# Philosophical Transactions of the Royal Society (1665-1886)/Volume 4/Number 46

Contents:
* Contents
* Promiscuous Additions to what was formerly publish't concerning Vegetation.⁠
* Some instances, shewing the Correspondence of the Pith and Timber with the Seed of the Plant; as also of the Bark or Sap in the Bark with the Pulp of the Fruit.⁠
* An Extract of a Letter, giving further directions about Melons.⁠
* A summary account of the Rules of Motion, by M. Hugens.⁠
* A narrative concerning the Resolution of Æquations in Numbers, by M. John Collins.⁠
* An Account of two Books,
** I. PRÆLUDIA BOTANICA Roberti Morison, M. D.⁠
** II. CL. SALMASII Præsatio in librum de HOMONYMIS HYLES JATRICÆ: Ejusdem de PLINIO IUDICIUM. Divione, A. 1668. in quarto.
Numb. 46.
PHILOSOPHICAL
TRANSACTIONS.
April 12. 1669.
The Contents.
       Promiscuous additions, made by Dr. Tong, to what was communicated by the same in Numb. 43. and 44. concerning Vegetation.
1. FOR perfecting the experiment of Sap, and to find out, whether it ascends more or less in the prict't Circles of the Body, then in those betwixt the Body and Bark; let the tree, exempted from all its sap the day before, be first peirced with an Auger, only through the Bark, and the quantity of Sap it yeilds, exactly measured and weighed: Then at the same time let also another hole be bored into the ​Body of the tree about 1½ inch deep, and so round, on every side of the same tree, and of others of the same sort, (all exhausted of their sap the day before) some deeper and some shallower, with a good large Auger; and one quite through, sloaping. From this experiment, after divers and various trials, may be found the difference of the Sap rising on the North and South in Sun and shade, and so likewise from that which comes from the Bark, and that which ascends in the inner part of the tree. The weight also may be compared of that, which issues from the Bark, with that which issues from the Body. The internall heart-sap may also be drawn apart, by boring a Smaller auger-hole in the midle of a Greater, and fitting it with a long pipe adjusted into the inner orifice. If no difference be found in these, by distillation after fermentation, nor otherwise, the presumption will be greater, that the difference of Heart (as when they call Heart of Oak) and Sap in Timber is not from the plenty or scarcity of sap, but from the season of felling.
2. From the observation of the woody Circle or pricks in the Branch, Arm or Body of a tree, it may be inquired, whether at such time when that Circle first encompass'd next the bark, the tree be or be not more subject to corruption, than at another season, when the jelly of the juyce is grown more condensed? I am inform'd by a curious and intelligent person, that the corruption of the Timber depends not upon the time of the year, and the ascent, or the plenty or scarcity of Sap so much, as upon the season of the Moon or Wind. And he affirms, that Timber-trees fell'd, when the wind is in the West, especially in the Old Moon, will keep them free from grubs (as they call it) i. e. from being worm-eaten; and on the contrary, that when cut down in an East winde, the worm will seize on them, in what season of the Moon soever it be fell'd: To prevent which corruption, 'tis advised, that such timber should be forthwith thrown into water. It's indeed worth inquiring, whether we may not ascribe somthing of the durableness of timber to the perfect condensation of the outward integument or coat, and so take care, that when trees are to be fell'd for timber or other durable materials, the outward coates may be of solid wood.
​3. Ethelbert Jay, an ingenious and expert planter in Lemster, supposeth, that the fittest time to inoculate is presently after mid-summer, because (saith he) the Sap descends; but I say, because 'tis then most plentiful, and begins to jelly. The same adscribes it to the sap ascending, to take the bud inoculated before mid-summer; and to the Sap descending, to take it after mid-summer. The time he limits to a few days before mid-summer, and to 8. or 10. dayes after it. Mr. Austin limits 14 dayes before, and as many after; and would have the bud unty'd after 14, days, as I remember.
4. It is all one, whether the Sap be exhausted below, by being converted into wood, roots, or other uses; or by diversion, as when the branch is cut, or the bark opened below: The Sap in both cases descends or rather sinks indifferently to supply the defect, and heal the wound; and so it coms to pass, that there being about mid-summer the greatest plenty of sap in apple- trees, a bud then inoculated will thrive, especially before mid-summer; for then it drawes its share in the Sap ascending, and, all the necessary uses of the upper branches being serv'd, it partakes of the flood of the abounding and superfluous Sap, remitted to it from them.
5. Hence I conclude, that to gird a tree at a convenient distance above the inoculated bud before mid-summer (so as is practised to stay the bleeding of Vines, to gird them below) is an experiment worth trying; that we may know, whether it will cause a stronger shoot of an inoculated bud or no? Or whether it be better, to cut off the head of the stock above the inoculated bud; which my friend informes me will make a better shoot, than in the usual inoculation, if this be done a few dayes before mid-summer. Further, when you gird, it must be tryed in several trees, whether girding long before mid-summer will not stay the ascent of the sap, and cutting of the head, much more? Whereby time may be gained by retarding the season of inoculation, to their benefit, who have very many to inoculate; and in wet season to stay for dry weather, onely fit for this work.
6. If then the Sap in it's subsiding be so considerable in the matter oi inoculation, it seems, that inoculation will hold best ​and longest in season in the Root. For I have observed the Sap to subside unto the Roots out of the Body at such times of the day and year, when in the Branches I found none to spare.
7. If Binding, or Cutting off the Head advances the shoot of the inoculated bud, then it ought to be experimented, Whether disbarking a few days before Midsummer on the contraries side, a little below the bud, and having wax apply'd or clay on the part disbark'd, may not by that direction of the Sap, necessitating it to pass by the bud, further its growth considerably; or, which is better, a gash cut in the wood in that place.
8. To make a barren Tree beare again, cherish, dung in trenches, and pare and renew the extremity's of its longest Roots, and cut off the outermost and shortest, nearest the Body. Hence it may seem, that Plowing helps Fruit-trees.
9. Crosse hackings promote fruitfulness, cure the Phyllomania, whereof the reason seems to be, that (as was above intimated) Outward Circles and Bark seed the Wood, and the Inner onely reach out to the uttermost spriggs of the last year, to which the Fruit is appendant. For, some Trees bear only on this years shoot, an some only on that of the last, possibly some only on the third years shoot; and cease bearing, when they shoot no new spriggs. Seasonable baring the Roots, which they call Ablaqueation, probably hath the same effect, because it hinders the nourishment especially of the outward coates, and of barke, leaves, and suckers: But, because it seems, that, as some suckers or shoots, lately sprung in outward coats, robb the fruit of the risen Iuyce, so later roots, come from the outward parts of the maine roots, rob them also of their first nourishment in the earth; they ought to be pruned, as well as all suckers and not- bearing branches and spriggs, every year. For which reason also, the better to increase and amend fruit, it may be observed, what was recommended above to the 15th Querie, viz. The applying of dung and other amendments in trenches nigh to and beyond the farthest points of the Roots, to draw them out of the shade and drops. To this end, Distance-and situation is to be observed.
​10. One of the best ways of obtaining the greatest store of Sap in the shorest time from the Body of any Tree, is, Not only to pierce the Bark, not to cut the Body with a chizel, almost to the Pith, (as some have directed,) but quite thorow all the Circles and the inner Rind it self, on both Hdes of the Pith, leaving only the outermost Circle and the Bark on the North-East-side unpierced. But this hole is ro be bored sloaping upwards, as large as the biggest Auger, you can get, will make; and that also thorough and under a large Arm near the ground. So will it not need any stone to keep open the orifice; nor Spigot, to direct the Sap into the Receiver. This way, the Tree will in short time afford liquor enough to brew with it. And with some of thes sweet Saps one bushell o£ Malt will make as good Ale, as four bushels with ordinary water, though you should brew even in March, held the properest time for brewing in regard of the goodness of the water at than season. Sycamore I take to yeild the best brewing Sap, being very sweet and wholesom.
11. To preserve Sap in the bell condition, for Brewing, what you gather first, must be insolated by a constant exposure of it to the Sun in Glasses or other fit vessels, till the rest be gather'd and ready; otherwise it will soon contract an acidity. Having been thus expos'd to the Sun, till a sufficient quantity is collected; put into it so much very thin cut and hard tosted but no ways burnt Ry-bread, as will serve to ferment it; and when it works, take out the Bread, and botle the liquor, stopping it up with waxed Corks. IF you bake Sage or any other Medicinal herbs in such thin Ry-paste, till they be very dry, you may expect a very wholesome drink, If you put a few Cloves in every Glass, into which the Sap runs from the Tree, it will certainly keep a twelf-month. But I have wonder'd, whilest I observ'd, How speedily it drew the taste and tincture of the Clove. In some few bottles I was so happy as to draw out my Cloves, with a cloth, in which I tyed them-up, in such a season, as not to change colour not taste; and yet I preserv'd the Birch-sap by that slight fermentation above a twelf month without any alteration, which else would have sowr'd in a few days.
​12. Some propose Oyle of Sulphur to perfume the Bottles with. I know not, whether that alter the tast; or onely stay the naturall fermentation; or what other change it gives the Sap.
13. Spirit of Wine ferments the Iuyce of some Berries, and possibly may not only preserve but advance the vertue of Saps; a little being powred on the top of them in the botles; or some other Oily Spirit.
14. Raisin infused in the liquor of Birch, is one Ingredient of the Durham-Gardner. I have been inform'd, that he uses Sugar; but I beleive, he puts it not in, till he opens a Botle, presently to be drunk, because it maketh the liquor sparkle in the Glasse.
15. A certain Lady ferments it with Ry-tost, not put in but only hung over it, in such quantity and at such distance, as may give some light warmth, motion and alteration to the surface of the liquor.
16. I fermented some with Ale-barm, which converted my delicat Birch-Iuyce, kept in Bottles, into pitifull small beer, which I wondred at; for I know one, who used by the barm of Ale to improve smal Beer, and thereby to keep it the better in Vessels.
17. I persuade my self, that Birch-water fermented by the Flemish Wheat-ferment, without any barm, would in time be excellently matur'd in Bottles; but not in a small time.
18. Let Cynamon also be try'd among the Ferments of these Iuyces. Hony will not mixe with Cyder though boyl'd therein to make Meath; but after a while the Cyder lets fall the Hony, and becomes simple Cyder again; Q. Whether it will not be so also in Birch-sap?
19. Some affirm, that the Tops and Leaves of Birch, decocted in the Sap, will preserve it from Sowring the whole year; and that any sort of dry'd Aromatick herbs, as Sage &c. boyled in beer, will keep it as well as Hops, Ling (Heath) Broom, or Worm-wood. I had a friend, who us'd Bay-leaves in his Beer and Ale. These things I propose to tryall, with green leaves and tops of the same year; decoct and dry leaves and herbs, infus'd or boyl'd, or former. The inner Bark yields Oyle, and probably, when infus'd will preserve Iuyces. So you have Oyle, Vinegar, and Wine from our own native Trees.
​20. Delicate and light French Manchet, tosted, may possibly be also good for our Sapps.
21. For the clearing of what was delivered Num. 43. p. 858. about prickt Circles in Trees, it may be added, That those Circle are suppos'd to be at some time of the year of one single row or pricks, and at some season, of more, and at others, of solid wood. Quere, 1. What alteration is found in Circles of Pricks, or Wood, in Spring, at Midsummer, and in Autumn &c? 2. Whether these single or double Circles of pricks and coats of Ielly or wood, increase betwixt the inner and outward bark, or not? Or, betwixt the one. and both of the barks, i. e. on one or both tides of the inner bark? I conceive, it doth on both sides of the inner bark, so that in some thick outward Barks those Circles mayo be observ'd, as in Wood. 3. Whether the Tree receives increase in all its inner coats, so as every coat yearly grows thicker, or in the outtermost only, or in some of the outward coats also?
Dr. John Beals Instances
    Promised in Numb. 42. and intended to shew the Correspondence of the Pith and Timber, with the Seed of the Plant; and that of the Bark or Sap in the bark, with the Pulp of the Fruit, so some encompassing Coat, or Cod containing the Seed.
The Author having prefaced, that he can promise no Method in the following Communications, gives these Instances.
First saith he, I had an excellent Summer-Apple, containing abundance of very pleasing Iuyce. It was of that kind, which never grows large. The Body by the burthen of the fruit always wreath'd towards the ground; the Branches all curld, and full of knots at every turning; and these branches apt to grow, if a good knot be set in the ground, assoon as 'tis cut off, especially about Candel-masse. This Tree was hollow, and very near all the Timber extremely rotten from the top of the Stem to the root; and every sprigg, how small however, appear'd Cork-color'd and rotten at the heart of the Timber. And so it was generally all over the Roots; and 'tis like, it had been so many years before: Yet the Tree bore ​abudantly with alternative rests every second or third year. The fruit had scarce any core; the kernels were very small; thin and emptie; neverthelesse the branches from the knots grew well enough to replenish a Nursery for me. This seems to indicate the Correspondence between the Pithy part, Heart or Timber, and the Seeds. And more to confirme this; A youug tree grew like a Sucker from the only sound Root of the aforesaid Apple-tree. This tree grew straiter then others of the same kinde usually do; of which I conceive the cause to be this: Suckers are commonly barren a pretty long time; and this continued barren, til the stem was strong enough to bear the fruit which loaded the branches. But that, which makes to our purpose, is this; All the fruit of r his young tree had ful and sound Kernels, and though it was the same fruit, growing from the Root of the same tree; yet it seem'd-not altogether so tender, delicious and juycy, as the fruit of the old tree; nor yet was the tree so fruitfull. The Sap in the old tree was less diverted, it seems, to sustaine the life of the timber, which was now confirmed; and thereby was wholy appropriated for the leaf, blossom, and the pulp of the fruit. For I do not undertake, that the Sap yeilds no relief to sustain the life and growth of the timber ordinarily, and whilst the timber is entire; but I rather conceive, that there is a more immediate and peculiar relation between the Sap and Pulpous fruit, and the like between the Timber or whole stock, and the Root of the Tree, to transmit the same spirit and nature to the Seed of what kind soever it be.
Some are of opinion, that there passes into the Timber no part of meer Earth to sustain the life and growth of the Plant, but it only feeds on the succulent part ascending by the Roots, and on the Air, and the moisture, which-the Dews of Heaven, the Rainy seasons, and the Air afford. And if we consider, that some lofty trees grow upon the Rocks, where little or no earth can be found; as also, how largly the Oak and Pear-tree grows and spreads, and how many years the one bears Acorns, the other Pears, somtimes to the quantity of yeilding 5. or 6. hogsheads yearly (as I have known them do;) and in comparison how little wast of Earth about the roots appears; we may find more cause to attribute this large expence of materials to the ​perpetual supply of Moisture, than of much Earth, I will give you an experiment, which-may seem to determine the point, though I yet suspend my Judgment.
took the largest of Kentish Codlins, Pearmains, Pepins and Deuxans; I wither'd them (which may be soon done many ways;) and then I cut them in the midle quite through the midst of the kernels, having carried them some dayes in my pocquet; all that saw them, took them to be very wood, and they were indeed like very close Cork. And some Philosophical persons (though I affirm'd no falshood, but concea'd the whole matter) did upon the view spread it abroad, that I had the Art of converting all Fruit into Wood; pulp and kernels and all was wood. The same may be done upon Pears, Cowcumbers, Turnips, and all the Grains and Vegetable Seeds, that are stuck in them, and are cherish'd by a supply of Marly Water. Thus I have had the blades of Wheat and the helme of Pease grow out of them to the length of a foot, and then by hanging it in a closet, all becoms turn'd into wood; and in some time after, all is turnd into Dust and Earth. And as we are well taught by Master Boyle, that pure Liquids may be converted into Earth; so these Terrestrial parts of the Fruit may be from the Liquors thither collected, and derived from the Mass of the Earth.
But to return to the clearing of the affinities above claimed; I Instance in Berbery roots, perforated by me, which bore Berries, that had no stones at all: And in hollow'd Apple-trees the kernels will be very thin, and empty skins, and incapable of growth. Gardeners tell me, that if you take the hard stick out of the root of Parsly, it will bear no kind seed. But it may be objected, that-a very hollow Oak and an hollow Elme doe bear pregnant seed. I answer, that an Elme is all Timber to the Bark; and an Oak, when 'tis all putrid at the heart, yet may have firm wood enough to convey the Spirit of the root into the Acorn; and the Roots may be found, when the Body of the Tree is much decayed by rain, beating in at the lopp'd tops, or by other passages through the Bark. We see, that Beans, Wheat, and other Grain grow kindly, if the Eyes and parts next adjoining be whole, though the Beans be lull of great holes in other parts, or the main body of the Wheat be cut off with Scissers. ​However, let the objection give us the more Caution, that, if we dessein to a Fruit without Stones, the perforation may be the bolder and the more compleat.
And to proceed further, some Trees are lesse fruitfull, or altogether barren by the excessive growth and firmness of the Timber; and these are recover'd by cross deep hacking: through the Bark: And such injuries done to the Timber both in the Stem and main Roots, they cleave the Roots, and put a stone in the cleft, that it may not close again too hastily. If this violence be not done both to the Stem and Roots, the remedy may fail. We see also, that Vines are less fruitful, when they are permitted to run out into many woody branches.
II. To shew also the Proximity between the Sap of the Bark and the Pulp of the Fruit; I did in Summer-time make Rests for water on the body of Kentish Codlin-trees, and caus'd water to be frequently powred into those Cavities. The effect was this, the Apples grew to an extraordinary bigness, and were very insipid, and many of them had parts in appearance much like the pulp of Lemons: some I suffered to hang on the Tree as long as they would, and those became full of Spots of the Colour of Corke, or like the rotteness of an Apple.
I omit the rest, and hasten to redouble a remark of the great use, which maybe made of the cheif Experiment. The Graft carries the mastery from the Stock for the Pulp of the fruit; So that we have little hope of much change by meer Graftings, how oft soever iterated. But if after many, and strange, and choice Engraftings you set the Kernel, Stone, or Seed of the grafted Fruit in a Kind Mould, you may then expect some new or mingled kinde of Plant, as Semi-Apricocks, &c. And thus the Almond and Peach may by many changes in the Graftings, and by Inteneration of the Stones of the Peaches, and of the Shell of the Almonds, and by Terebrations of the Stem and Root here and there, alter their guises, so that the Coat of the Almond may approach to the Pulp or the Peach, and the kernel of a Peach be enlarged to a kinde of Almond; and great store of better contrivances may from hence take rise.
Extract of a Letter
MY great care this last Month* * This letter was written June 15th. St. Nov. in Parishath been, altogether to remove the smal feeble branches (on which 'tis not likely that any or any good fruit will grow) and to leave none but good branches. When-ever you have a Melon, which coms well, knit on a branch, you must not fail to cut away the rest of that branch, on this side of the fruit, to the end that all the nourishment, that would have been dispersed into the whole branch, may pass into that fruit, which is found at the extremity of the branch; taking care notwithstanding, that the fruit be covered by some leavs of the other branches, for its better growth under the shade, in those parts where 'tis very hot.
As to the time of the maturity of Melons, I must tel you, that I should have begun to eat some, 8. or 10. dayes agoe; but that the Season hath been very unkind for 3. months together, a North-winde having reigned all that time, and reigning still, and causing cold nights; insomuch that I have not yet remov'd my Glass-bells from them, which else I had done 3. weeks agoe. I had knitted ones since the end of April, so that, there commonly needing no more than 40. days from the time of a Melons knitting to that of its ripeness, I should have eat of them before-this time. But to tel you the truth, I have the advantage mage of having Melons knit, 3. weeks sooner, than any body, I know, in this Country.
For the keeping of the Seed, you must take no other Seed, but such, as is found in that part of the Melon, which hath been towards the Sun: And at the same time you eat the Melons, you must well cleanse such Seeds, and rub them with a linnen cloth, until they be very clean and dry; then putting them up in some convenient Closet till Seed-time.
Remember, not to eat the Melons but some 24. hours after they have been gather'd; putting them in the mean time in a ​place, neither too hot nor too cold, and free from any dry scents, good or ill.
Observe also, to gather them seasonably, when they are neither too ripe nor too green: which you may know by their Yellowish Colour, and by their Taile, commonly splitting, and their Smel. A Melon ordinarily requireth one day from the time of its being smitten, to that of its being gather'd. I call the time of its being smitten, when it begins to shew its being ripe by a little Yellowness, appearing in some part or other of it. This will oblige you, (as I also admonished in my former) to walk through the Melon-garden 2. or 3. times a day, mornings, at noon, and in the evening.
A Melon, that ripens too fast, is never good, such a ripeness not being a good one, but proceeding from the poorness or sickness of the foot, which maketh it thus turn suddenly.
The Melon mutt be full, without any vacuity, which, you know, is discern'd by knocking upon it. And the meat must be dry, no water running out; only a little dew is to appear, issuing out of the Pulp; which must be of a very Vermilion Colour.
Trouble not your self to have big Melons, but good ones. Those who covet great Melons, may have their desires either by sowing Seeds of the great kinds, or by much watering others; Which watering is a thing, wherein great care and discretion is to be used. As I have hitherto kept my Glasses over my Melons, yet so that within this month they are raised from the ground to the height of 4. inches, supported by smal forks; so I seldom water them, and but little at a time; which is once every Week. In short, you must judge of the necessity of watering by the Vigour, which is required in the foot and leaves, without which the fruit cannot be good for want of good nourishment.
A Summary Account
BEfore these Rules of Motion be here deliver'd, 'tis necessary to preface something, whereby the worthy Author of them may receive what is unquestionably due to him, yet without derogating from others, with whom in substance he agreeth. But, forasmuch as this Subject is of that nature, that all Philosophy and generally all Learn'd men are therein concern'd, it will be most proper, to publish these Rules, as well as we did those of D. Wallis and D. Wren (Numb 43) in the Language of the Learn'd, together with some Historicall passages relating thereto: Which we now doe, as follows.
CUm novissimis mensibus nonnulli e Societate Regia in publico ejusdem Consessu enixius urgerent, ut gravissimum illud de Regulis Motus Argumentum, non semel inter Ipsos ante hac agitatum, sed, pluribus aliis intercurrentibus rebus, nunquam, uti par erat, discussum expensumve, tandem aliquando Examini rigido subjectum conficeretur; Visum equidem fuit Illustrissimo isti Cætui decernere, ut quotquot e Sociis suis indagandæ Motus indoli præ cæteris incubuissent, rogarentur, ut sua in rem illam Meditata et Inventa depromere, simul et ea, quæ ab aliis Viris præcellentibus, Gallilæo puta, Cartesio, Honorato Fabri, Ioachimo Iungio, Petro Borrelli, aliisque, de argumento isto fuerant excogitata, congerere & procurare vellent; eo scil, fine, ut consultis hoc pacto collatisque omnium sententiis illa dehinc Theoria, quæ cum Observationibus et Experimentis, debitâ cura et fide crebo peractis, quam maximo congrueret, Civitate philosophica suo Iure donaretur.
Edito hoc celeusmate, incitati protinus e dicta Socictate fuerant, imprimis Christianus Hugenius, Iohannes Wallisius, Christophorus Wrennus, ut suas de Motu Hypotheses et Regulas, quibus condendis aliquamdiu insudassent, maturare atque ​expedire satagerent. Factum hinc, ut selectus ille Virorum præstantissimorum Trias, post pancarum septimanarum spatium, Theorias suas, eleganter compendifactas, tantum non certatim transmitterent, Regiæque Societatis super iis sententiam exquirerent. Primus omnium D. Wallisius, sua de Motibus æstimandis Principia, literis d. 15. Novemb. 1668. datis, ejusdemque mensis die 29, traditis et prælectis, communicavit. Mox eum excepit D. Christophorus Wren, qui Naturæ Legem de Collisione Corporum, proximo mense Decembri, ejusque die 17. eidem Societati publico exhiberi curavit: quæ in mandatis mox dedit (præ-habito tamen utriusque hujus Authoris consensu) ut ad commodiorem horum Scriptorum communicationem, discussionemque diffusiorem, res tota typis mandaretur.
Hæc dum apud Nos geruntur, Ecce adfert Nobis tabellarius d. 4. Ianuarij insequentis (St. Angl.) Dn. Hugenii literas, ejusdem Mensis d. 5. (at st. nov.) exaratas, ejusque Scripti, de Motu Corporum ex mutuo impulsu, priores Regulas quatuor, una cum demonstrationibus, continentes. Habebam ego in promptu Theoriæ Wrennianæ Apographum, idque actutum eodem plane die, sic favente Tabellione publico, D. Hugenio, redhostimenti vice, remittebam, dilata interim literarum Hugenianarum (quibus tale quid includi, ob molem, et antegressum Authoris promissum, suspicabar) resignatione, donec ferret occasio Nobilissimum et. Sapientisimum Regiæ Societatis Præsidem, Dn. Vice-Comitem Brouncker, compellandi. Quo facto, amborumque Regulis in modo dicta Societate collatis, mirus confestim in utroque consensus offulsit; id quod insignem in nobis lubentiam pariebat, utrumquq hoc Scriptum prælo nostro committendi. Nihil hic nobis deerat a parte Hugenii, quam ejus consensus; absque quo fas nequaquam judicabamus, ipsius Inventum, maxime cum illud haud integrum eo tempore nobis dedisset, in lucem emittere. Curæ interim nobis erat, scriptum Ipsius publicis Regiæ Societatis monumentis inserendi; simul & Authori d. 11. Januar. solennes pro cordata illa communicatione gratias reponendi; additâ dehinc (die scil. 4 Februarij) sollicitâ commonefactione, ut suam hanc Theoriam vel Parisiis (quod proclive erat factu in Etuditorum, ut vocant, Diario) vel hic Londini in Adversariis Philosophicis, inprimendam curaret, vel saltem parmitteret. Quibus expeditis litteris ​paulo post secundas accepimus ab Hugenio, scripti Wrenniani de hoc argumento recte traditi mentionem facientes, nil tamen quidquam de suimet scripti Editions, vel Parisiis vel Londini paranda, commemorantes.
Unde liquere omnino autumem, ipsum sibi defuisse Hugenium in illa publicatione maturanda; quin imo occasionem dedisse procrastinando, ut laudatus Dn. Wren, pro ingenii sui sagacitate geminam omnio Theoriam eruens, in gloriæ, huic Speculationi debite, partem jure veniret; cum extra omne sit dubium, neutrum horum Theoriæ illius quicquam, priusquam Scripta eorum simul comparerent, rescivisse ab altero, sed utrumque, proprâ ingenii fæcunditate, pulchellam hanc sobolem enixum fuisse.
Solvit equidem Hugenius, ante aliquot jam annos, Londini cum ageret, illos de Motu Casus qui ipsi tunc proponebantur; luculento sane argumento, cum jam tum exploratas habuisse Regulas, quaram id evidentià præstaret. At non affirmabit ipse, cuiquam se Anglorum suæ Theoriæ quicquam aperuisse; quin fateri tenetur, se ab eorum nonullis ad communicationem ejus sollicitatum, nec tamen unquam, nisi nuperrime, ad id faciendum pertractum fuisse.
His itaque veritati et Iustitiæ litatis, ipsas jam Hugenii Regulas sermone Latino, in ampliorem Eruditorum usum, sic donamus.
Regulæ de Motu Corporum ex mutuo impulsu.
1. Si Corpori quescenti duro aliud æquale Corpus durum ocurrat, post concatum hoc quidem quiescet, quiescenti verp acquiretur eadem quæ fuit in Impellente celeritas.
2. At si alterum illud Corpus æquale etiam moveatur, feraturque in eadem linea recta, post contactum permutatis invicem celeritatibus ferentur.
3. Corpus quamlibet magnum à corpore quamlibet exiguo et qualicunque celeritate impacto movetur.
4. Regula generalis determinandi motum, quem corpora dura per occursum suum directum acquirunt, hæc est:
Sint Corpara A et B, quorum A moveatur celeritate A D, B. verso ipsi occurrat, vel in eandem partem moveatur celeritate ​B D, vel denique quiescat, hoc est, cadat in hoc casu punctum in B. Divisà lineà A B in C, (centro gravitatis Corporum A B.) sumatur C E æqualis C D. Dico, E A hebebit celeritatem corporis A post occursum; E B vero, corporis B, et utrumque in eam partem, quam demonstrat Ordo punctorum E A, E B. Quod si E incidat in punctum A vel B, ad quietem redigentur corpora A vel B.
5. Quantitas motus duorum Corporum augeri miniuive potest per eorum occursum; at semper ibi remanet eadam quantitas versus eandem partem, ablatâ inde quantitate motus contrariì.
6. Summà Productaram factorum à mole cujuslibet corporis duri, ducta in Quadratum suæ Celeritatis, eadem semprr est anté et post occursum eorum.
7. Corpus durum quiescens, accipiet plus motus ab alio corpore duro, se majori minorive, per alicujus tertii, quod mediæ fuerit quantitatis, interpositionem, quam si percussum ab eo fuisset immediatè. Et si corpus illud interpositum, fuerit medium proportinale inter duo reliqua, fortius aget in quiscens.
Corsiderat Author in bis omnibus (ut ipse ait) Corpora ejusdem materia, sive id vult, ut eorum moles astimetur ex pondere.
Cæterim subjngit, notasse se miram quandam Naturæ legem, qua demonstrare se posse affirmat in corporibus Sphæricis, quæque generalis ipsi u datur in reliquis omnibus sive duris sive mollibus, sive directe sive oblique sibi occurrentibus, viz. Centrum commune Gravitatis duorum, trium, sel eu rhbet Corporum, æqualiter semper promoveri versus eandem partem in linea recta, ante et post occursum.
       An AccountConcerning the Resolution of Equations in Numbers; imparted by Mr. Iohn Collins.
This Account should have been annex'd to what was discoursed of Monsieur Slusius his Mesolabe in the precedent Tract, if then we had found room for it. For, the Reader having there understood, how farr the Geometrick part of Algebra is advanc'd by that excellent person, 'twas likely, he would be inquisitive to hear somewhat concerning the Exegeis Numerosa, or the Resolution of AEquations in Numbers. For whose satisfaction herein, we shall here insert the Account then omitted, being part of a narrative, formerly made by M. Iohn Collins touching some late Improvements of Algebra in England, upon the occasion of its being alledged, that none at all were made since Des Cartes.
1. It hath been observ'd by divers of this Nation, than in any Equation, howsoever affected, if you give a Root, and find the Absolute number or Resolvend (which Vieta calls Homogeneum Comparationis) and again give more Roots and find more Resolvends, that if these Roots or rather rank of Roots be assum'd in Arithmetical progression, the Resolvends, as to their first, second or third differences, &c., imitate the Laws of the pure Powers of an Arithmetical progression of the same degree, that the higest Power or first term of the Equation is of. e. g. In this Equation aaa—3 aa + 4a = N,
| | | | | | | 1. dif | 2. dif | 3. dif. |
| If a be = | 10 | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | Then N. or the | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | 740 | 218 |
| If a be = | 9 | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | Absolutes or Re- | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | 522 | 218 | 48 |
| If a be = | 8 | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | Absolutes or Re- | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | 352 | 170 | 42 | 6 |
| If a be = | 8 | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | solvends will be | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | 352 | 128 | 42 | 6 |
| If a be = | 7 | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | found to be | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | 224 | 92 | 36 |
| If a be = | 6. | $\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$ | | $\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right\}\,$ | 132 | 92 |
To wit the 3d. differences of those Absolutes are equal, as, in the Cubes of an Arithmetical Progression.
2. To find, what habitude those differences have to the Coefficient, of the Equation, 'st best to begin from an Unit.
3. In any Arithmetical Progression, if you multiply ​Numbers by pairs, you shall create a rank of Numbers whose 2d. differences are equal; and if by ternaries, then the 3d. differences of those Products shall be equal. And how to find the greatest Product of an Arithmetical Progression of any number of terms having any common difference assign'd, contain'd in any Number proposed, is shew'd by Pascal in his Tract du Triangle Aritbmetique, where he apply's it to the Extraction of the Roots of simple powers.
4. It appears, How this rank may be caried easily by Addition, till you have a Resolvend either equall or greater or lesse, than that proposed.
5. When you have a Majus and Minus, you may interpole as many more termes in the Arithmetical Progression as you will, that is to say, Subdivide the Common difference in the Arithmetical Progression, and render it lesse; and then renew, and find the Resolvends, which are easily obtain'd out of the Powers and their Coefficients, which are suppos'd knowe, and may be readily rais'd from a Table of Squares and Cubes, &c. with which kind the Reader may be furnisht in Guldini Centrobaryca and Babingtons Fireworks: By this means you may obtain divers Figures of the Root; and then the General Method of Vieta and Harriot runs away more easily, and is so far improv'd, that after any figure is plac'd in the Root, most certain Characters are given to know by aide of the subsequent Dividend and Divisor, Whether the figure before assum'd be too great or too small: or lastly it may well be concluded, that, as in Logarithmes, when you propose, such an one as is not absolutely given in the Canon, you doe by Proportional Work, using the aid of their first differences (when their Absolute Numbers differ by Unit) find the absolute Number true to 5. or 6. places further than the Canoon gives it (the reason whereof is, that the first Differences doe likewise agree to about the same Number of places;) that I say, the like maybe done in, Æquations, after divers of the first figures of the root are found; provided there be the like agreement in the first differences of the interpoled Resolvends.
Moreover we ought here remake notice of a more subtle kind of Interpolation, common to all gradual Ranks or Progressions of Numbers, wherein Differences happen to be equal: Of which ​kind the Reader may find Examples in Briggii Arithmetica Logarithmica et Trigonametria Britannica, relating to Logarithmes, Sines, and the Powers of an Arithmetical Progression: But the method there deliver'd may be rendred more easy and general, viz. by aid of a Table of figurat Numbers, by deriving Generating differences sought, from those given; a doctrine, that easily flows from Mercators Logarithmotechnia, and of use in the Case in hand, should we suppose these Powers and their Coefficients vnknown, or a Table of Squares and Cubes wanting, and give nothing more, than a few Resolvends belonging to equal Moments or Spaces. And this may likewise be of good use in Guaging, when having the Contents of a Solid, for every 3. Inches, more or lesse, given, without knowing the dimensions of the Figure, and even in most Cafes, when the differences are Progressive of one kind, without knowing the Figure it self, having nothing given but its Contents at several equal Parallel distances, each such distance may be subdivided, and made as many as you please, and the respective Contents found by this general Method of Interpolation.*
* Nota. The Author (M. Collins) haveing explain'd Mercators Logarithmotechnia in English, and illustrated the elegant Doctrine thereof with Examples, hath likewise handled this work of Interpolation, and makes the Logarithemes true to 25. or 30. places of figures by meer Division (or Proportion;) having herein advanc'd that Author's doctrine therof by Division, which (as 'tis there illustrated) did not seem to extend farr enough. This hath already been communicated, some Months since, to some of the Members of the R. Society, and may be expected hereafter.After one Root is obtained, the Methods of Huddenius and others will depresse the Equations so as to obtain more, and consequently all of them.
6. It is easy, by a Table of figurate Numbers to give the sum of any such Rank or any term in it relating to a known part of the Series of Equals or Roots; but è coverso, giving the Resolvend to find the Root, coms to an Eqnation as difficult as that proposed; as in D. Wallis his Chapter of Figurate Numbers.
7. Some affirm, they can give good Approaches for the obtaining a Root of any pure power, affected Equation, or for the finding of any of the mean Proportionals in any Rank between two extreams given.
8. Others pretend to have found out a method (incited thereto an example in Albert Gerards Invention Nouuelle en Algebre à Amsterdam 1629.) so much, by comparing of Equations, to ​increase or diminish the unknown Root of Equation, as to render it a whole number (or lesse differing therefrom, than any Error assign'd,) and by Albert Gerards Method of Aliquot parts to find the same, and thereby the Root sought, although it be a Mixt Number, Fraction, or Surd.
Probably this may sympathise with what is promised by the Learned Huddenis in Annexis Geometriæ Cartesianæ. where he saith, he intended not then to publish certain Rules, he had ready; whereof one was, To find out all the irrational Roots both of Literal and Numeral Equations. This must be understood when such Roots are possible; for 'tis certain, there are infinite Equations, whose Roots are noways explicable, either in whole or mixt numbers, Fractions or Surds, and can be no otherwise explain'd, but by a quàm proxime.
9. The Author of this Narrative considering, that the Conick Sections may be projected from lesser Circles placed on the Sphere, and thence easily (otherwise than hitherto hath been handled) described by Points, and that by their Intersections same Spherick Problem is determined, accordingly he found, that this following Problem according to the various Scituation of the Eye, and of the Projecting Plain, would take in all Cases.
The Distances of an unknown Star are given from two Stars of known Declination and Right Ascension; the Declination and Right Ascension of the unknown Star is required.
And saith, he hath observed, that, admitting the Mechanisme of dividing the Periphery of a Circle into any number of equal parts, or (which is equivalent) the Use of a Line of Chords, that this Problem, wherever the Eye be plac'd, may be resolved by Plain Geometry, and yet the Ey shall be so plac'd, as to determin it by the Intersections of the Conick Sections; consequently those Points of Intersection (the Species and Position of the figures being given) may be found without describing any more Points than those sought; and the Lengths of Ordinates falling from thence on the Axes of either figure calculated by mixt Trigonometry, and hence likewise the Roots of all Cubick and Bi-quadratick Equations found by Trigonometry.
For giving from the Mesolabe mention'd the Scheme that finds these Roots, it will then be required to fit those Sections into Cones, which have their Vertex either in the Center; or an assigned point in the Surface of the Sphere, to which they ​relate as projected, and proceed to the revolution of the Problem propos'd: And how to fit in those Sections, see the 7. books of Apollonius, Mydorgius, the 3d, Volume of Des Cartes's Letters, Leotaudi Geometrica practica, Andersonii Exerciat. Geometricæ.
As to the Problem it self, it is determin'd on the Sphere by the Intersections of the two lesser Circles of Distance, whole Poles are the known Starrs, And this Problem hath divers Geometrick ways of revolution.
1. By Plain Geometry (in the sense before mentioned;) Supposing a Plain to touch the Sphere at the North-pole: if the Eye be at the South-pole, projecting those Circles into the said Plain, they are still Circles (by reason of the sub-contrary Sections of the Visual Cones) whose Centers fall in the sides of the Right-lin'd Angle, made by the Projected Meridians, that pass through the known Starrs; and thus the Problem is easily solv'd in this manner.
2, If it be required to be performed by Conick Geometry; in one case it may be done, by placing the Ey at the Center of the Sphere, and projecting as before; to wit, when the longer Axes of the figures being produced concur above the Vertex; Here the Problem is determined by the Intersections of two Conick Sections (whereof a Circle cannot be one, unless its Center be in the Axis of the other figure.) And in this second Case these points of Intersection fall in the same right line or projected Meridian, they did before, but at a more remote distance from the Pole-point, to wit, in the former Supposition, the Solar distance was measur'd by a Right line, that was the double Tangent of half the Arch; here it is the Tangent of the whole Arch. Hence it is evident, how one Projection may beget another, yea infinite others, altering the Scale; and how the lesser Circles in the Stereographick Projection help to describe the Conick Sections in the Gnomonick Projection: But (to reduce the matter to one common radius) if we suppose two Spheres equal, and so placed about the same Axis, that the Pole-point of the one shall pass through the Center of the other, and the Touch-plain to pass through the said Center or Pole-point, and that a lesser Circle hath the same position in the one as in the other; Then, if the Ey be at the South-Pole of the one, it is at the Center of the other, and any projected Meridian drawn from the projected Pole-point to pass through both, the projections of these ​lesser Circles, the distances of the Points of intersection are the Tangents of the half and the whole Arch of the Meridian so intersected. But as to the Points of Intersection; which determine the Problem proposed, they may be found without the aid of the former way, from a Gnoomnick and Stereographick method of measuring and setting off the sides and angles of Spherical Triangles in those Projections, which is necessary in what follows.
3. If the Problem is to be perform'd by Mixt Geometry, as by Circle and either a Parabola, Hyperbola, or Ellipsis, the Circle may be conceived to be the Sun-contrary Section of a Cone projected by the Eye at the South-pole, and any of the rest of the Sections by the Eye at the Center of the Sphere.
4. It by any of the Conick Sections however posited; the projecting Plain may remain the same, but the Eye must be in some other part of the Surface of the Sphere, and not in the Axis.
These things were mention’d to invite the Learned to their Consideration: I shall only further adde, that we cannot say, what may be expected from the labours and endeavors of divers Learned men of this Nation, particularly from Dr. Wallis, who hath so excellently resolved and constructed all Cubick Æquations at the end of the first Treatise of his Opera Mathematica by aide of a Cubick Parabolaster, mentioning, that by such Curves the Roots of all Equations may be found: And who hath promised a Treatise of Algebra and Angular Sections, wherein the Reader need not doubt to meet with satisfaction in these Mysteries. Nor ought we to omit the mentioning of the Modest and Learned Mr. Barrow, who (among many other excellent Subjects, and particularly his Opticks now, at the Press) hath perform'd, what the famous Italian Geometer Mich. A. Ricci hath promis'd in Exercitat. Geometrica (printed at Rome 1666. and lately reprinted here) about Curves of several degrees, that serve to determine and resolve all Æquations: which hath likewise been done by other Learn'd men of this Nation.
An Account of Books.I. PRÆLUDIA BOTANICA Roberti Morison Scoti Aberdonensis. Londini, impensis Jac. Allestry, 1669. in 8o.
This Prelude of this Excellent Botanist hath two parts; The first gives us an Alphabetical Catalogue of all the Plants in the ​Royal Garden of Blois in France, as the same was enriclfd by the Munificence and Encouragement of the Most Illustrius Prince Gaston, late Duke of Orleans, with 360 Plants, in the space of five years, by the singular care and Skil of our Author; who in this Catalogue hath not only given a succint and pithy description of the Plants here enumerated, but also by certain marks distinguish't the Perennial ones from the Annual; adding some general Observations, collected from the Garden above mentioned, very necessary and useful to all that are studious in Botanicks.
The second, contains some Animadversions not inconsiderable, both on the Pinax of Caspar Bauhinus; shewing his mistakes as well in the Digesting as Naming of Plants; and on the 3. Tomes of the Universal History of Plants of Johannes Bauhinus,
To which is annexed a Dialogue between a Fellow of the R. Society and the Author, containing an Answer to several Queries proposed, where is intimated the best General Method taken from Nature it self, of digesting all Plants, and reducing them to certain Classes or Heads according to the difference of their Seeds, Podds and Flowers; by the advantage whereof the Study and Remembering of Plants may be much facilitated, and the Contemplation thereof among all sorts of Men exceedingly promoted: For the publishing of which kind of Method our Author professeth himselfe to be already in great forwardness, entertaining good hopes, he shall by the Assistance and Encouragement of the Generous, be enabled to give good satisfaction to the Curious therein.
II. CL. SALMASII Præfatio in Librum De HOMONYMIS HYLES IATRICÆ Ejusdem de PLINIO JUDICIUM. Divione, A. 1668. in quarto.
This Book is an Introduction to a large Volume; compos'd by the famous Salmasius, and now in the hands of those two Honourable persons, that have taken care of the Publishing of this Preface; both Counsellors of the Parliament of Burgundy; Messieurs Lantin and De la Mare; which Volume gives an Account of the many and great mistakes committed hitherto in the history of Plants; upon the score of Naming them: In the doing of which it hath come to pass, that severall names being often given to one and the same Plant, and vice versa, one and the same name to different Plants, there hath ensued a great and dangerous confusion in that large part of the Materia Medica, highly requiring to be rectified. Now to that Work this Preface prepares the way, by shewing to-the studious in ​Botanicks and Medicine, the Argument, Order, and Usefulness of the same, interspersing withall the Causes and Origin of those many Errors, which both Antients and Moderns have fallen into upon this Subject; as also the negligence of those Antients; the Progress of Physick among the Romans; and the Age of the cheif Writers on this Argument: Adding also the Authors opinion concerning Pliny, what is to be approvd, what to be condemned in him, and how far we are to proceed in the admiration oi that Writer.
But the Reader will doubtless receive the best satisfaction concerning this Book, from M. Lantin himselfe, as he was pleas'd to give it in a late Letter of his to the Publisher, accompanying the Present, he made of several Copies of it to the R. Society, and to divers particular Members thereof, delighting in Botanical Studies; to this effect.
SIR, I send you some Exemplars of the Introduction to a great Work, which M. Dela Mare and I have caus'd to be printed, to excite the Lovers of Learning to facilitate the impression of the Whole Book. I promise my selfe, that this Present will not he unacceptable to you, on well in respect of the Author, who, besides his great Learning generally known, had the Honour to he lov'd by his Majesty of G. Brittain, as for the worth of the Treatise it selfe; of which you may Judge by this Preface. Although it he a work altogether Critical, and which, Correcting only Errors about the Names of Simples, may seem to contribute but little to the knowledge of Nature, for the Advancement of which your Illustrious Society employs all its Studies and Labors with so much reputation; yet I may say, that even this Book may serve for the accomplishment of that great Design, forasmuch as in discovering the Errors and Negligence of the Antients, and of the Moderns that have follow'd them in the History of Plants, it shews the necessity there it to labour after a new Natural History, that may be free from those defects, if we intend to lay solid foundations for knowledge, and particularly for the Art of Medicine. In the mean time, those that practice it, being often constrain'd to use Simples, the virtue of which it not known to them but by the Experience of the Antients, may be Ayd of this Book avoid very dangerous mistakes.
But what Judgment soever you shall make both of the Book and its Preface, I hall be satisfi'd, if you and your Illustrious Friends, (to whom I intreat you to present some of the Copies accompanying this,) shall receive them as a mark of my esteem of the R. Society, the design of which I admire as the Noblest, that ever was undertaken by men. I uncessantly praise their Industry, Prudence and Sincerity, and in finitely value the parts and knowledge of those, that compose it. And this occasion shal also serve Me to &c.
LONDON,
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, 1669.