DIA
[ 205 ]
DIA
the Perimeter of the inferibed Polygon is found 377, and t hatofthecircumfcribed5f.
_/\fter his Example, later Authors have found out 'vjtio's nearer Truth 5 but none fpent fo much Time on ' it as Van Ceuleni who, after immenfe Pains, found, that fuppofing the Diameter 1, the Circumfe- rence Is lefs than 3. 1 4i59^535 8 975>3 2 384<3=6433838795°> and yet greater than the fame Number with the lait Figure o changed into 1. But as fuch prolix Numbers are too un- weildy for Practice, many of our prefent practical Geometri- cians afliimc the Diameter to be to the Circumference as jco to 314; or in greater Circles as 10000 to 51415, jn which Proportion Ttolomy, Vieta, and Huygens agree with Van Ceitlen.
Ad. Metius gives us the Ratio 113 to 355, which is the moil: accurate of all thofe exprefs'd in fmall Numbers 5 as not erring 3 in 100000000.
4, The Diameter of a Circle given, to find the Circum- ference, and. Area $ and the Circumference given, to find ikttffiameter.
The Ratio of the "Diameter to the Circumference being had, as in the lait Article, that of the Circumfe- rence to the Diameter is had like wife. Then the Cir- cumference being multiplied into the fourth Part of the ipUmeteri gives the Area cf the Circle. Thus, if the e Z : iameter be ico, the Circumference will be 314, and the Area of the Circle 7850. But the Square of the Dia- -,,.cter is igooo : Therefore, this is to the Area of the Cir- cle as looco to 7S50, that as 1000 to 785 nearly.
y. The Area of a Circle being given, to find the Dia- tyteter. To 785, 1000, and the given Area of the Circle c : . 176" find a fourth Proportional, viz. 3113 6000, which i he Square of the Diameter. Out of this extract the Square-Root, and it is the Diameter itfclf.
Diameter of a Curve, or Conick SeBion^ is a right I me, as AD, (Tab. Cotticks Fig. y.) biffecting all the Ordi- nates MM, &c. in P, H$c. This, when it cuts the feid Lines at right Angles, is particularly call'd the Axis of the Curve, or Se&ion.
A Tranfverfe Diameter, is a right Line, as AB (Tab. Conicks Fig. 6.) which being continued each Way. between two Curves, biffefts parallel right Lines between the fame, as MM. See Transverse.
Conjugate Diameter, is a right Line, birTecting Lines drawn parallel to the Tranfverfe Diameter. See Conju- gate.
Diameter of a Sphere, is the Diameter of the Semi- Circle, by whofe Rotation the Sphere is generated 5 call'd alfo Axis of the Sphere. See Sph ere.
Diameter of Gravity, is a right Line pafling through the Centre of Gravity. See Centre of Gravity.
Diameter, in Aftronomy. The Diameters of the heavenly Bodies, are cither Apparent, i. e. fuch as they appear to the Eye 5 or Real, i. e. fuch as they are in tuemfelves.
The Apparent Diameters meafur'd with a Micrometer, are found different, in different Circumilances and Parts of their Orbits.
- (jgw. Dl AM. of the Sun accord, to Ptolemy. 3 3 20
to Tycbo 32 o Kepler 3* 4
Ricclolus 32 8
Caffini 32 10
de laHire 3 2 43
ef the Moon accord, to Ptohmy 35 20
Tycho in the Conjunct. 28 48
iVffoOppef. 36 o
Kipler 32 44
de la Hire 3° 33
ef Jupiter according to Tycho 212
■Hevelitit o 19
Huygcns -
ef Saturn according to Tycho 3 59
Rcvelius o 24
Huygens
ef Mars according to Tycho 6 46 Hsvelius o 20 Huygens • ef Venus according to Tycho 4 40 Hevelius 1 5 Huygens — - * ef Mercury accord, to Tycho 3 57 Bcvelittt
"That notable Difference between ^tycho, and the other two Aftronomers, is owing to this, that Tycho, in Imita- tion of the Ancients, meafured the Diameters as they appear to the naked Eye 5 whereas Hevetius and Huygens ufed Telefcopes, whereby a deal of fpuriousLuftre, which other- wife makes them appear bigger than they are, is fhaven off.
For the true Diameters of the Sun, and Planets, and their Proportion to each other. See Semidiameter.
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Diamet-ek of a Column is that taken ju ft above the Bafes. From this the Module is taken, which mcafurcs alt the other Parts of the Column. Sec Module.
Diameter of the Swelling, is that taken at the Height of one Third from the Bafe.
Diameter of the Diminution, is that taken from the Top of the Shafts. See Diminution.
DIAMOND, in Natural Hiitory, by the Ancients call'd Adamant, a prctious Stone, the firft in Rank, Value, Hard- nefs, andLuftre, of all Gems. See Precious Stone.
The Goodnefs ol Diamonds confifts in their Water or Colour, Luftre, and Weight : The moil perfect Colour is the White. Their Defecls are Veins, Flaws, Specks of red or black Sand, and a bluifh, or ycllowifiiCaft. In Europe, the Lapidaries examine the Goodnefs of their rough Diamonds^ their Water, Points, £?c. by Day-Light : In the Indies^ they do it by Night 5 In order to which, a Hole is made in a Wall, a foot-fquare, and therein a Lamp placed, with a thick Wick, by the Light whereof they judge of the Stone, holding it in their Fingers. The Water, call'd Ceeleftis, is the worft of all, and yet is fomewhat difficult to difcover in a rough Diamond. The only infallible Way is to examine it in the Shade of fomc tufted' Tree.
As to the Diftingui filing Diamonds from other Stones, Dr. Wall, in our 'PhilofophicalTranfatlions, feems to have found an infallible Method : A Diamond, with an eafy, flight Friction in the Dark, with any foft, animal Sub- itancc, as the Finger, Woollen, Silk, &c. appears luminous in its whole Body : Nay, if you keep rubbing for forne Time, and then expofe it to the Eye, 'twill remain fo for fotnfe Time. If the Sun be iS Degrees below the Horizon 5 holding up a Piece cfBays, or Flannel itretch'd tight be- tween both Hands, at fome Diflance from the Eye; and another rubbing the other Side of the Bays, or Flannel, pret- ty briikly with a Diamond; the Eight is much more vivid and pleaiant than any other Way. But what he judges mott furprizing is, that a Diamond being expofed to the open Air, in View of the Sky, gives almoit the fame Light of it felf, without rubbing, as if rubb'd in a dark Room: But, if in the open Air, you put the Hand, or any Thing a little over it, to prevent its immediate Communication with the Sky - 7 it gives no Light 5 which is a diflingui /hing Criterion of a Diamond.
A Rough Diamond, is that not yet cut, but jolt as it comes out of the Mine.
A Facet Diamond, is that cut in Faces both a-top, and Bottom, and whofe Table, or principal Face a-top is flat.
A Rofe Diamond, is that quite flat underneath, but its upper Part cut in divers little Faces, ufually Triangles, the uppermoft whereof terminate in a Point.
K'Tahle Diamond, is that which has a large fquare Face a-top, encompafs'd with four kffer.
Diamonds are only found in the Eafi-Indics, and that only in the Kingdoms of Golconda, Vifapour, Sengale^. and the Ifland of "Borneo. There are four Mines, or ra- ther two Mines, and two Rivers, whence Diamonds are drawn. The Mines are, 1. That of Raolconda, in the Province of Carnatica, five Days Journey from GolcOnda % and 8 from Vifapour. It has been difcover'd about 200 Years. 2. That oiGani, or Contour, 7 Days Journey from Golconda, Eaftwardly. It was difcover'd 120 tears ago by a Peafant, who digging in the Ground found a natural Frag- ment of 25 Caracls. 3. That of SoumelpOJtf, a large Town in the Kingdom otSengale, near thcDiamond-M/he. This is the molt ancient of them all. It fhould rather be call'd that oiGoual, which is the Name oftheRiver, in thcSand whereof thefe Stones are found. Laftly, the 4th Mine, 01- rather the fecond River, isthatttf Suctudan, in the Hie of Tiorneo.
Diamond- JIf/#e of Raolconda. In the Neighbourhood of this Mine, the Earth is' Tandy* and full of Rocks, and Copfe. In thefe Rocks are found feveral little Veins, of half, and fometimes a whole Inch broad, out of which the Miners, with a Kind of hooked Irons, draw the Sand, or Earth, wherein the Diamonds arc 5 breaking the Rocks, when the Vein terminates, that the Track may be found again, and continued. When a fufficicnt Quantity of Earth, or Sand is drawn forth, they warn it two or three times, to fe par ate the Stones therefrom* The Miners work quite naked, except for a thin linnen Cloth before them, and befides this Precaution, have like* wife Infpeclors, to prevent their Concealing of Stones; which, however, maugre all this Care, they frequently find means to do 5 by watching Opportunities when they are not obferved, and fwallowing them down.
DiamondJ//w o/Gani, or Couloun
In this Mine are found a great Number of Stones from
10 to 40 Caracas, and even more 5 And it was here
that famous Diamond of Aureng-Zeb, the Great Moguls
which before it was cut, weighed 780 Caracas, was found,
M* Tbfl
