Medicina hydrostatica, or, Hydrostaticks applyed to the materia medica shewing how by the weight that divers bodies, us'd in physick, have in water : one may discover whether they be genuine or adulterate : to which is subjoyn'd a previous hydrostatical way of estimating ores / by the Honourable Robert Boyle ...

CHAP. II.

THO' the Way of weighing So∣lids in Water hath been deli∣vered

by the ingenious Marinus Ghe∣taldus, and, out of him, by some few other Authors, and tho' therefore I might excusably dispense my self from delivering it distinctly: Yet since their Books are scarce, and the knowledge of this Way is almost every where supposed in these Pa∣pers, I hold it very fit, that it should once be proposed in this Tract, not only for that Reason, but for Two others. One, that a dextrous way of finding out the Weight of Bodies in Liquors, may be of far more use than Men seem to be yet aware of, being capable of being made, by a little Variation and Improvement, of good use to Naturalists, and even to Chymists. And the Other, that per∣haps you will find cause to think, that Experience and Reflections on it may have furnisht me with some few Expedients and Cautions for the bet∣ter Practice of this Art, and for the avoiding of some Errors, that may be very easily, and perhaps have been, run into, for want of the Cautions here given.

The Way of weighing sinking Bodies in Water.

The Solid Body, given to be exa∣mined, is to be ty'd about with an Horse-hair of a competent length, which Hair at its other end is to be fastened to one of the Scales of a tender and exactly equilibrated Bal∣lance, so that, the proposed Body, be∣ing exactly weighed in the Air, and then immersed in a Glass or other fit Vessel, almost full of fair Water, may hang freely in that Liquor, be∣ing on every side encompassed by it. This done, you must put into the opposite Scale as many Weights▪ as serve to bring the Body hanging in the Water, to an exact Aequilibrium with the Counterpoize, and conse∣quently the Beam of the Ballance to an Horizontal Scituation. Then take out the Weights newly imployed, which give you the Weight of the Body in the Water, and deducting it from the Weight formerly taken of

the same Body in the Air, and by the remainder, which will be the diffe∣rence of these two, divide the whole Weight of the given Body in the Air, and the Quotient (whether consist∣ing of whole Numbers, or a Fraction, or both) will shew the Proportion, in specifick Gravity, between the examined Solid, and as much Water as is just equal to it in Bulk. To make this more easily intelligible by an Example; We took a fine piece of white Marble, (that Stone seem∣ing the most pure, and most free from Mineral Tinctures of any com∣mon opacous Stones) this being put into a good Ballance, whose Scales were well equilibrated, was found to weigh in the Air, ℥ij ʒiij ℈1. Grains IX. which, for Conveniency of Supputation, we reduce to 1169 Grains, then an Horse-hair was ty'd about this piece of Marble, and the other end of the same Hair was fa∣stened to one of the Scales, under which, at a convenient distance, was plac'd a somewhat deep Glass, almost

full of fair Water, in this Liquor the Stone was made to hang freely, be∣neath the Surface, and in the oppo∣site Scale, there were put Weights enough to bring it to an Aequilibrium with the other, these Weights were found, being reduced to the former Denomination, to amount to 738. Grains, which gave us the Weight of the Marble in Water, (which was much less Weight than the for∣mer, because the Stone was partly sustained by the Water) this being substracted from the Weight of the same Stone in the Air, there remai∣ned 431. Grains, which gave us the Weight of as much as was equal to the Stone in Bulk. By this remainder the Weight of the Marble in the Air, viz. 1169 being divided, the Quotient was found to be 2 & 71/100, or near enough 7/10 for the Proportion in specifick Gra∣vity of White Marble to water. The Demonstration of this Practice is foun∣ded on what I have elsewhere given, and it may, in another way, be found in some of the Commentators on

Archimedes, de Insidentibus, humido.

For understanding of the Summa∣ry Direction newly given, it may be useful to subjoyn the following Notes: First, 'tis manifest by the Nature of the thing, that the Body, proposed to be weighed, ought to be heavy enough to sink in Water, since otherwise its Weight in that Liquor being none at all, cannot be signifi∣cantly deducted from its Weight in the Air; but if there be occasion to Weigh in Water a Body lighter in Specie than it, as Bees-wax, a piece of Firr-wood, &c. It may be done, tho' not without some trouble, by joyning to it a Body, heavy enough to make the Wax sink with it, but this Case belongs not to this place.

2. An Horse-hair is made choice of, for Hydrostatical Operations, be∣cause its said to be Equiponderant to so much Water; and tho' I have not found that to be strictly true, yet an Horse hair is fitter to be imployed in these Tryals, than any other string, I know of; and its specifick Weight

usually differs so little from That of Water, that the Difference may be safely enough neglected; and if the Solid proposed be too heavy to be sustained by a single Horse-hair, one may twist two, (or, if need be) more of them, to make the string strong enough to sustain the Solid.

3. I shall add, that I have met with Bodies, about which, by Rea∣son of their Roundness, as in Bullets, or of some other inconvenient Figure, we could not well fasten an Hair, or other string, wherewith to tye it to the Ballance. Now, on such occasions, I caused some Hairs to be so contex'd, as to make a kind of a little Hoop∣net, whose Meashes were not great enough to let the Body slip through them. In this small Vessel, whether you call it a Net or a Basket, which was ty'd by an Horse-hair (single or twisted) to one of the Scales, we put the solid Body to be weighed, and proceeded in the Operation, as if the Body were tyed but with a string.

4. But here it must be carefully noted once for all, that whensoever any Hydrostatical Tryal is made with an Horse-hair; there must be put in∣to the Scale that holds the Counter∣poize, as much of the same Hair, as can be guest to be of the same Weight with that part of the string that su∣stains the Body in the Water, which appears to be above the Surface of the Water; for this Liquor takes off the Weight only of as much of the Hair as is immers'd in it, so that the unimmers'd part of the string adds to the Weight of the Solid hanging in Water; and therefore, ought to be compensated by an equal Weight put into the opposite Scale.

5. When I kept a Ballance, only or chiefly, for Hydrostatical Tryals; I found it expedient, on divers occa∣sions, to take off one of the Scales with the strings belonging to it, and substitute in its room a piece of Lead, or other Metal of a Conical, or som other convenient, shape, exactly Equiponderant to the opposite Scale,

and at the same end of the string, to fasten one end of the Horse-hair that tyed the Body to be weighed in Wa∣ter. And sometimes also, when I did not take off one of the Scales, I caused it to be perforated in the middle, (yet, without lessening its Weight) that so the Body, to be im∣merst, might hang very Perpendi∣cularly from the midst of the Scale. The Motives, that induced me to these Practices, cannot be so well set down in few words; and therefore shall be now left unmentioned, especially because the Practices themselves, tho' on some occasions convenient, are not necessary.

6. There remain yet a couple of Remarks, which must less than any be pretermitted, if Men would avoid some Errors, that are but too often slipt into, by the Makers of Hydro∣statical Tryals. We are then (First,) to take notice, that the Body, to be examined, hang freely in the Water, so that no part of it any where touch the bottom or the sides of the Vessel,

or reach above the upper Surface of the Water contained in it; for, if any of these Circumstances be not taken care of, (as it happens, when we are not heedful enough) the true Weight of the Solid is somewhat altered; and if any Corner, or other part of the Body, (and the like may be said of the Horse-hair, 'tis tyed with) tho' but a small one, appear above the Surface of the Water: That extant Portion, being not at all sustained by the Li∣quor, adds (more or less) to the Weight, that the immerst Body should have. Care also must be had, that, as nothing but the Water do touch the hanging Body, so, no part of the Water may touch the Scale whence it hangs. I have several times obser∣ved, that immerst Bodies have been concluded to weigh more in the Wa∣ter than really they did; because, through such a want of Heedfulness, as is not uncommon, the Experi∣menters did not take notice, that if the string were too short, or the Vessel too full; the vibrating Moti∣ons

of the Ballance, would, at one time or other, carry down the Scale, the suspended Body was ty'd to, so low, as to make one part or other of it touch the Surface of the Water: some Drops of which Liquor would readily stick to it, and, because they adher'd to the nether part of it, would lye concealed from an Eye that was not prying, and by conse∣quence would sensibly add to the Weight of the Scale, and make the Body be thought heavier than indeed it was; which Over-sight must needs be very prejudicial, when one makes Experiments that require Exact∣ness.

7. But the most usual Cause of Mistakes i•• Hydrostatical Tryals, (especially such, as are made on small Bodies) wherein a little Error may be greatly considerable, is this; that Men are wont to think it sufficient, (in these Tryals) that the Body to be examined, be totally immerst in the Water; whereas it does not only often, but most commonly happen,

that the given Solid, and the string that is tyed about it, carry down with them divers Particles of Air; and perhaps too, it may find and ex∣tricate others, that lay concealed in the Pores of the Liquor it self; which Aerial Particles fasten themselves to the little Asperities, that they meet with on the Surface of the immerst Bodies, in the form of Bubbles, which, like so many little Bladders full of Air, endeavour to buoy up the Body they adhere to▪ and on that account do, in Proportion to their Number and Bigness, lessen the Weight, which the immerst body would otherwise have in Water. And therefore, great care is to be had, especially in nic•• Expe∣riments; that, by shaking the string, and warily knocking the Body a∣gainst the sides of the Glass, the ad∣hering Bubbles may be displaced, and emerge to the top of the Water▪ And I shall add a desire, that on some occasions this Caution be made use of more than once in the same Tryals; because I have several

times observed, that now & then after the immerst Body was freed from the first Bubbles that appear'd about it, o∣thers did succeed, before an end was made of weighing the Body; out of some of whose unperceived Cavities, or Pores, (whether superficial or lying deeper) perhaps the latent Air could not easily on a sudden be driven by the Water. I have been the more Circumstantial in explaining the summarily proposed Method of Weighing Bodies in Water, because Experience hath shewn, that 'tis not near so easie, as, upon the first reading of it, one would presume▪ to be ex∣act in the Practice of it.

Having obtained the Weight of a Body proposed; First, in the Air, and then in Water, according to the Me∣thod plainly delivered; 'twill not be difficult to discover Practically the Proportion in Weight, between the Solid and the Liquor. I say Practical∣ly, because the Rule is easie enough, tho' the Demonstration is not so rea∣dily to be understood by them, that

are not acquainted with the Prin∣ciples of the Hydrostaticks. The Theorem, upon which our Practice is grounded, was first, that we know of, delivered by the most sagacious Ar∣chimedes; whose Commentators have busied themselves in demonstrating it in a Mathematical way, as I have since endeavoured to do in a Physi∣cal way, and more easie to Natura∣lists in the Hydrostatical Paradoxes. Archimedes's Proposition is this, That a Body, heavier than Water, weighs less in Water than in the Air, by the Weight of as much Water as is equal to it in Bulk or Magnitude: Whence 'tis not diffi∣cult to deduce a Rule sufficing for our present purpose. For if you subtract the Weight of the Body proposed, whilst it is every way environed with Water; from the Weight of the same Body, which it was found to have in the Air; the residual Number or Diffe∣rence gives you the Weight (taken in the Air) of as much Water as is equal in Magnitude to the Solid pro∣posed;

so that, having now two Bo∣dies, one Firm, and the other Liquid, together with the Weight of each of them apart; to find their Proportion, you need but divide the greater by the lesser; and the Quotient compared to One, that is, to an Unite, will be the Antecedent the of the Proportion de∣sired between the solid Body and the Water; which is mentioned, but, as it is the Liquor that is generally im∣ployed in these Experiments, for otherwise the Rule will hold, mutatis mutandis, in other Liquors, as well as in Water.

Notes

• Hydrosta∣tical Pa∣radoxes.