The great and new art of weighing vanity, or, A discovery of the ignorance and arrogance of the great and new artist, in his pseudo-philosophical writings by M. Patrick Mathers, Arch-Bedal to the University of S. Andrews ; to which are annexed some Tentamina de motu penduli & projectorum.

AN EXAMINA∣TION OF M. SINCLAR'S Hydrostaticks.

Non equidem hoc fludeo, bullatis ut mea nugi•• Pagina turgescat, dare pondus idonea fumo. Secreti loquimur:—Pers.

THat I had sufficient reason to quarrel the offer of thirty new and unheard-of Hydro∣statical Theorems, shal appear from the examination of this Treatise; whereof all that is true, (for a considerable part of it is false and ridiculous) is the same with the do∣ctrine of Archimedes and Stevinus, in the following Propositions: only our Authors doctrine is more loose, and less precise.

As for what he hath written concerning the Bensil of fluids, generally applyed, is

false; seing no Bensil hath hitherto been perceived in any fluid, except Air. And seing the doctrine of the spring of the Air, is called by most of Authors, and par∣ticularly by M. Sinclar himself, Aërosta∣ticks: I think not my self obliged to re∣duce it to the writings of Archimedes and Stevinus, who wrote only Hydrostaticks pro∣perly so called: yet in that subject also, (where he speaks truth) I shal in its due place trace him in Aërostatical Writers ex∣tant before him.

In the review of this Tractat, I shal, for my hires sake, begin with the Theorems; and afterward take notice of a few things in the Observations and Experiments.

§. 1. The Theorems reviewed, whereof a great part are proven false, others ridiculous, and the rest not new.

I Shal here at once discover the falsity and ridiculousness of a considerable part of our Authors Theorems, and reduce the rest to these following Propositions of Archi∣medes and Stevinus.

Archimedis Positio 1.

Ponatur humidi eam esse naturam, ut, parti∣bus ipsius aequaliter jacentibus & continuatis in∣ter sese, minus pressa à magis pressa expellatur. Ʋnaquae{que} autem pars ejus premitur humido supra ipsam existente ad perpendiculum, si hu∣midum sit descendens in aliquo aut ab alio aliquo pressum.

Prop. 2.

Omnis humidi consistentis atque manentis superficies Sphaerica est, cujus centrum est idem quod centrum terrae.

Prop. 5.

Solidarum magnitudinum quaecunque levior humido fuerit demissa in humidum manens, us{que} eò demergetur, ut tanta moles humidi, quanta est partis demersae, eandem quam tota magni∣tudo gravitatem habeat.

Prop. 6.

Solidae magnitudines humido leviores in hu∣midum impulsae, sursum feruntur tanta vi, quantò humidum molem habens magnitudini aequalem, gravius est ipsâ magnitudine.

Prop. 7.

Solidae magnitudines humido graviores de∣missae in humidum, ferentur deorsum, donec descendant: Et erunt in humido tantò leviores,

quanta est gravitas humidi molem habentis so∣lidae magnitudini aequalem.

Stevini Postul. 3.

Pondus à quo vas minus altè deprimitur, le∣vius; quò altiùs, gravius; quò aeque altè, aequi∣pondium esse.

Prop. 5.

Corpus solidum materiae levioris quàm aqu•…•… cui innatat, pondere aequale est tantae aquae moli, quanta suae parti demergitur.

Prop. 8.

Corpus solidum in aqua levius est quàm in aëre, pondere aquae magnitudine sibi aequalis.

Prop. 10.

Aquae fundo horizonti parallelo tantum in∣sidet pondus, quantum est aquae columnae cujus basis fundo, altitudo perpendiculari ab aquae su∣perficie summa ad imam demissae aequalis sit.

Now, Reader, consider well these Pro∣positions: my Authors Theorems; and my Censure, which is this.

His first two are no Theorems; but only Suppositions. And the third, a sort of a definition, or rather, aliquid gratis dictum.

The fourth, as he wordeth it, is false: for a broad fluid counterpoyseth more then a narrower; seing a cylinder of Mercury

one inch thick and twenty-nine inches high, counterpoyseth a cylinder of Air of the same thickness, and of the altitude of the Atmosphere: and one two inches thick with the former height, counterpoyseth four times as much Air. As he explicateth it, it is true, and the same with Archimedes's second Proposition; for the Demonstra∣tion holds, suppose ye divide the fluid by several pipes, if they have entercourse.

Here he maketh a mystery of a very easie thing: for one pillar of water being ten times thicker then another of the same height, and consequently an hundred times heavier, hath no more effect then the other; for because of its base, it hath an hundred times as much resistance. And it is most clear, that if the resistance be pro∣portional to the pressure, the effect must constantly be the same.

His fift, is a part of Archimedes's first position.

His sixt also; for Archimedes's expulsion hindered with equal resistance on all sides, he calleth, Pressure on every side. I suppose he will hardly affirm, that this lateral pres∣sure was not known before him; seeing

Stevinus doth demonstrat, how much it is upon any plain howsoever inclining, in his Prop. 11. 12. 13. which our Author can∣not do yet; at least, there is nothing in his Book either so subtil or useful.

His seventh is the same with the last part of Stevinus's third Postulatum.

The eight is manifestly false, (if fluids have a Bensil, as he supposeth, Prop. 17. 19.) which I demonstrat from his own fi∣gure thus. The first foot E having one de∣gree of weight, and the second foot I ha∣ving equal quantity or dimension, and be∣ing lower then E, must have more weight; (according to his 17.) let it therefore have 1½ degrees of weight: then the weight of both these must be 2½. Now the third foot N, being of equal quantity with I, and lower, must (according to his 17.) have more gravity then it hath; (to wit, 1½) let it therefore have 2. degrees; and then the weight of all three is 4½ degrees: but 1. 2½, 4½, are not in Arithmetical progression; and therefore the Theorem is false.

I must take notice, that if our Author had understood so much as the terms of

Art; he would have said, The pressures of fluids are in direct proportion with their profun∣dities. His inference there concerning a Geometrical progression is false; for there are many Geometrical progressions more then 1, 2, 4, 8, &c. And it may be in many several progressions, albeit it nei∣ther be in Arithmetical nor Geometrical progression. And, suppose he had not con∣tradicted himself, his Theorem is evident from the 10. of Stevinus: For, according to it, the weights or pressures of fluids are equal to the weights of respective Cylin∣ders upon the same, or equal bases; but the weights of such Cylinders are in pro∣portion with their quantities, which is the same with the proportion of their alti∣tudes.

The ninth and tenth (as he explicateth himself) are only this, That fluids press up∣on bodies within themselves, and press up bodies lighter then themselves in specie; which is the same with his 6. and 13. The first of which we have examined already: and the o∣ther we leave to its own place. But what ground he hath for his sensible and insensible gravity, I shal discuss in the examination

of his Ars magna & nova, which is all built upon this wild notion.

His eleventh is manifestly false, as I shal afterward demonstrat from his own prin∣ciples: for the Cylinder acquireth only a greater base, (our Author must under∣stand that an Horizontal surface is the base, and sustains the pressure) and con∣sequently a greater resistance, which ma∣keth the same weight of less effect. It is e∣vident that a weight of lead cannot press two foot in square, so much as one: yea the pressures of the same weight are al∣wayes caeteris paribus in reciprocal propor∣tion with the surfaces they press; as it is known by all Mathematicians, except on∣ly such pitiful ones, as our Author.

The twelfth is evidently false; for, if ye take a bladder, or any tender vessel half full of water, and put the sides of it toge∣ther, the fluid shal be moved from the un∣equal pressure of the vertical surface.

The one half of the thirteenth is a part, but a very smal one, of Archimedes's se∣venth, and eigth: The other half is also a smal parcel of Archimedes's sixth.

His fourteenth is so much as he under∣stands

of Archimedes's fifth, and Stevinus's fifth.

The fifteenth, seventeenth and nine∣teenth are false; unless the fluid have a spring, or be heterogeneous; none of which he hath made out: but if it were made out, the thing is obious, and noticed by M. Boyl in the thirty-sixth Experiment; yet only in the Air, which is known to have a spring.

His sixteenth is ridiculous; seing we see daily fishes, little particles of earth, horse hairs, and many other such bodies betwixt the surface and bottom of the wa∣ter. Yea by adding a sufficient quantity of lead to a body lighter in specie then water, it may be made practicable: and is demon∣strat both by Archimedes and Stevinus, sup∣posing the water homogeneous; the con∣trair of which, our Author hath not yet made out. And more, even a bodie consi∣derably heavier in specie then water, beaten out thin and broad, especiallie if it be con∣cave below, may be suspended for a consi∣derable time betwixt the surface and bot∣tom of the water, providing it be laid pa∣rallel to the Horizon. But passing by all

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this, his method is unpracticable, and sup∣poseth, without proving any thing, that wa∣ter can suffer any degree of compression; and stones, lead, with other bodies, none at all.

His eighteenth is the same with Archi∣mede's seventh, and Stevinus's eighth.

His twentieth is the same with his se∣venth, otherwayes he grants it not exactly true.

His twentyone (as he wordeth it) is most manifest from that Statical demonstration I mentioned: For seing pressures of the same weight are in reciprocal proportion with their resistances, and the resistances or resisting surfaces can be diminished in infinitum; it is evident that the least weight can produce any pressure, whether the hea∣vy body be fluid or solid. But he explica∣teth himself otherwayes, relating to the spring of fluids, which is not yet proven in any fluid, save Air; and besides this, the Theorem is ridiculous, seing the spring of any part (where all are equally pressed) is equal to the spring of the whole: for one pound weight presseth one foot as much, as two pound presseth two; and even so in any spring.

His 22. and 23. are made manifest by Pecquet in his fourth Experiment, and M. Boyl in his 19. Physico-Mechanical Expe∣riment, yea throughout all that book and many others, constantly calling the weight and spring of the Air diverse, and yet brin∣ging them both in for that same effect.

The 24. is ridiculous; seing it is true and obvious in all things, if there be no pe∣netration of bodies.

The 25. is evidently false, seing wa∣ters upon the tops of hills support less, and in valleys more. Yea Doctor Wallace sho∣weth in his Mechanicks, pag. 728. that the Mercury both in M. Boyls Baroscop, and his, fell sometimes at Oxford below 28. inches, and other times above thirty, and in the page 740. he mentioneth unquestio∣nable experiments of 34. 52. and 55. in∣ches. The contrair of this Theorem is al∣so evident from many of our Authors own experiments, if any man think them wor∣thy the looking over. And suppose he had hit right, this is nothing but the old To∣ricellian Experiment.

His 26. is imperfect; first, seing he speaketh only of fluids to be pressed up, it

being also true in all other bodies. Se∣condly, he doth not determine how far the sphere of activity reaches; and yet all this is easily done and demonstrat from Stevinus his 10. For the body is pressed up, till it together with the fluid betwixt it and the bottom (not regarding what else inter∣veen, but reckoning all for fluid) be equal in weight with a column of fluid, whose height is the same with the height of the fluid, and its base the same with the base of the former fluids portion, or equal to it: and besides all these, this is not different from M. Boyls eleventh Paradox.

His 27. is to say, that a pound of wool weigheth as much, as a pound of lead.

His 28. is the same with that which he would say in the 4. and is true also in so∣lids; if ye speak only of columns: For two unequal columns of the same hight and matter press equally, seing their re∣sistances are proportional with their weights. In fluids (as I said alreadie) it is the same with Archimedes's Second.

His 29. might have been more general, to wit, That there can be no motion in fluids, without an unequal pressure: And then it

had been the same with Archimedes's first position.

His 30. is also a part of Archimedes's first position. For seing pressure is jud∣ged only by expulsion the effect of it; and the expulsion is always caused where the least resistance is, which may be in a croo∣ked line: wherefore then is not pressure also in crooked lines?

His 31. is the 10 of Stevinus. Here again he justleth with that great difficulty, which I discussed in the 4. and telleth there is no way to answer, but his.

In his 32. the Pondus & Potentia, are to say in plain Scots, a pressure and a resistance. He hath told in his 5. that in all fluids there was a pressure; but now it comes in his head, that a man may fancy a pressure with∣out a resistance; & therefore he must guard against that. I suppose here, that his defini∣tion of the Staticks is new; otherwise the Tron-lords are the greatest professors of it.

His 33. is to say, that there must be a motion, when the pressure is greater then the resistance; which is yet a part of Archi∣medes's first position, and never doubted of by the greatest ignorants.

§. II. The Authors last Theorem, for its good ser∣vice, examined by it self.

NOw let us examine his last Theorem, which certainly should be the utmost reach of his wit; and therefore I will exa∣mine it more narrowly.

First, let his two fluids in aquilibrio be, Water the one, and Quick-silver the other, The natural weight of Water being 1. the natural weight of Quick-silver is 14. Therefore according to his Theorem; as 1. the weight of the one is to 14. the weight of the other, so is the height of the one, to wit, Water, to the height of the other, to wit, Quick-silver: and therefore the Quick-silver should be 14. times higher then Water, which I leave to be determi∣ned by experience. He should have said, as the natural weight of the second, is to the natural weight of the first: Or rather, that their altitudes are in reciprocal pro∣portion with their weights, or in direct proportion with their levities.

Secondly, then in his progress, he saith,

That by what proportion the one liquor is naturally heavier or lighter then the other, by that same proportion the one Cylinder is higher or lower then the other: here insinuating, that the weights and levities of two bodies are in the same proportion; and yet their proportions are reciprocal, and that is to say, just contrair: or other∣wise, he must take the heights proportio∣nal with the weights, and the lowness with the levities; which are both false. At last, when he comes to his example, he makes the heights proportional with the levities, which I grant to be his meaning; but this showeth an intolerably confused wit.

Thirdly, even this being granted, I shal demonstrat, that it doth contradict almost all his Theorems. And to that purpose, I assume these two Postulata.

Post. 1. Fluids which have their weights or pressures proportional to their profundities, can have no Bensil: For if they have a Bensil, their pressure is not proportional to their profundities, (as I did demonstrat at his 8. Theor.) which is against the hypothesis.

Post. 2. Quick-silver or water, have their weights and pressures in proportion with their

altitudes. At least, so far as any man yet hath made tryal; as M. Boyl witnesseth in the first Appendix to his Paradoxes: yea, our Author affirmeth it of all fluids, in his 8. Theor. and many places of his Experi∣ments. The demonstration follows.

Here upon the surface of the Earth, let the height of a Cylinder of Mercury be A, its weight, or the weight of the Cylinder of Air counterpoysing it B, the height of this Cylinder of Air C. Also let the same Cylinder of Mercury be lifted up some distance from the Earth, and the Mer∣cury will fall, so that the Cylinder of Mer∣cury is now lower, whose height we call D, and weight, or the weight of its counter∣poysing aërial Cylinder E, the weight of this aërial Cylinder F; let the proportion betwixt the weights of Mercury and Air be as G unto H. By our second postulatum, A is unto D, as B is unto E; and by this 34. Theorem, H is unto G, as A is unto C: and also H is unto G, as D is unto F; and there∣fore A is unto C, as D is unto F; & permu∣tando, A is unto D, as C is unto F; but A is unto D, as B is unto E; And therefore B is unto E, as C is unto F; and consequently (by

the first Postulatum) the Air hath no Bensil; which is contrair to many of his Theorems, and all his Experiments.

This destroys all his methods of measu∣ring the height of the Air, Clouds, and At∣mosphere, both here and in his Ars magna & nova. He might have known this mistake many years ago; for M. Boyl rejecteth this proportion betwixt the altitudes of the Air and of the Quick-silver in his 36. Physico-Mechanical Experiment, upon the same account. This letteth our Author see, that if fluids have no Bensil, his Theorem was obvious, and known to all.

§. III. The Authors great skil in Dioptricks, examined.

IN his third Observation, he maketh him∣self exceedingly ridiculous. For, first, he showeth hot how much the Telescop re∣quired, should magnifie.

Secondly, he showeth not how far the Telescop should be drawn out for this ef∣fect; for that draught which serves for a di∣stinct and clear sight, will not serve exactly

to project an Image; seing sight requireth always parallel, or diverging rays, and the projection of an Image, converging.

Thirdly, he seemeth to attribute the magnifying of Telescops to their length and goodness of the glasses; and yet there may be the best glasses imaginable placed in their due distance in a tube of 50. foot long, and not do so much as an ordinar tube of 5. inches; and yet both the glasses may do wonders with others which give them their due charge.

Fourthly, he requires both the glasses to be very good, and there is no excellency required but in the object glass.

Fifthly, he speaks of the Image, as if it were both near to the Tube, and far from it; and yet it hath one determinat place, the draught of the Tube never being alte∣red, which he never once mentioned.

Sixthly, he speaks of the Image of the Sun, that it is the more distinct, the nearer the glass; and yet this brightness near the glass, is nothing but a confused concurse of rays.

Seventhly, when he hath observed his inches, he reduceth them not to degrees,

minuts, or seconds, &c. for the Suns mo∣tion is not reckoned in inches.

Lastly, suppose he had done all these things aright; this method hath been ordi∣narly practised above these thirty years: Let him look Hevelij Selenographia, Schei∣neri Rosa Ʋrsina, and Doctor Wallace in the end of his Arithmetica infinitorum.

It is here to be observed, that these Au∣thors by such observations designed not to render the Suns motion sensible to the eye. (which our Author values so much, and by some here was formerly called ridicu∣lous) but only to observe its spots toge∣ther with their motion, or else its eclipse: noticing only by the way, that swift mo∣tion of the Suns Image, which was trouble∣some, and constrained them oft to alter the position of their Telescop.

§. IV. Our Authors new Diving Ark, put to tryal.

THere is nothing in which our Author is more mistaken, then in his Diving Ark; for in all his discourse, he not only

contradicts himself, (which is ordinar, and no great matter) but also the general do∣ctrine of the Hydrostaticks. I shal there∣fore, to undeceive his Reader, demonstrat, That his Dyving Ark sustains precisely as much pressure under water, as if it were hung in the Air with as much water in it, as now it hath of Air, rebating only a smal matter which the compressed Air in the Ark weigheth. I do it thus.

In his own figure, pag. 179. let PQ be the sufface of the water within the Ark, PY the distance of that surface from the upper horizontal surface, NY the distance of the top of the Ark from the upper sur∣face. According to his 7. Theorem, the pres∣sure is equal at P and at 4; and therefore according to his 8. Theor. seing the water hath no sensible spring, the pressure at N without the Ark is to the pressure at P, as YN to YP; therefore the pressure at PQ, overcometh the pressure without the Ark at EH, by the pressure of a column of wa∣ter, whose base is PQ, and the altitude HQ; but the pressure at EH within the Ark, wanteth only the weight of the co∣lumn of Air PQHE, to make up the

pressure at PQ; therefore the pressure within at EH, exceedeth the pressure without at EH, by the weight or pressure of a column of water, whose base is PQ, and altitude QH, abating the weight of the column of Air PQHE; Which wa•• the conclusion to be demonstrated.

I demonstrat this conclusion, supposing no man within the Ark; but if a man be there, it holds only of the Air about him, taking the man to be equal in weight with so much water. I would gladly know if our Author now would affirm, that, sup∣pose the Ark were no stronger in the sides then a wine glass, yet it might go down 40. fathom without hazard, and that it may have a glass window a foot in square, and holes in the top, wherein ye may put your little finger: Yet I shal help him in one particular; There is more hazard in the first three fathoms, for the bursting or lee∣king of the Ark, then in the next three hundred, seing the space filled with Air groweth less. Are these the great matters, which our practical Mathematicians in∣vent, whilst others are nibling at petty de∣monstrations?

§. V. The honourable M. Boyl vindicated from our Authors ignorant censure, in his Exper. 17.

I Resolved only (having considered the extraordinary pains it would take to exa∣mine all the non-sense, contradictions, ab∣surdities, and superfluities in his Experi∣ments and Observations, which almost every page is filled with) to take notice of these he mentioned in his Edict: but seeing him so bold, as (in his 17. Experiment) to insult over that learned Gentle-man M. Boyl, I must, by permission of more learned Pens, which this great mans vindication doth deserve, undertake to demonstrat the truth of what M. Boyl affirmeth: that is to say, That the water REF (see the Authors fig. 24.) weighed in the Air, is of the same weight exact∣ly, which it hath weighed in the water, accor∣ding to M. Boyls method. I do it thus.

By my former Demonstration, before the water EFR enter the glass, the glass PR, is as much pressed upward in the wa∣ter, as it would be pressed downward in the Air by its fill of water, rebating the

weight of the Air now within it: There∣fore the weight which keepeth the glass PR, in aequilibric in the water, must be the same with the weight of its fill of water in the Air, substracting the said weight of Air. Now when the water EF entereth, the glass PR is as much pressed upward in the water, as it would be pressed downward in the Air by EPF, full of water, rebating the weight of the Air EPF, which is the same with the former: and seing at first the pres∣sure of the glass upward, was equal to the weight of all PR, full of water rebating such a weight, and now the pressure is on∣ly equivalent to the weight of the water EPF, rebating the same weight; the pres∣sure of it is now diminished by the weight of the water ERF: but the pressure is like∣wise diminished by the weight put in the scale O; and therefore that weight is equal to the weight of the water ERF, in the Air; Which was the conclusion in question.

All that our Author speaks against this, is to no purpose. First, he saith, that tho lead casteth the ballance; but that cannot be, seing the lead was there, before the bal∣lance was casten. He concludeth, That water

doth press in water, but not weigh in water: I will not call this non-sense, but only retort, that upon the same account, Air will not weigh in Air; and yet I believe, he thinks, that he hath weighed Air in its self. It is like, he may say, that this is done by the Toricellian tube, where the air is exhausted: so might M. Boyl have said, that is in a glass buble, where the water is exhausted: And I may also say of this whole Hydrosta∣tical doctrine, that it is exhausted also, and can be no longer, without prejudice, kept back from its grave.

THis waterish doctrine hath past off with more credit then it deserved, ha∣ving gasped out its last by vertue of that noble name, The Honorable Robert Boyl. I doubt not, Reader, but by this time thou art made weary by it; and so am I. Where∣fore unwilling to return, and rake up its ashes, to thy further annoyance and mine, I shal go forward to the Ars nova & magna, and quickly show thee what novelty and greatness is there, without any prefacing; having no other testimony for it, then what is due to the rest of its fellow-works.