# Philosophical Transactions of the Royal Society (1665-1886)/Volume 3/Number 39

Contents:
* Contents
* An Addition to the formerly publisht Narrative, about Empty Tubes serving for a decay'd sight.
* ⁠An Extract of a Letter written from Dantzick, containing the success of some Experiments of Infusing Medicins into Humane Veines.
* ⁠Additional Answers to the Queries of Mines.⁠
* Extracts of two Letters;
** whereof the one written from Franckford on the Oder concerning Osteocolla, and some other Observables in those parts
** the other written by an Ingenious Person in England, about some Effects of Antimony.⁠
* A second Letter of Dr. John Wallis on the same Printed Paper of Fr. Du Laurens, which was mentioned in the next foregoing Transactions.
* Account of some Books.
** I. OLAI BORRICHII, Med. Regii, & in Acad. Hafniensi Prof. De ORTU & PROGRESSU CHEMIÆ, Dissertatio.
** ⁠II. An IDEA of the Perfection of PAINTING: originally written in French; and now rendred English by J. Evelyn Esq;⁠
** III. STEREOMETRICAL PROPOSITIONS, variously applicable, but particularly intended for GAGING, by ROB. ANDERSON.⁠
** IV. ELAPHOGRAPHIA sive CERVI Descriptio Physico-Medico-Chymica, Auth. JOH. ANDREA GRABA, Med. Doct. Erfurtensi.⁠
** V. A DISCOURSE of SPEECH, Originally written in French, now rendred English.
PHILOSOPHICAL
TRANSACTIONS.
Monday, Sept 21. 1668.
The Contents.
A Note,
SIr, I pray you, give notice, That I have now tried Convexe Spectacles, which about 3 years agoe (before my sight fell into this decay) agreed very well for my use; and putting these ​Glasses into the Tapers, I found the smallest Prints somewhat larger, but not so clear, so distinct, nor so pleasing to the Eye, as when I use the Empty Tapers. Also I am so confirm'd, that these empty tapers do preserve, strengthen, and in some small degree recover the sight. This may give occasion to consider, Whether to a sight much decay'd, a hindrance of the Refractions may be a Remedy? And whether the hindrance of Refractions, which helpes some Eyes, helpes not others?And I find my self best at ease with those Leathern Tubes, I first used; and rather without any fastning to the bone of the Spectacles: For, as they hang in that slight manner, I can with a touch of my finger raise them up, or bow them down, divide them, or unite to take in the same object, which is more than I said at first. And I put them off and on as speedily and as easily as any other Spectacles.
An Extract of a Letter,
MOnsieur Smith, Physitian in Ordinary to this City, having liberty granted him to try an Experiment upon some persons desperately infected with the Poxe, then in the publick Hospital here, adventur'd the opening a Veine, and infusing some Medicines into the blood; which was tryed upon two persons, whereof the one recover'd, and the other dyed, Yet being since farther encouraged by corresponding with some of the Royal Society in England, about a Moneth since, the said Physitian, together with Monsieur Scheffeler, another ancient Practitioner in this City, repented the Experiment by infusing Altering Medicines into the Veines of the right Armes of three persons: the one, lame of the Goute; the other, extreamly Apoplectical; and the third, reduced to extremity by that odd distemper, the Plica Polonica. The Success of this, as Monsieur Hevelius (who was the person only admitted to be present at the operation) informes me, was; That the Gouty man found himself pretty well next day, and shortly after went to work, it being Harvest time, and ​has continued well ever since, leaving the Hospital yesterday, and professing himself cured. The Apoplecticall hath not had one Paroxysme since: And the several Sores, which the Plica Polonica had occasioned, are healed; and both these Persons have been able to work any time these three Weekes. Dated August 18. 1668.
Additional Answers
To the Queries of Mines.
What the Worthy and Learned Mr. Joseph Glanvil intimated in his Answers to the Queries concerning Mines, publisht Numb. 28. p. 525. viz. That he did not think himself by the return, then made, absolv'd of his Tasks, but intended to pursue that matter further, He now proveth to have been his real purple, by the following Additions, very obligingly imparted by him; concerning the same Mendip-Mines; To which he premiseth this short instructive Letter;
SIr, I now send you a more perfect account of the Mendip-Mines, which by the help of an Ingenious friend I procured from some very experienc'd Mine-men. I have face communicated these Informations to the Gentleman, who gave me the former, which I also sent you; and he assures me, that they are exact. Only in some little things they differ some circumstances of his; as the Virgula he never knew practis'd; whereas these say, it hath, but is not much valued, For which, allowance must be made to the difference of 30 yeares; it being so long agoe, that my fist Informant had to do in those matters. He also saith, that the Trees are sooner wither'd in their leaves upon this Hill; whereas they observe, that when a Mineral-vein runs up into the Roots of Trees, yet they have not noted any difference at Top; which must be understood with respect to other Trees there, into whose roots no such veins ran. I can perceive no difference in the account else, that is any wafer material. What defects you find in it, if you intimate them to me, I shall inquire again for further satisfaction, &c.
To the 10–16 Qu. (Viz, Numb. 19. p. 333.) the Grass is rank and good, There are few Trees on this part of the Hill; but the Workmen have known the Vein to run up into the roots of Trees, when they have observ'd no difference an the Top. They esteem the water healthy to drink, and to dress Meat with it. ​The Snow and Frost near the Grooves melt quickly, but continue long at further distance.
To the 18, 19. Sometimes, when a Mine hath been very near the surface, the Grass hath been yellow and discolour'd. Some have made use of the Virgula divinatoria; but the Experience Work-men have no value for it; yet they say, when the Mine is open, they may guess by it, how farr the Vein leades.
To the 20, 21, 22, 23, 24, 25, 26, Qu. White, Yellow and m'xt Earth are leaders to the Country (as they call it;) Changeable colours alwayes encourage their hopes. For Stones, they are sometimes 12 fathom deep, before they meet any: Otherwhile, when at stony Reak at top, they meet Ore just under the sword (superficies) of the Grass, which Ore hath gone down above 40 fathom. A black Stone is of bad signification, and leads to a Jam (a black thick Stone, that hinders their work.) A grey cleer dry one they account best. They seldome encounter Damps. If in linking they come to wet moorish Earth, they exspect a Jam, and to be closed up with Rocks. The nearness they guess by short britle Clay; for the tough is not leading. As to the rest of the Queries, belonging to this Title, the Minemen can give no satisfaction to them.
To the 31, 32. The Ore sometimes is Shole, and again, it is 14 or 20 fathom more or less, before they hit it. They follow a Veine inclining to some depth, when it runs away in flat Binns (their terme.) When the Stones part it, then they find a Veine again. Their Draughts are 14 or 16 Fathom, till they come to a Stone, where they call aside a Draught call'd a Cutt. Then they sink plum again 4 or 5 Cutts one under another. They find Ore at 50 Fathom. Their best Reaks are North and South; East and VVest are good, though not so deep. But 6 and 12 are proper Reakes, the rest not so.
To the 33 and 34. The Groove is 4 foot long, 2½ foot broad, till they meet a stone, when they carry it as they can. The Groove is supported by Timber of a Divers bigness, as the place gives leave. A piece of an Armes bigness will support 10 tun of Earth. It lasts long; that which was put in beyond the memory of man (nay, which by the difference in the manner of working their mines, they know to have layn above 200. years) ​will serve in new VVorks. It is tough and black, and being expos'd to the Sun and Wind for 2 or 3 dayes, will scarce yield to an Axe. That which hath layn 40 yeares to their own knowledge, they have taken up, and set again.
To the 35. VVhen they have sunk a Groove, they will not be at the charge of an Air-shaft, till they come at Ore; and for the supply of Air have boxes of Elme, exactly closed, of about 6 inches in the cleer, by which they carry it down above 20 Fathom. They cut a Trench, at a little distance from the top of the Groove, covering it with Turf and Rodds disposed to receive into the pipe, which they contrive to come in, sidewayes, to their Groove, 4 foot from the top; which carries down the Air to a great depth. When they come at Ore, and need an Air-shaft, they sink it 4 or 5 fathom distant, according to the convenience of the breadth, and of the same fashion with the Groove, to draw as well Ore as Air.
To the 36, 37, 38. The waters are more plentiful in Winter, according to the downfalls of Rain. They-make use of Leathern-baggs, 8 or 9 Gallons a piece, drawn up by Roapes, to free the water.
To the 39, 40. If they rind a Swallet, they drive an Adit upon Levell, till 'tis dry. Seldome Damps.
To the 41, 42. I referr to a Melius inquirendeum: Only they find no prejudice from any Iron-ore.
To the 43, 44. If they cannot cut the Rock, they use Fire to aneale it, laying on Wood and Coale, and the Fire so contriv'd, that they leave-the Mine before the Operation begins, and find it dangerous to enter again, before it be quite clear'd of the Smoak; which hath killed some.
To the 45, 46, 47, 48. Beetles, Axe, Wedge, unless so hardned as to make a deep Impression upon the head of an Anvill, are not Ht for their use; and yet they sometimes break them in an hour; others last 3 or 4 dayes, as it happens. They work cloath'd in Frocks and Wait-coats, by Candle-light of Tallow; 14 or 15 to the pound, each whereof lasts 3 houres, if they have Air enough: which if they want to keep in the Candle, the Work-men cannot stay there. A Vein-being lost, they drive 2 or 3 fathom in the breast, as the nature of the Earth directs ​them. They conv out their Materials in Elme-Buckets drawn by Ropes. The Buckets hold about a Gallon. Their Ladders are of Ropes.
To the 49, 50, 51. The Ore runs sometimes in a Vein, sometimes dispers'd in Banks. It lies many times between Rocks: some of it is hard, some milder, They never find any perfect, but it muff be refined. Many times they have branched Ore in the Sparr.
To the 53--till 60. There is Sparr and Caulk about the Ore; and another substance, which they call the Crootes, which is a mealy white stone, marred with Ore, and soft. The Sparr is white, transparent, and britle like Glass. The Caulk, white and heavy, heavier than any stone. The Vein lies between the Coats, and is of different breadths. It breakes of sometimes abruptly in an Earth, they call a Deading Bed, and after a fathom or two may come again, keeping the same point. It terminates sometimes in a dead Earth Clayie, without Croot or Sparr; sometimes in a Rock called a Fore-stone.
To the 62 till 65. There is much difference in the goodness of the Ore. The cleerest and heaviest, best. 36 hundred of Ore may yield a Tun of Lead. Some small eyes of other mixtures, Brass, &c.
To the 66. They beat the Ore with an Iron flat piece; cleanse it in Water from the dirt; lift it through a Wire-sive. The Ore tends to the bottom, and the Refuse lies at top. And these are the Preparations, they make use of, before 'tis fit for fusion. Then they have a Hearth about 5 foot high, set upon Timber, to be turn'd as a Wind-mill, to avoid the inconvenience of smoak upon a shifting VVind. The Hearth contains half a bushel of Ore and Coal, with bellowes on the top. The Charcoale is put upon the Hearth, where the Ore is; laying dry Gads upon the top, which they call their VVhite coales. There is a sink upon the side of the Hearth, into which the Lead runs, that holds about an hundred and an half. Then it is cast into Sand, and runs into those Sowes (as they call them) which they sell. They have a barr, to stir the Fire; a shovel, to throw it up; and a Ladle heated red-hot, to cast out the Metal.
​To the 82, &c. Once melting is enough. The good melts best, and the best, first, There is sometimess half odds in the goodness. The best is distinguisht by its weight.
To the 88, 89. There is a flight in the smoak, which falling upon the Grass, poysons those Cattel that eat of it. They find the taste of it upon their lips to be sweet, when the smoak chances to fly in their Faces. Brought home, and laid in their houses, it kills Rats and Mice. If this flight mix with the Water, in which the Oar is wash't, and be carried away into a streame, it hath poisoned such Cattel, as have drunk of it after a current of 3 Miles. What of this flight falls upon the sand, they gather up to melt in a Flagg-hearth, and make Shot and Sheet-lead of it.
To the 90. They sometimes find Slaggs, 3, 4, or 5 foot under ground, but such as they judge cast aside heretofore.
The Promiscuous Inquiries, annexed in the Numb. 19, are most of them satisfied in the former Answers.
But as to the Mineral Lawes of Mendip, I am promised an Account of them, which I shall transmit to you, as soon as I have received it.
Concerning subterraneous Dæmons, they have never seen any, but sometimes have heard knockings beyond their own Works, which, when follow'd by them, have afforded plenty of Ore.
About 2 years since, one King of Wells in his Groove found a piece of Ore, in which they fancied the shape of a Man, Eyes, Armes, Leggs, full Breast: The whole was about 4 inches in length; the Mine proved rich.
An Extract of a Letter.
Written from Franckfurt in the Oder, by the learned Professor Johannes Christophorus Beckman to the Publisher, concerning Osteocolla, and some other observations in those parts; Englished out of the High-Dutch, as follows.
SIr, the Conversation with several worthy Members of the R. Society, I had the honor to be admitted to, when I was in England, as it then awakned me, and begot in me a revolution, ​better to employ the remainder of my travelling-time, in making Observations of a Philosophical nature, so the remembrance of it, since my return into my Native Soyle, hath prompted me to enquire after, and to take special notice of the Productions of Nature there: Among which I shall at this time chiefly impart to you, what hath occurr'd to me about the Osteocolla; which I have therefore the more carefully observ'd, because I have hitherto met in Authors with little satisfaction concerning the same.
1. Therefore, I find, that it growes in a Sandy, yet not Gravelly Soyle, and not at all (that I know) in any rich or Clayie Ground.
2. It shoots down two mens depth under ground, so that, being found above the surface of the Earth, you may still find downwards of its branches till you come to the said depth. Where it is to be noted, that the branches moll commonly grow streight up, yet sometimes also spread sideways.
3. The branches are not of an equal thickness, but, like plants growing above ground, some of them thicker, some slenderer; and the farther they are distant from the common stem, the thinner they are, the stalk being thickest of all, usually equalling the thickness of an ordinary Arm or Legg, and the branches, the thickness of on's little linger.
4. The Place, where 'tis to be found, hath its peculiar mark, to find the Osteocolla by, which is, that upon the Sand, which is here every where yellowish, there appears a whitish fatty Sand, -which, if it be dug into, hath under it a dark fatty, and, how hot and dry soever the other Sand be, a somewhat moist and putrid matter, like rotten Wood, which matter spreads it self here and there in the Earth, just as the Osteocolla it self doth, and is called by those, whom I have employ'd to look for it, the Flower of this Substance.
5. The Osteocolla being thus found, is altogether soft, yet rather friable than ductil: Wherefore if one hath the curiosity of getting out of the ground a whole piece of it with its branches, he mutt very carefully remove the Sand every way from it, and then let it lie so a while; its quality being, That remaining exposed to the Sun for half an hour or somewhat longer, it ​growes to that hardness, as 'tis found in the shops of Apothecaries.
6. It seems to be a kind of Marle, or to have great affinity with it; of which we here also have great store, yet not near those places, where, I have found Osteocolla.
7. It requireth also time to come to maturity; which appears from hence, that in the very same place, where I digg'd some of it the last year, I this year found others; yet with this difference, that those were grown hard, after the manner before described, but these remain still soft and friable, though now in the fifth Moneth.
8. The cause of its being divided into so many branches, I conjecture to be from the Roots, which spread themselves here and there in the Earth, so that the matter gathers and setleth its self about them, and afterwards according to the division of the roots, acquires a plantal form and appearance. Whence it also seems to proceed, that through the midi! of the Osteocolla there alwayes passeth a dark line, which is thought to be a piece of the Root. And it often happens, that that stroke loseth it self by little and little, and the Osteocolla in the middle grows clear; which comes to passe, when the Root by the corruption, begun in the Osteocolla, is reduced to powder. Yet have I found a place hereabout, where the Osteocolla was not hollow at all; but there I observed, that in stead of setling about a big root, it had gathered it self about many small fibres; whence also this sort had acquired pores thorough its whole length, but no cavity, like the other.
On another occasion I may also communicate to you some particulars concerning the Gramen Ischæmon, call'd by others Gramen Dactyloides, or Sanguinella; and the Gramen Aquaticum cum longissima pannicula, mention'd by Bauhinus, and growing here in great plenty; as also the Observables in the Forest, call'd the Hartz, which I intend shortly to visit, and wherein are to be found very considerable both Copper and Silver-Mines, store of Lapis fissilis, and a sort of stone, which by Raine grows altogether soft, and a place, call'd Bawmans Hole, like that of Oky-hole about Wells in England, &c.
I shall now conclude with giving you notice, that the 1. of ​March last, there fell an unusual sort of Snow, which I considered with more than ordinary attention. It had none of the ordinary figures, but was made up of little Pillars, whereof some were Tetragonal, some Hexagonal, with an neat basis. On the top they were somewhat larger, as the heads of Columnes are. Considering the whole shape, we thought fit to give it the name of Nix Columnaris.
ITryed that a Boare, to whom I had given an ounce of crude Antimony at a time, putting him into the Sty, would be fat a fortnight before another, having no Antimony, upon the like feeding. Antimony will recover a Pig of the Measles; by which it appears to be a great purifyer of the Blood. I knew a Horse, that was very lean and scabbid, and could not be fatted by any keeping, to whom Antimony was given for two Moneths together every morning, and that upon the same keeping he became exceeding fat. One of my own Horses having had the fashions, and being cured, had notwithstanding extream running leggs; so that after he had passed the course of Farryers twice, to be cured, it was not done; but upon my giving him Antimony but one week, he was presently healed.
The manner of using it, is this. Take one drachme of crude Antimony powder'd for one Horse, and when you give him his Oats in a morning, shake it out upon his Oats in a little heap in the middle: If he be hungry, and you keep off his head from every other part of the Oats, he will snap it up in his mouth at one bite, when you let him goe. Some Horses greatly like it, others refuse it after the first. If he refuse it, cover it with Oats thinly; its done: or make it in Balls.
DIxeram, vit clarissime, in fine cujusdam ad Te Epistolæ, nonnisi ex multis pauca, ea esse specimina, eorum quæ apud Dulaurensium occurrunt, vel parum sana, vel minimè accurate tradita. Si vis, ut paucis, illis annumeram plura, Obsequor, modo ne petaa ut Omnia.
Ab initio itaque ut ordiar; Quantum (inquit, sect. 1) vocamnes id omne, quod extensionem vel Distinctionem in se recipit; eadem videlicet Quantitatis denominatione duabus his rerum affectionibus significandis accommodata. Quantitatis itaque vocem jam definivit, qua nempe sinificatione intellectam vult. Eandem (sect. 2.) dividit (ut alii) in Continuam, & Discretam;; seu Separatam, quam multitudinem vocat. Mox autem (sect. 3.) Quantitas, inquit, separata, etiam in rebus omni quantitate destitutis locum habet. Dic, quæso, Quomodo possuat res illæ Quantitatem habere, quæ sunt Omni quantitate destitutæ? vel (quod statim occurrit) Subjectum, Quantitatis Discretæ, Quantitatis expers esse?
Sed exempla subjicit, Duo Puncta Tria Momenta, Decem Spiritus, &c. At vero annon Duo Puncta (etiam juxta illum,) Distinctionem habent, adeoque Quantitatem discretam? Quomodo igitur Omni quantitate destituta dicit? Vel, di non habenr, Quomodo dici poterunt discretæ Quantitatis Subjectum?
Dices forsan, hæc cum velle, Puncta singlua non esse Quanta, esse autem Bina. Esto. At peto, an in Punctis singulis locum habeat, Discreta Quantitas? sintve singlua discretæ quantitatis subjectum? si sic; tum non sunt omni quantitate destituta: si non; quomodo hinc ostenditur, quod subjectum quantitatis discretæ, sic Quantitatis expers?
Sed &, ut de singulis prospiciamus. Dicit ille, sect. 3. Quantitatis ideo esse expertia, eo quod in unoquoque subjectorum nec ulla distinctio fit, nec extensio. Taceo hic unumquodque dici quantitatis subjectum (quod tamen quantitatis expers esse vult:) Quoniam id expressius dicitur, sec. 4. Numerorum, inquit, natura, non simplicem magnitudinem repræsentat, sed ex pluribus Quantitatibus aggregatam. Si itaque Duo Puncta sint ex pluribus Quantitatibus aggregata; horum singula sunt Quantitates, non omni quantitate destituta. Vides tu, quàm hæc inter se bene conveniunt.
Porro, sect. 2. Distinctio, inquit, arguit plurium rerum aggregatum, Disjunctis inter se partibus compositum; ut est Populus, Acervus, & unumquodque eorum, quorum partes propriis extremitatibus terminantur & ab alterius fine discretæ sunt: Atque hujusmodi rerum congeries peculiari nomine Multitudo dicitur. Habes hic tum Distinctionis, tum Multitudinis definitionem: Et utrobique requiruntur Partes disjunctæ, & quæ suis extremitatibus terminatæ ab aliis sint Discretæ, non Continuæ. Et sect. 5. ​Quantitati Discretæ, nimirum multitudini, præcipuê convenit Divisio: Dividi autem nihil aliud est quàm separai, seu Distingui: Multitudinis autem naturam in Distinctione pofitam esse vidimus. At statm, sect. 6. Distinctio, inquit, à Divisione differt, &c. unde si Distinctio pro quodam genere accipiatur, erit Divisio pro ejus specie assumenda. At vero, si Dividi nihil aliud sit quàm Distingui; etiam Divisio nihil aliud erit quàm Distinctio? Quomodo igitur Distinctio à Divisione differt? Aut, altera Genus, altera Species ejusdem censenda erit?
Eo, inquit, differunt, quod Distinctio quamcunque pluralitatem exprimit; Divisio vero eam solum, quæ à rerum separabilitate ex ritur. Imo vero non quamcunque Pluralitatem exprimit Distinctio, sensu suo, sed rerum tantum, quæ sunt inter se disjunctæ, extremitatibus propriis terminatæ, atque ab aliis discretæ, Quippe hoc arguere modo dixerat Distinctionis vocem. Quæ vera ita sunt, non modo separabilia, sed & ata Divisa sunt & separata: Nec erit Distinctio Divisionis genus quoddam, sed Divisionem in sua significatione includet.
Subdit, sect. 7. Neque Actualis tantummodo Divisio Multitudini concedenda, verumetiam Potentialis tribuenda videtur; non enim unquam ita divisa est, ut pluribius aliis modis secari non possit: Veluti numerus Duodenarius non ita divisus est in partes suas Duodecimas, ut in tertias, quartas, sextas, & adhuc alias quasdem sine nomine dividi nequeat. Verum mihi dicat velim, (ut ab exemplo suo non recedam,) an Duo Puncta (quam esse Multitudinem fatis diserté dixerat,) sint hujusmodi Divisionis capacia? Nempe, ut nunquam ità divisa esse possint, quia & pluribus adhuc modis secari possint? Vel etiam, an Duodecim puncta (quoniam & hunc numerum jam insinuat) postquam in multitudinis partes duodecimas, (nedum in tertias, quartas, sextas, alisaque Assis partes, quæ suis nominibus censeri solent, quales sunt Quincunx, Setunx, Bes, Dodrans, Decunx, & Deunx,) distributa suerint; in alias adhuc partes sine nomine dividi queant? Quippe sinon possint, retractandum videtur quod hic dicitur: si possint, retractandum erit quod modo dixerat, sect. 3. in horum unoquoque subjectorum nullam esse vel distinctionem vel extensionem; secandum utique erit, punctorum quodvis.
Postquam autem hæc dixerat, sect. 7. quodque hanc actualem, virtualemque divisionem Multitudo sibi principaliter æssumit, (cum Magnitudo potentialem tantum derivatamque participet;) ne sibi non statim contradiceret; sub jungit sect. 8. Ex hoc discrimine sequitur, Cunctam vim Multitudinis, (quæ certo, inquit, determinatoque partium numero conflatur,) modum in Divisione recipere, sive Divisionis terminos habere, ultra quos sectio amplius procedere nequit; Magnitudinem vero Divisionem in infinitum admiterre. Dic, quæso, (modo Oedipus sis) quî hæc simul constare possint, Nunquam ita dividi posse multitudinem, quin & pluribus aliis modis secari possit; Habere tamen certos divisionis terminos, ultra quos sectio nequit amplius procedere? Sed & endem plurius prosequitur, Nam, inquit, quando Multitudo dividitur, quia in illa partium numerus determinatur, necesse est ​divisionis modos in codem determinari; & consequenter potentiæ divisivæ vim, quæ tunc ad certos illos modos contrabitur alligaturque, aliquando, hauriri & tandem omino sisti,quando videlicet ad ultimam usque divisionem perventum erit. Atque ad hunc sensum plura.
Putan hæc sana esse posse omnia, quæ ita contradictionibus seatent?
Tum sect. 9. 10. Multitudinis ortum & incrementum, à Continuæ Magnitudinis Divisione, arcessere fatagit. Satis frigidè. Quippe ex suis omnino principiis oritur Multitudo, à continui natura plane diversis. Nisi & decem spirituum (quos modo memorabit) Multitudinem, ex Continui Sectione oram censeri velit. Rectius Euclidas; Multitudini, non ex divisione Continui, sed ex Unitatum compositione, ortum asscribit, 2. def. 7 Et quidem, si quando accidit, continuum aliquod in membra dividi; non eo magis Multa dicenda erunt, quàm si continua non fuissent: est utique ad hoc, omnino accidentarium, quod aliquando fuerint unum. Imo vero Numerus Quadrantum in eodem Continuo, Quaternarius non mi us jam est, quàm post sectionem erit.
Nec rectius sect. 11. 12. à Divisone rerumque Distinctione, Æqualitatem, Inæqualitatem, aliaque, similia, primum orta, dicit. Quippe eorum, quæ ab invicem satis distincta sunt, fieri potest ut nulla sit vel Æqualitas vel Inæqualitas; (puta Temporis, & Lineæ;) Æqualitas enim atque inæqualitas, non est nisi inver Homogenea; cum tamen & Heterogenea sint inter se satis Distincta. Sed & ejusdem Continui Duo similles sunt invicem Æquales, & Triens Quadrante Major, quamquam (suo sensu) neque Distincta sint neque Divisa; Quippe Dividi nihil aliud est, quam separari sive distingui, sect. 5. hoc est, sect. 2. inter se disjungi, propriisque extremitatibus terminari, atque ab invicem discreta esse, non continua. Et quidem Æquale esse, vel Inæquale, omino abstrahit ab eo quod res continuæ sint vel disjunctæ. Duæ Horæ Continuæ, non minus sunt inter se æquales, quàm si essent totis annis Disjunctæ. Sed & Idem est sibi-ipsi Æquale, (quippe tantundem est quantum ipsum est; quæ vera est Æqualitatis notio:) sed à seipso Distinctum esse vel Disjunctum, non erit dicendum. Item, si Æqualibus A, B, additur commune C, tota fiunt æqualia A+C & B+C (propter communem notionem, si æqualia æqualibus adantur, tota erunt æqualia;) cum tamen C, quod utrobique additur, non sit à se distinctum. Item, aggregata illa A+C, B+C, æqualia esse posse nemo negabit, quamquam non sint ita propriis extremitatibus terminata, ut ab alterius fine sint discreta, (quod ad Distinctionem requiritur, sect. 2.) sed sint in eodem C communicantia. Sed & Totem parte sua majus esse, nemo non dixerit, utut ab ea Distinctum atque Disjunctum non sit. Perperam itaque concludit, Æqualitatis atque Inæqualitatis principium non aliunde quam ab ipsa Divisione petendem. Quippe Æquale esse vel Inæquale; non minus est immediata Entis affectio, quam Continuum esse vel Discretum. Neque illud ab hoc ortum, magis quam hoc ab illo.
​Quod artem ait, sect, 13. Æqualitatem atque Inæqualitatem certas esse Quantitatum inter se habitudines; omnino verum est. Sed novum non est; quippe hoc ipsum norunt omnes; ipseque jam olim definiverat Euclides, nempe tum has, tum rationes alias, Homogeneorum invicem habitudeines esse, 3 def. 5. Quod vero mox sequitur, Sola quantitatum inter se comparatio, non sufficit ut æquales inæqualesve dicantur; sed inter se secundum corporis sui mole conferri debent: Quapropter Æqualitatem Inæqualitatemque certas esse Quantitatum inter se juxta corporis molem amplitudinemve comparatarum habitudines, colligere licet: Novum quidem est; sed verum non est: nec omnino admittenda est hæc sua Æqualitatis & Inæqualitatis definitio. Certum utique est, Æqualia esse posse atque Inæqualia, quæ corporis molem nullam habent, adeoque non possunt secundum hanc comparari: Sic duo tempora, æqualia possunt esse vel inæqualia; Sed & duo puncta duobus punctis, tria momenta tribus momentis, decem spiritus decem spiritibus; numero æquales esse possunt; utut non habeant, secundum quam comparentur, corporis molem. Requiritur utique ad Æqualitatem atque Inæqualitatem, non quidem sola quantitatum comparatio; verum etiam ut quantitates comparatæ sint Homogeneæ; (quod ex Euclide modo diximus;) ut juæta corporis molem amplitudinemve comparentur, non requiritur: ob causas modo dictas.
Neque tam ego ipsi hac in re contradico, quàm ipse sibi. Quippe (tanquam dictorum sect. 13. oblitus,) subjungit sect. 14. inter duos numeros, duas-ve lineas, (quæ molem corpoream non habent,) æqualitatem vel inæqualitatem repiri; non vero inter numerum atque lineam. Ar vero, quî fieri potest, ut numerus numero (qui corporis molem non habent) æqualis sit vel inæqualis, si ad hoc requiratur, ut juxta corporis molem comparentur? Imo vero, quæ molem habent corpoream, non est necesse ut quoad hanc comparentrur, quoties Æqualia dicantur vel Inæqualia. Posssunt utique duo corpora, longitudine æqualia, vel æeque alta, vel æque lata, vel æqualiter inclinata, vel etiam æque gravia dici; quæ quoad corporis molem sunt inæquala. Sic duo montes, duobus muribus, sunt æquales numero seu multitudine; utut non magnitudine seu corporis mole
Verum quidem est, inter lineam & numerum (quatenus tales) æqualitatem aut inæqualitatem non reperiri; utpote quantitates heterogeneas:) neque inter alias, quam quæ sunt ejusdem generis quantitates. Verum hoc non ille primus docuit, sed Euclides olim; (ut modo dictum est;) atque post illum alii, nedum qui illo suerunt superiores. (Quamquam hoc ipsum à Dulaurensio vix tuto dicitur; ut qui Æqualitatem atque Inæqualitate non in ipsa Qunatitatum Homogeneorum natura fundatem esse vult, sed in rerum Distinctione; adeoque Heterogeneis, utpote non minus inter se distinctis pariter convenire debent, atque Homogeneis:) Id autem requiritur, ut quoad saltem illud mensuræ genus, quo comparantur, sint homogeneæe; ut autm illud sit moles corporea, non requiritur. Sic Triangulum Pyramidiæque altum dici posse, (sin altitudine æquale,) nemo non dixerit?? utut ​hæc corporis molem habeat, illud non habeat: Quoniam quoad altitudinem (secundum quam comparantur) Homogenea sunt, utut alias Heterogenea. Dum vero ille, ad Æqualitatem aut Inæqualitatem requiri docet, ut juxta corpors melem comparentur; tu mecum juxta judicabis, credo, hoc minus sanum esse. (Sufficit utique ut juxta Longitudinem, Latitudinem, Altitudinem, angulum Inclinationis, Curvedinem, Durationem, Numerum, Vim, Pondus, Celeritatem, aut aliud quodcunque demum fuit quantitatis genus comparentur, quod utrique comparatorum commune sit; non minus quam juxta molem corporis.) Vides itaque quo tendunt ipsius nova principia, hucusque nondum tradita, quorum hoc unum est.
An Account of some Books.
THis Author makes it not his maine business in this Book to shew the progress of the Performance sand Effects of Chymistry, and to what pitch men are arrived thereby, to evince its great usefulness both in Physick and the Discovery of Nature (though he toucheth something of both;) but he chiefly informes the Curious of its first Original, and Progress from place to place, how it sprung up and flourished in Ægypt; passed thence, into Greece, Italy, Arabia, China, Spain, France, and all Europe. And because Conringius and Ursinus do mainly interpose in this Progress, he endeavours to remove the rubbs, which they cast in the way.
Here and there he inserts some Observations, which would be considerable enough, if they might be relyed on. E. g. About Metallick Germinations; where he relateth one of them, very admirable, seen by one San-Simon, to whom he giveth the Character of it man of great veracity, and of no credulity; who living about 25 years agoe at Brussels, was visited by a stranger, who having prefaced to him, what some had told him of his curiosity and ingenuity, as well as of his incredulity concerning ​the celebrated great things perform'd by Chimistry, said, that, to convince him, all was not vain what this Art professed, he did herewith trust him with a small powder, scarce of the weight of a Barly-corne, on condition, that after the process, he was to make with it, in 6 houres time, he should return it to him. This process was, That he should take 3 or 4l. of Fountain or River-water in a Glass, and call this powder into it, and by frequently shaking the Glass, make something of the powder incorporate with the water. Then, after some hours, he should decant the liquor into another Vessel, and dry the powder. All which the said San-Simon performed. The stranger being return'd at night, taketh his powder again, and bids San-Simon to put some ounces of common Mercury into the impregnated Water, and to look for a beneficial germination, when he was gone. Eight ounces being put in, after a little while there were seen to rise by little and little out of the Mercury a thousand small Silver-like branches or threds, spreading themselves every where through the whole Liquor, and shooting up even above the surface of the Water, on which appear'd here and there an oleosity, that was taken off, as being some matter of a grosse excrementitious nature, and heterogeneous to the substance it self of the Mercury, hindring the coagulation of the Mercury, but being remov'd, the Mercury runs and sticks close together, and becomes a firm Mettall. San-Simon having powred out the liquor into another Glass, gather'd the branches, and found them by the best Goldsmiths of that place esteem'd very excellent pure Silver, after the severest examinations by Fire, After this, San-Simon poures new Mercury to the remainder, and fees a new Wood arise like the former, very pure Silver likewise, repeating it to the sixth time, alwayes with good success, yet so, that by degrees the liquor grew languid, and at last was quite deprived of its force: many persons flocking in, and beholding the wonder.
Another Observation is of a Ductil Salt, said to have been made by himself of Sal Armoniack, often dissolved in a large Glass, and frequently and slowly Chrystallised, whence at length proceeded Chrystals as long as the Vessel was large; some of them being at times 6 inches long, flexible, and apt ​to be restored again into a streight line; This he illustrates by that substance, call'd Cornu Lunæ, which is nothing else, but Silver, whose texture is changed by the particles of acid Spirits, which is fusible at a Candle, and sequacious, and may be reduced into small leaves, transparent, and somewhat obedient to the Hammer. Farther, having taken notice that Glass is a very brittle body, because the surfaces, according to which its particles touch one another, are exceeding small; he excites Mens curiosity, to labour after a way, whereby the parts of Glass may be comminuted into such small parts, as to touch one another in many points, and that then malleable Glass will not be hard to make: All which he concludeth with examining Dr. Merrets Arguments, produced by him in his Ars Vitraria Englished; desiring that it may be made our, how the different figures of the Salts and Sands can remain unchanged by the violence of the Fire?
Besides, he relateth to have reduced Venice-glass into an Alcohol, and upon pouring hot distilled water upon it, drawn a small quantity of Salt out of it, (not a hundred part of the body of the Glass) of an unlike Figure to the Salt, which entred into the composition.
He examins also, whether common Salt may be changed into Vitriol, Alum, Niter. Some (among whom is Kircher) esteeming that the common Salt, according as 'tis variously tinged by Minerals, is sometimes converted into Niter, sometimes into Alum, sometimes into Vitriol, and yet may be reduced into common Salt again. But our Author finds not this in Laboratory's, but that Niter by a flaming fire degenerateth into an acid liquor; being burnt by coals, into a Lixiviat Salt highly different from the nature of Common Salt; if heated with Sulphur by an intense Fire, blown with Bellows in a close Vessel, into Stone; but hitherto by no art into common Salt, He thinks, Kircher has been deceived by this, that the Spirit of Niter being poured on Salt, maketh Crystals again in the appearance of recover'd Niter: But he saith, than this esculent Salt seems to be Niter but is not. For saith he, that any Niter results thence, is not to be assign'd to the Salt, but the Spirit of Niter, i. e. to the attenuated particles of ​Niter, conjoining themselves again by means of the Salt, to resume their pristine forme. Nor will Niter (adds he) or Allum, or Vitriol, if well purged, ever return into common escuflent Salt.
Yet this he grants to Kircher, that common Salt will turn into Niter, Alum, and Vitriol, when it hath changed its particles by the motion of subterraneous Fires, and so being comminuted into small particles hath converted its former Salt-taste into a present acid one, yet so as that for the composition of Niter there must be mixt some ramenta of Lixiviat Salt; for that of Alum, some ramenta of Lead; for that of Vitriol or Copperas, some of Iron or Copper.
Yet however this be, he denies, that there should lye concealed in the Center of common or Nitrous Salt any thing; that is unchangeable, coagulating and fixing all things; because an Artist can without any great difficulty bring both these Salts wholly over the Helme, and reduce them into a volatil Spirit, with but a very little sediment left behind; and can also reduce them both into an insipid Earth destitute of all vertue or operation, but only that, which is a little (but very little) adstringent; as may be seen by Blasius Vigenere, in his Tract de igne & Sale, but by his own Experiment affirmed to have been often and easily made; so as that the most purifyed salt, having its pungency obtunded by a fit and often repeated fire (whereby it may be often freed, dissolved, coagulated) will affect the tongue no more, than common Potters Earth.
Here he censureth, what Kircher affirms in his Mund, Subterr. viz. That in salt, how -much soever depurated, there will be found a true Earth, which though seemingly destitute of all salt, yet being for some dayes exposed to a clear sky and the Sun, will be again impregnated with new salt. To which he declares, that if Kircher had continued his method of purging salt to the utmost, he would have found, that the whole body of salt would have been at last thus changed into a saltless Earth, altogether inefficacious, save a little adstringency; directing withall, that he should have farther burnt the Earth, which he thought destitute of all salt, thoroughly, ​and boiled it in water, till it had altogether put off its salin taste, and that then he would have found, it would not have imbibed salt anew, any more than any other body calcin'd. 'Tis true, saith he, seeing the Air is full of salin steames, it cannot be otherwise, but that that cadaver of salt, having admitted the impression of the corpuscles flying in the Air, will taste saltish upon the Tongue, as all other bodies, that have past the fire; will do the like.
He relateth further, that two yeares agoe, when he was at Rome, in Clivo Scauri, there was digg'd out a whole house, which for above 10 Ages had been buried, from under the roots of herbes in a Garden of a Cittizen, a House of a very handsome structure, of Corinthian-work; and that there he met himself, among the rudera, very many vasa lacrymalia of Glass, which by length of time were become laminated into divers leaves, beautifyed with pavonaceous colous: the places like to Muscovy-Glass, fissil into leaves.
He maketh also mention of a vegetable seed, very common in the Fields of Denmark, which having been once heated red-hot, and then taken out and put in a cool place, would remaine hot and burning for fifty Houres together.
He describes also the method, which a certain Abbot, call'd Boncaudius, used to obtain a perpetual Heat; which was, that he thrust into the Earth a Pike oi about 20 foot long, and having thereby made a deep hole, (which was to be secured from the falling in of other matter) he poured into it ten pounds of Mercury, which by its ponderosity and the yielding of the subjacent soft Earth (for if that were hard and stony, or had springs of water, the effect was not like to follow) would continually sink lower and lower, and in some Moneths time insinuate it self into the lowermost parts of the Earth, and there meet with the Chambers of the subterraneous Heat; which issuing forth through that hole uncessantly, would moderately warm and cherish whatever should be placed over it; and so furnish us with a perpetual spring of warmth. Which device seems to our Author to be countenanced by what Acosta relateth Hist. Ind. l. 3. c. 19. viz. That in Guancavelica in ​Peru, whence is extracted store of Quicksilver, there is a perpetual spring oi Hot Water, and that not only it is a common complaint there, that the cataracts and fences of the Millers (whereby the water, necessary to drive the Mills, is kept in, that it may be sufficient for the work) are pierc'd through by Mercury, at times thrown in by malicious persons, to the great detriment of the Water and Mills; but also that 'tis notorious, that in some places there are deep under-ground Stoves and Pitts, which, when all others are frozen, steam out of their midst a tepid fume, the inward Bowels of the Earth thus constantly furnishing matter for calefaction, &c.
THis excellent Idea, very lately come out of the London-Press, in thin 8°, is drawn in that manner, as that 'tis demonstrated from the Principles of Art, and by Examples conformable to the Observations, which Pliny and Quintilian have made upon the most celebrated Pieces of the Antient PAINTERS; parallel'd with some works of the most famous Modern Painters, LEONARDO da VINCI, RAPHAEL URBINO, JULIO ROMANO, and N POUSSIN.
Those Principles of Art, constantly observ'd by the Antients in their Works, are here enumerated to be five: 1. Invention, or the History. 2, Proportion, or Symmetry. 3. Colour, (wherein is also contain'd the just dispensation of the Lights and Shades.) 4. Motion, in which are express'd the Actions and Passions. 5. The regular Position of the Figures of the whole Work. Of which the Invention and Expression are more Spiritual and refined; the Proportion, Colouring, and Perspective the more Mechanical part of this Art.
The Works, made use of among those of our most eminent Painters, for applying those Principles unto, are 1. the Judgment of Paris. 2. The Massacre of the Innocents. 3. Our Lords descent from the Cross, all three by Raphael. 4. The last Judgement of Michael Angelo. 5. The ​Representation of a Vast CYCLOP in a narrow Table by Timanthes. 6. Imitation of the same kind by Julio Romano. 7. The Gymnasium or Academy of the Athenian Philosophers, by Raphael. 8. The seven Sacraments by Poussin, the real Parallel of that famous Master-piece of Timanthes upon the sacrifice of Iphigenia.
All this is now represented in English with so much perspicuity, and rendred so weighty by every Period of the Excellent Interpreters addition, that it justly deserves high recommends, and will doubtless animate many among us to acquire a perfection in Pictures, Draughts and Chalcography, equal to our grow thin all sorts of Optical Aydes, and to the fulness of our modern Discoveries. Painting and Sculpture are the politest and noblest of Antient Arts, true, ingenuous, and claiming the Resemblance of Life, the Emulation of all Beauties, the fairest Records of all Appearances whether Celestial or Sublunary, whether Angelical, Divine or Humane. And what Art can be more helpful or more pleasing to a Philosophical Traveller, an Architect and every ingenious Mechanician? All which must be lame without it.
III. STEREOMETRICAL PROPOSITIONS, variously applicable, but particularly intended for GAGING, by ROB. ANDERSON: Printed in small 8°. 1668, LONDON.
WHat the Poet once said of a Gardner,
Sæpa etiam est Olitor valdè opportune locutus,
May congruously, in consideration of the Authour of this Book, be thus altered without marring the Verse;
Quandoque est Textor * valde opportuna locutus.
And as 'tis observe able, that sometimes among Tradesmen and others de plebe, are found very intelligent and sagacious persons, excelling others, that have confum'd their whole life in publick places of Learning, so should they awaken all, that profess the study of Arts and Sciences, not to dwell for ​ever in useless Notions and insignificant Generals, but to search after the Knowledge of those things which really enoble and enrich the Mind, and are beneficial to the Life of man, But, this by the by: The Book it self contains 25, considerable Propofitions, to touch some of which, we shall take notice, that
The 1. is to find the solidity of Pyramids and Cones, or frustum Pyramids and Cones, applicable to the Measuring of all Solids or Vessels of that form; whether whole or in part, or gradually, i.e. foot by foot, or inch by inch.
The 2$^d$ and 3$^d$, may be apply'd to the measuring of irregular Solids, and useful for the exact measuring of all sorts of Stone and Timber; also of all sorts of Elliptick, Parabolick and Hyperbolick irregular Solids, or Vessels made of that Form; seeing that such Solids may be cut into Parallelepipedons, Prismes and Pyramids, and then reduced to their own nature by the proportion of the Parallelogram, adscribed about those Figures, to the Figures themselves.
The 4th shews the measuring of frustum Pyramides, when their Bases are not parallel.
The 5th is about the relation of the Sphere and Spheroide, to the Cylinders of their bases and altitudes, as well of the parts as the whole.
The 6th hath the measuring of the midle Zone of a Sphere and Spheroide: And in regard that the midle Zone of a Spheroide hath been generally taken for the Figure representing a Cask, the one being measured, the other will be so also.
To pass, with the Author (in the Application of his Book) to the 12th Propos. there is the measuring of a portion of a Sphere, which is applicable to the measuring of the inverted Crown of Brewers Coppers, or several other uses.
The 13th gives the measuring of Parabolick Conoides, which may be taken for a Brewers Copper, the Crown inverted.
The 14th measureth the Hyperbolick Conoid, which may be taken for a Brewers Copper.
The 15th, 16th, 17th, and 18th give the measuring of a Sphere, Spheroid, Parabolick Conoid and Hyperbolick Conoid, as well the whole as their parts.
The 20th measureth Circular and Elliptick Spindles.
​The 21. measureth the 2$^d$ Section in a Sphere and Spheroid, which may be of use to measure the midle Zone of a Spheroid, cut by a Plane parallel to the axis; i.e. when the superfice of the liquor cuts the head of the Cask.
The 24th measureth right Cylindrick Hoofs, viz. Circular, Elliptick, Parabolick and Hyperbolick, and may be used for the measuring of Brewers leaning Vessels.
To these is added a Table of Squares and Cubes, very useful in finding the portions of a Sphere, Spheroid, Parabolick and Hyperbolick Conoides.
IN this small Tract is delivered out of the best Writers of this Subject, and the Author his own practice and observations, the Nature, Qualities, and Uses of the Stagg. In it is particularly considered the Longevity of this Animal, and its cause conjectured at, viz. the plenty of a Balsamick preservative Salt, with which 'tis said Nature hath stored this above many other Animals: Then the successive growth and annual casting off of its horns, together with the causes thereof, is examined, viz. its superabundance of Salin Juyce protruded, and then condensed by the Air (witness the great plenty of volatil Salt, that may be obtained out of those Hornes, as well as out of the blond and urine of the Stagg:) which matter being continually furnished from the body of the Animal, and passing uncessantly to the head, forceth away the old horns, and yearly substitutes new in their room.
But the Author chiefly and largely insists on the several uses of the parts of a Stagg, which he finds to be very many, and of divers kinds, viz. Ornamental, Mechanical, Culinary and Medicinal. Among the Culinary, he commends the young downy horns for a very delicious dish, used by the Grandees. And, as to the Medicinal, he enumerateth a vast number of them, especially of the volatile Salt, Spirit, Oyle, Magisrery, made of the several parts of the Stagg; where he inserts the particular uses of the ​Stag's tears, bloud, urine, dung; taking from the two latter occasion to commend the Medical usefulness of the Excrements of all sorts of Animals, as that of Swallows for the Colick; of Peacocks, for the falling sickness; of Dogs, (which they call Album Græcum for a disguise) against the Angina; of Hogs and Asses against Hæmorrhagies; of Cows, against the stings of Bees and Wasps, and other Inflammations; of Horses, against the Colick, Plurisie, Suffocation of the Matrix, expulsion of Fœtus, and the secundines; and that of Men, against the Plague, &c.
But the Principal uses in Physick, for which he commends the volatil Salt and Spirit made of the horns and bloud of Stags, is, its piercing, opening, attenuating, abstersive, discussing vertue.
He intersperseth here and there, as he hath occasion, many Philosophical and Spagitical remarques: e.g. How all Acids change the nature of volatil Salts: How nature produceth the volatil Salt out of Acids or fixed Salts: How plants, and divers parts of Animals may by their volatil Salts be Chymically represented: by what method the volatil Salt of Harts-horn may be freed from its ungrateful Smell, without much impairing its virtue: why Harts-horns taken off from the beast between the middle of August and that of September, yield more and stronger spirit: whether Harts-horn be better and more efficacious, when calcined, or crude, or prepared by a steamy heat: &c.
And among the many Medical prescripts, set clown here, the Author gives us the Podagrick unguent of the so much famed Franciscus Jos. Borrhi, made up of almost all the parts of a Stag: which how far it deserves commendations, must be learn'd from experience.
V. A Discourse of SPEECH, originally written in French by MONSIEUR CORDEMOY, now Englished in 12°. This Discourse, written conformably to the Cartesian Principles, hath been Formerly given an account of viz. Numb. 37. p. 236. and is only mention'd again here, because of its being now rendred English, for the use of those that are not skill'd in the French.
Errat. p. 766. l. 3. del so. p. 776. l. 14. r. actu. ib. l. 24. r. qain. p. 778. l. 1. r. autem.
In the SAVOY,
Printed by T.N. for John Martyn, Printer to the Royal Society, and are to be sold at the Bell a little without Temple-Bar, 1668.