< 4. The latitudes and the fuperficies of the map being exact, by the conftruction, it follows that the exceffes and defects of distances now mentioned, compenfate each other; and are, in general, of the least quantity they can have in the map defigned.

5. If a thread is extended on a plane, and fixed to it at its two extremities, and afterwards the plane is formed into a • pyramidal or conical furface, it may be eafily fhewn, that the thread will pafs through the fame points of the furface C as before; and that converfely, the fhorteft diftance between two points in a conical furface is the right line which joins them, when that furface is expanded into a plane. Now, in the prefent cafe, the fhorteft diftances on the conical furface will be, if not equal, always nearly equal to the corref⚫ponding distances on the sphere: and therefore, all rectilinear ⚫ distances on the map, applied to the meridian as a scale, will nearly, at least, fhew the true diftances of the places re• presented..

6. In maps, whofe breadth exceeds not ten or fifteen degrees, the rectilinear diftances may be taken for fufficiently exact. But we have chofen our example of a greater breadth than can often be required, on purpofe to fhew how high the errors can ever arife; and how they may, if it is thought needful, be nearly estimated and corrected.'

The Author fhews, that this conftruction may, without fenfible error, be applied to fea-charts; and gives feveral numerical examples, for that purpofe, which prove plainly his affertion. His reafonings are fo very obvious, that it would be needless to animadvert upon his conftructions: for which reafon we shall close this article with a few obfervations.

All the prefent maps have fcales for measuring distances, though there is not the leaft proportion in them; which is extremely abfurd, and generally misleads people, who cannot conceive that these scales are abfolutely ufelefs. The cafe is quite different in the paper before us: a table of corrections is propofed to be inferted in fuch maps as are very large, and which are the only ones that want them in regard to longitude; but in maps of ten or fifteen degrees, they need no corrections; and as thefe particular maps of provinces or ftates are the moft ufeful with regard to the pofitions and diftances of particular places, which a common fcale of miles will fhew with as much accuracy as is neceffary.

It has been obferved, that this method does not admit of a zone, containing N. and S. latitudes;—but why this objection? for if the north and fouth parts of the zone are either

equal,

Tranfactions of the Royal Society, Vol. L. Part II.
equal, or nearly fo, the conic furface becomes, or may be
made, cylindric; and when the difference is more confider-
able, the center of the parallels will, it is true, be at a great
distance, but yet not fo much as to become impracticable.

Article 74. A fhort differtation on Maps and Charts. By Wil-
liam Mountaine, F. R. S.

The author begins with fhewing, that the invention of globes, maps and charts, deferves a place among the feveral improvements, made in arts and fciences, by ingenious men : globes perhaps where firft invented, as bearing the nearest refemblance to the natural form of earth and fea; but as they contain but a small furface, maps and charts where afterwards thought of, as being more convenient for laying down the appearance, or face, of particular parts of the earth, and as being more portable for travellers. He then enters upon the defcription of the different kinds of maps, as they are divided into general and particular; in which it may be obferved, that as the difficulty naturally arofe, in reprefenting a part of a fpheric surface upon a plane; different conftructions were invented, which for the most part are fo defective, as not to be applied with accuracy and facility, in determining the courfes, bearings, or diftances of places.

Among all the different reprefentations of a small part of the globe's furface, the rectilinear, which confiders that furface as a plane, must have naturally occurred first to the geographers; and as the rhumbs were confequently right lines, the courses, or bearings of places could more easily be determined. It is for this reafon, that these kind of maps and charts, are ftill generally ufed to reprefent provinces and kingdoms, as likewife for fhort courfes in navigation; notwithstanding the many improvements fince suggested.

The first step towards the improvement of maps, or charts, our author fays, was made by G. Mercator, who about the year 1550, published a map wherein the degrees of latitude were increafed from the equator towards each pole; but upon what principles this was done, he did not explain. About the year 1590, Edward Wright, an Englishman, discovered the true principles upon which fuch a chart fhould be constructed; and in the year 1599, he exhibited his method of conftruction, in his Correction of errors in navigation; in the preface to which, may be feen how far Mercator has any right to share in the honour due to this great improvement in geography, and navigation.

The

The author obferves, that fince Mr. Wright's map made its appearance, the globular and various other conftructions were invented, but none, according to his opinion, is fo convenient as Mr. Wright's for fea charts, because the meridians and parallels, as likewife the rhumb lines, being represented by right lines, are better adapted to the capacities of moft navigators: notwithstanding, that the parts towards the poles are extended much beyond what they are on the globe. However, he thinks that a map conftructed according to Mr. Murdoch's principles, fhews the fituation of places nearer, and is better calculated for determining fuperficial and linear measures, than the former, and that his courfes alfo agree nearly with the computations made from the table of meridional parts, but he does not think it fo eafy and fimple, in the practice of navigation. To this we may add, that navigators who have been used to Mercator's chart from their youth, will never approve of any other, though much better in all respects; their attachment to the old practice being fo ftrong, that no reafoning can prevail upon them.

Article 87. An account of diftilling Water fresh from Sea-water by Wood-afbes. By Capt. William Chapman.

The captain having by accident, loft the greatest part of his stock of water, was in fear of scarcity if the voyage fhould prove long, having neither Still nor other conveniency provided, to make fea-water fresh, by the several methods published by authors: neceffity, however, the mother of invention, made him try experiments, as far as his circumftances would allow ; whereby he fortunately contrived a method to fupply the want: and it appears to be the moft fimple and practicable, that could be wifhed. It will not be difagreeable to the curious, to fee the account in his own words, as it may be of use to others under the fame circumstances.

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I was not a stranger to Appleby's method; I had alfo a pamphlet wrote by Dr. Butler, intituled, An eafy method of procuring fresh water at fea; and I imagined, that foap might fupply the place of capital lees, mentioned by him. I now fet myself at work, to contrive a ftill; 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 clofe; fo that it was eafily made tight by luting it with pafte. We had a hole through the cover, in which was fixed a wooden pipe, nearly perpendicular. This I call the ftill-head; it was bored with an augre of one and a half-inch diameter, to

'

worm.

within three inches of the top, or extremity, where it was left folid. 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 defcend to the tub in which the worm fhould be placed. Here again, I was at a lofs; for we had no lead pipe, nor any fheet lead on board, 'I thought, if I could contrive a ftrait pipe to go through a large cafk of cold water, it might anfwer the end of a We then cut a pewter difh, and made a pipe two feet long; and at three or four tryals (for we did not let a little difcourage us) we made it quite tight. We bored a 'hole through a cafk, with a proper defcent, in which we fixed the pewter pipe, and made both holes in the cask tight, ' and filled it with fea-water; the pipe ftuck without the cafk three inches on each fide. Having now got my apparatus in readiness, I put feven quarts of fea-water, and an ounce of foap into the pot, and fet it on fire. The cover was kept from rifing 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 his cavity. We easily made the joint ' tight.

I need not tell thee*, with what anxiety I waited for 'fuccefs: but I was foon relieved; for as foon 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 hy'drometer I had on board, and found it as light as river 'water; but it had a rank oily tafte, which I imagined was given it by the foap; this tafte diminished confiderably in two or three days, but not fo much as to make it quite palatable. Our fheep and fowls drank this water very greedily, without any ill effects. We conftantly kept our ftill at 'work, and got a gallon of water every two hours; which, if there had been a neceffity to drink it, would have been fufficient for our ship's crew.

'I now thought of trying to get water more palatable, ' and often perused the pamphlet above-mentioned, especially the quotation from Sir Richard Hawkins's voyage, who "With four billets diftilled a hogfhead of water, wholesome "and nourishing." I concluded, he had delivered this account under a veil, left his method fhould be difcovered:

་

This letter is addreffed to Dr. Fothergill, an eminent phyfician in. London, and one of the people called Quakers. Capt. Chapman appears alfo to be of the fame perfuafion.

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• for

for it is plain, that by four, billets he could not mean the fuel, as they would fcarce warm a hogfhead of water. When ruminating on this, it came into my head, that he burnt his four billets to afhes, and with the mixture of thofe afhes with fea-water, he diftilled a hogfhead of fresh water, wholefome and nourishing. Pleafed with this difcovery, I cut a billet fmall and burnt it to afhes; and after cleaning my pot, I put into it a fpoonful of thofe afhes, with the ufual quantity of fea-water (viz. feven gallons). The refult anfwered my expectations: the water came off bright and transparent, with an agreeable pungent tafte, which, at first, I thought was occafioned by the afhes, but ⚫ afterwards was convinced, it received it from the refin, or • turpentine in the pot, or pipes annexed to it. I was now ⚫ relieved from my fears, of being diftreffed through want of water; yet, thought it neceflary to advise my people, not to be too free in the ufe of this, whilft we had any of our • old stock remaining; and told them, I would make the ex'periment first myself; which I did, by drinking a few glaffes every day, without any ill effect whatever. This water was equally light with the other, and lathered very well will foap. We had expended our old ftock of water, ⚫ before we reached England, but had referved a good quantity of that which we diftilled. After my arrival at Shields, I invited feveral of my acquaintance on board, to tafte the water; they drank feveral glaffes, and thought it not inferior to fpring-water. I made them a bowl of punch of it, which was highly commended.

I have not the conveniency of a ftill here, or should have repeated the experiment for the conviction of fome of my friends for as to myfelf, I am firmly perfuaded, that wood-afhes mixed with fea water, will yield, when diftilled, as good fresh water as can be wifhed for: and, I think, if every fhip bound a long voyage, was to take a small ftill, with Dr. Hales's improvements, they need never want fresh C water. Wood-afhes may eafily be made, while there is any wood in the fhip; and the extraordinary expence of fuel will be trifling, if they contrive fo that the ftill may • ftand on the fire along with the ships boiler.'

The ufeful tendency of this paper, is too manifeft to need any comment; it may, however, not be amifs to observe, that the afhes of beech wood are faid to be preferable to any other, for the purpofe above-mentioned.

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