuck without the cask 3 inches on each side. Having now got his apparatus:

in readiness, he put 7 quarts of sea-water, and 1 oz. of soap into the pot, and set it on the fire. The cover was kept from rising by a prop of wood to the bow. They fixed on the head, and into it the long wooden pipe abovementioned, which was wide enough to receive the end of the pewter one into its cavity. They easily made the joint tight.

It need not be mentioned with what anxiety he waited for success: but he was soon relieved; for, as soon as the pot boiled, the water began to run; and in 28 minutes he got a quart of fresh water. He tried it with an hydrometer he had on board, and found it as light as river-water; but it had a rank oily taste, which he imagined was given it by the soap. This taste diminished considerably in 2 or 3 days, but not so much as to make it quite palatable. Their sheep and fowls drank this water very greedily without any ill effects. They constantly kept their still at work, and got a gallon of water every 2 hours, which, if there had been a necessity to drink it, would have been sufficient for the ship's crew. He now thought of trying to get water more palatable; and often perused the pamphlet above-mentioned, especially the quotation from Sir R. Hawkins's voyage, who "with 4 billets distilled a hogshead of water wholesome and nourishing." He concluded he had delivered this account under a veil, lest his method should be discovered: for it is plain, that by 4 billets he could not mean the fuel, as they would scarcely warm a hogshead of water. When, ruminating on this, it came into his head, that he burnt his 4 billets to ashes, and with the mixture of those ashes with sea-water he distilled a hogshead of fresh water wholesome and nourishing. Pleased with this discovery, he cut a billet small, and burnt it to ashes: and after cleaning the pot, he put into it a spoonful of those ashes, with the usual quantity of sea-water. The result answered his expectations: the water came off bright and transparent, with an agreeable pungent taste, which at first he thought was occasioned by the ashes, but afterwards he was convinced it received it from the resin or turpentine in the pot, or pipes annexed to it. He was now relieved from his fears of being distressed through want of water; yet thought it necessary to advise his people not to be too free in the use of this, while they had any of their old stock remaining; and told them, he would make the experiment first himself; which he 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. They had expended their old stock of water before they reached England; but had reserved a good quantity of that which they distilled. After his arrival at Shields, he invited several of his acquaintance on board to taste the water: they drank several glasses, and thought it nothing inferior to spring water. He made them a bowl of punch of it, which was highly commended.

He had not the convenience of a still, or he should have repeated the experi

ment for the conviction of some of his friends: for as to himself, he was firmly persuaded, that wood-ashes mixed with sea-water would yield, when distilled, as good fresh water as could be wished for. And he thought, 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 might easily be made, while there was any wood in the ship, and the extraordinary expence of fuel would be trifling, if they contrived so that the still should stand on the fire along with the ship's boiler.*

LXXXVIII. A Lunar Eclipse observed at Matritus,

July 30, 1757. By the Jusuit Father John Wendlingen. p. 640. From the Latin.

The eclipse began at 9h 47m 34s, and ended at 12h 52m 15s, true time. Another lunar eclipse was observed by the same, Jan. 24, 1758. It began at 4h 7m 425, and the total immersion was at 5h 13m 10s.

LXXXIX. Observations on a slight Earthquake, though very particular, which may lead to the Knowledge of the Cause of Great and Violent ones, that ravage whole Countries, and overturn Cities. By J. A. Peyssonel, M. D., F. R. S. p. 645. From the French.

Dr. P. went to make observations on the natural history of the sea; and when he 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 N.E. and S. w. the sea being much agitated that day flowed from the N. w. 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 phenomenon is common to many places in this island. The explanation of it is easy: but the following is what he particularly observed.

As he walked within about 40 paces from the brink of the sea, where the waves broke, he perceived, in one place, the plants were much agitated by some cause, that was not yet apparent. He drew near, and discovered a hole about 6 feet deep, and half a foot diameter; and stopping to consider it, he perceived the earth tremble under his feet. This increased his attention; and he heard a dull kind of noise underground, like that which precedes common earthquakes.

* The addition of wood-ashes, or any other alkaline substance, is quite unnecessary; sweet water being obtainable from sea-water by simple distillation in clean vessels; provided the degree of heat be duly regulated, and care be taken to stop the distillation when the brine becomes too much concentrated. See note at p. 549, vol. i. of these Abridgements.

+ Neither the latitude nor longitude of this place is given.

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