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6. To determine the Ratio which the Specific Gravity of a Fluid has to the Specific Gravity of a Solid, that is Specifically heavier than the Fluid.
Weigh any Mais of the Solid in the Fluid, and note the juft Weight therein : The Specific Gravity of the Fluid will be to that of the Solid, as the Part of the Weight loft by the Solid, is to its whole Weight.
' 7- Tec ffecific Gravities of equally heavy Eodies, are re- ciprocally as the Quantities of Weight loft in the fame Fluid. Hence we find the Ratio of the Specific Gravities of Solids, by weighing Maffes thereof, that are equal in Air, in the lame Fluid j and noting the Weights loft by each.
The Specific Gravities of various Solids, have been de- termined by many Authors. Marin Ghetalhn, particularly tried the Specific Gravities various Bodies had, eipecially metallic Ones 5 which were borrowed thence by Oltgbtred. In the 'P/jiloSoptiical'I'raitfetffions, we have very prolix Tables of Specific Gravities, by various Authors.
'Twill be lufficientfor ustogive thole of fome of the more ufual Bodies, as determined with great Care and Accuracy by M. 'Petit ; and publilh'd by F. Merfinne ; and from him by ftveral others.
table of the Specific Gravities of Several Solids. .
An Hundred pound Weight of Gold, is equal in bulk to
c m :
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71 ~ of Mercury 60 l of Lead 54 £ of Silver 47 | of Copper 45: of Brafs 42 of Iron 39 of Tin
38 ;£ of fine Tin 26 of Load-ftone 21 of Marble 14 of Stone 12 I of Sulphur 5 of Wax 5 f of Water.
8. A Body fpecifically heavier, defcends in a Fluid fpecifi- cally lighter, with a Force equal to the Excefs of its Weight, over that of an equal Quantity of the Fluid.
Hence, i°, The Force which fuftains a fpecifically heavier Body in a Fluid, is equal to the Excels of the abfolute Gravity of the Body above that of the Fluid, under the iame Bulk 5 E.gr. 47 -i Pound of Copper lofes 5 | Pounds of its Weight in Water 5 therefore a Power of 42 Pounds is able to fultain it.
2 Since the Excefs of the Weight of a Solid over the Weight of a Fluid fpecifically heavier, is lefs than that over the Weight of a fpecifically lighter Fluid under the lame Bulk 5 it will defend with lefs Force in a fpecifically hca-vier Fluid than in a lighter ; and, conlequently, will defcend more flowly in the former than in the latter,
9. A. fpecipcally lighter Body, finks in a heavier Fluid, till the Weight of a Quantity of the Fluid, equal in Bulk, to the Part iminerfed, is equal to the Weight of the whole Body.
Hence, i°, Since the Specific Gravities of Bodies cf the fame Weight, are reciprocally as rheir Bulks ; and the Bulks of Fluids equaj in Weight, are as the Parts of the fame Solid immerged therein ; t\it fpecific Gravities of Fluids are reciprocally as the Parts of the lame Body immerged therein.
2 A Solid, therefore, immerges deeper in a lighter Fluid than a heavier ; and deeper as the Proportion of the fpecific Gravity of rhe Solid to that of the Fluid is greater.
3 If a Body be of the fame fpecific Gravity with a Fluid ; the whole Body will be immerged ; and it will remain in any given Place of the Fluid.
4 If a specifically lighter Body be wholly immerged in a Fluid ; it will be urged by the collateral Columns of the Fluid, to atcend with a Force equal to the Excefs of the Weight ot the Fluid, Bulk for Bulk, over the Weight of the Solid.
5 A Body, therefore, specifically lighter, lying on the Bottom ot a VelTel, will not be railed up, unlefs the heavier Fluid rife above fuch a Part, as is equal in Bulk to a Quantity of the Fluid of the fame Weight with the whole Solid.
lO.The jperific Gravity of aSolid, is to the fpecific Gravity of a lighter Fluid, wherein 'tis immerged, as the Bulk of the Part immergedj is to the whole Bulk.
11. The fpecific Gravities of equal Solids, are as their Parts immerged in the fame Fluid.
12. The Weight and Bulk of a fpecifically lighter Body, and the Weight of the fpecifically heavier Fluid, being given, to find the Force required, to keep the Solid wholly immerged under the Fluid.
As this Force is equal to the Excefs of the Weight of the Fluid, beyond that of an equal Bulk of the Fluid; from the given Bulk of the Solid, and the Weight of a Cubic Foot of Water, find, by the Rule of Three, the Weight of a Bulk of Water, equal to that of the Body. From this, fub- ttaft the Weight of the Solid ; the Remainder is the Force required. E. gr. Suppole the Force necefTary to detain a Solid Eight Feet in Bulk, and 100 Pounds in Weight, under Water, required : Since a Cubic Foot of Water is found
to weigh 70 Pound , the Weight of Water under the Bulk ° L H^?*?** ls S6o; whence, 100 Pound, the Weight of the Solid, being iubtrafted; the Remainder 460 Pound, is the Force neceflary to detain the Solid under Water.
Hence, fince a fpecifically lighter Body attends in a heavier Fluid, with the iame Force that would prevent its Afcent : by the prefent Problem, we can likewife find the Force wherewith a fpecifically lighter Body afcends in a heavier.
13. The Weight of a Veffel, to be made of a fpecifically heavier Matter ; and that of a. fpecifically lighter Fluid, be- ing given : to determine the Cavity the VeOel mult have, to fwim on the Fluid.
The Weight of a Cubic Foot of the Fluid being given ; the Bulk of the Fluid equal to the Weight of the VetTel, is found by the Rule of Three. If, then, the Cavity be made a little bigger than this, the VelTel will have lefs Weight under the iame Bulk, than the Fluid, and will therefore be fpecifically lighter than the fame, and confequently, wilt fivim. E.gr. Suppofe it required to make an Iron Ball of 30 Pounds Weight, fo as it mall fwim upon Water. Since the Weight of a Cubic Foot of Water is 70 Pound, the Quantity of Water equal to 30 Pounds, will be found 728 57i'"j and therefore the Cube of the Diameter of the Sphere 1392174'", whence the Cube Rnot being extracted I 1 \" \"' is the Diameter of a Sphere of Water of 30 Pounds. If, therefore, theDiameter of the Cavity be made a little bigger, e.gr. 1 ± or 2 Feet; fo much lefs of the Ball will be im- merged as the Diameter is increafed.
14. The Force employ'd to retain a fpecifically lighter Solid, under a heavier Fluid; and the Weight loft by a heavier Solid in a lighter Fluid ; are each added to the Weight of the Fluid, and weigh together with it.
The ieveral Theorems here delivered, are not only all demonstrable from the Principles of Mechanicks ; but are conformable to Experiment. In effect, Experience is here found to anfwer exactly to Calculation, as is abundantly evident from the Courtes of philolbphical Experiments, now frequently exhibited ; where the Laws of fpecific Gravitation are well iliuftrated.
SPECILLUM, is an Inftrument, wherewith Surgeons fearch Wounds ; in manner of a Probe.
SPECIOUS Arithmetic, is that converfant in Quantities, defign'd by Species, that is by the Letters of the Alphabet ; in contradistinction to that, where the Quantities are ex- prefs'd by Numbers, which is call'd Numerous Arithmetic See Arithmetic; fee alfo Species.
Specious Arithmetic, is what we more ufually call Algebra* See Algebra.
SPECTACLE, Shew ; fome extraordinary Object, which draws the View and Attention ; and is not beheld without lome Emotion.
The Term is chiefly ufed by the Ancients, for theatrical and amphitheatrical Performances : For Comedies, Combats of Gladiators, of Bealts, and even for folemn Proceffions, as thofe of the Circus, ££fc.
The People of Rome were extremely fond of Spectacles $ and the Roman Hiiforians obferve, There was no furer Way of gaining their Affeclions, and making Parties to introduce Tyranny and Oppreffion, than by the Ufe- of Spectacles.
SPECTACLES, an Optic Machine, confifting ot two Lens's fet in Horn, or other Matter ; and applied on the Nofe 5 to affiit in Defects of the Organ of Sight. See Lens.
Old People and all Presbytx, ufe Spectacles of convex Lens's, to make Amends for the Flatneis of the Eye, which does not make the Rays converge enough to have them meet in the Retina. See Presbyt^:.
Short-fighted People, or Myopes, ufe concave Lens's, to keep the Rays from converging fo fait, through the great Roundnefs of the Eye, as to make them meet e'er they reach. the Retina. See Myopes.
In Spain, and at Venice efpecially, Spectacles are ufed with a different View : All the People of Note and Faffiion there, have them continually on their Notes ; a Folly, that has its Source in the natural Pride of thole People, who value them- lelves on a profound Wifdom ; and affect to flare very near at every Thing; as if their Eyes were weakned, and wore out with Excefs of Attention. Vign.de Marv.
F. Chembiv, a Capuchin, defcribes a kind of Spectacle- Telefcopes, for the viewing of remote Objects with both Eyes ; hence called Binoculi. Though F. Rheita had men- tioned the fame before him, in his Oculus Enoch and Eliee. See Telescope.
The fame Author invented a kind of Spectacles, with three or four GlafTes, which perform'd extraordinarily.
Spectacles were certainty unknown to rhe Ancients; yet are they not of fo late a Date as the Telefcope. Francifco Redi, in a very learned Treatife on Spectacles, will have them to have been invented in the 13th Century, betweea ■ the Years 1280 and 131 1 5 and adds, that Alexander De- fpina, a Monk of the Order of Predicants of St. Catherine at 'Pifa, firft communicated the Secret, wh ; h was of his own Invention; upon learning, that another Perfon had it as [ D d ] well
