SPH
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SPH
Quadrant. Hence, if the two Sides be lefs than a Quadrant, the two Angles are acute.
14. If in a Spherical Triangle ^ the feveral Sides be each greater than a Quadrant 5 or only two of them greater, and the Third equal to a Quadrant 5 the feveral Angles are obtufe.
15. If in an obliquangular Spherical Triangle, two Sides be lefs than a Quadrant, and the Third greater ; the Angle oppoiite to the greateft will be obtufe, and the reft acute.
Refoli'.tim of Spherical 'Triangles. See Triangle.
Spherical Geometry, the Doctrincof the Sphere ; parti- cularly of the Circles described on the Surface thereof, with the Method of projecting the fame on a Plane. See Sphericks.
Spherical Trigonometry^ the Art of refolding Spherical Triangles ; i. e. from three Parts of a Spherical Triangle given, to find the reft. E.gr. From two Sides of one Angle 5 to find the other two Angles, and the third Side. See Sphe- rical Triangle and Trigonometry.
SPHERicAc^woffl-r, that Part of Altronomy which considers the Univerfe, fuch as it appears to the Eye. See ^ Astronomy.
Under Spherical Agronomy, then, come all the Phenomena and Appearances of the Heavens and heavenly Bodies, fuch as we perceive them ; without any Inquiry into the Reafon, the Theory, or the Truth thereof; by which it is diftinguifh- ed from Theorical Aftrommy, which confiders the real Structure of the Univerfe, and the Caufe of thofe Pheno- mena.
In the Spherical Aflronomy, the World is conceived to be a concave, fpherical Surface, in whofe Centre is the Earth, or rather the Eye, about which the vifible Frame revolves, with Stars and Planets fix'd in the Circumference thereof. And on this Suppoiition all the other Phenomena are deter- mined.
The Theorical Agronomy teaches us, from the Laws of Optjcks, %§c. to correct: this Scheme, and reduce the whole to a juffer Syftem. See System.
SPHERICITY, the Quality of a Sphere ; or that whereby a thing becoms Spherical-, or round. See Sphere.
The Sphericity of Pebbles, Fruits, Berries, &c. of Drops of Water, Quick-filver, &c. of Bubbles of Air under Water, %$c Dr. Hook takes to arife from the Incongruity of their Particles wirh thofe of the ambient Fluid, which prevents their Coalefcing; and by preffing on them, and encompafling them all around equally, turns them into a round Form. See Drop.
This, he thinks, appears evidently, from the Manner of making fmalKround Shot of feveral Sizes, without calling the Lead into any Moulds 5 from Drops of Rain being form'd, in their fall, into round Hail-ftones ; and from Drops of Water falling on fmall Duft, Sand, &c. which ftrait produce an artificial round Srone ; and from the fmall, round, red-hot Balls, form'd by the Collifion or Fufion of Flint and Steel, in finking Fire.
But all thefe Cafes of Sphericity feem better accounted for, from the great Principle of Attraction 5 whereby the Parrs of the fame Fluid drop, ££?c. are all naturally ranged as near the Centre as poffible, which necefTarily induces a fpherical Figure; and, perhaps, a repelling Force between the Particles of the Drop, and of the Medium, contribute not a little thereto. See Attraction.
SPHERICKS, theOJoBrim of the Sphere, particularly of the feveral Circles defcribed on the Surface thereof; with the Method of projecting the fame in Piano. See Sphere.
The principal Matters /hewn herein, are as follow :
1. If a Sphere be cut in any Manner, the Plane of the Section will be a Circle, whofe Centre is in the Diameter of the Sphere.
Hence, i°, The Diameter H I (Tab. Trigon.Fig. 17.) of a Circle, palling through the Centre C, is equal to the Diameter A B of the generating Circle ; and the Diameter of a Circle, asFE, that does notpafs through the Centre, is equal tofome Chord of the generating Circle.
Hence, ^°, As the Diameter is the greateft of all Chords ; a Circle paffing through the Centre, is the greateft Circle of the Sphere ; and all the reft arc lejjer than the fame.
g° Hence, alfo, all great Circles of the Sphere are equal to one another.
4 Hence, alfo, if a great Circle of the Sphere pals through any given Point of the Sphere, as Aj it muft alfo pafs through the Point diametrically oppofite thereto, as B.
5° If Two great Circles mutually interfecfc each other, the Line of the Section is the Diameter of the Sphere, and there- fore two great Circles interfect each other in Points diametri- cally oppofite.
6° A great Circle of the Sphere, divides it into two equal Parts or Hemifpheres.
2. All great Circles of the Sphere, cut each other into two Parts ; and, converfely, all Circles that thus cut each other, are great Circles of the Sphere,.
3- An Arch of a great Circle of the Sphere, intercepted
, as AFBD, pafs through the Poles rele D E F, it cuts it into equal Parts 5
between another Arch H I L (Fig. i g.) and its Poles A and B, is a Quadrant.
That intercepted between a lefs Circle DEF, and one of its Poles A, is greater than a Quadrant ; and that between: the fame and the other Pole B, lefs than a Quadrant ; and, converfely.
4. If a great Circle of the Sphere pafs through the Poles of another, that other pailes through the Poles of this. And if a great Circle pafs through the Poles of another, the Two cut each other at right Angles, and converfely.
y. It a great Circle, i ' A and B of a Iefler Circ] and at right Angles.
6. If two great Circles AEBF and CEDF (Fi?. 19.) in- terject each other in the Poles E and F of another great Circle ACBD ; that other will pafs through the Poles Hand h I and i of the Circles AEBF and CEDF.
7. If two great Circles AEBF and CEDF, cut each other mutually ; the Angle of Obliquity A E C, will be equal to the Diftance of the Poles H I.
g. All Circles of the Sphere, as GF andLK (Fig. 20:) equally diftant from its Centre C, are equal; and the further they are removed from the Centre, the lefs they are. Hence, finceofall parallel Chords, only two, D E and EK are equally diftant from the Centre ; of all the Circles parallel to the fame great Circle, only two are equal.
9. If the Arches FH and K H, andGI and IL, inter- cepted between a great Circle I M H and the leffer Circles G N F and LOK; be equal, the Circles are equal.
10. If the Arches FH andGI of the fame great Circle AIBH, intercepted between two Circles GN F and IMH, be equal , the Circles are parallel.
11. An Arch of a parallel Circle I G (Fig. 11.) is fimilar to an Arch of a great Circle A E 5 if each be intercepted between the fame great Circles C A F and C E F.
Hence the Arches A E and I G, have the fame Ratio to their Peripheries ; and, confequently, contain the fame Num- ber of Degrees. And hence the Arch I G is lefs than the Arch A E.
1 2. The Arch of a great Circle, is the fhorteft Line which can be drawn from one Point of the Surface of the Sphere to another : And the Lines between any two Points on the fame' Surface, are the greater, as the Circles whereof they are Arches, are the lefs.
Hence, the proper Meafure, or Diftance of two Places on the Surface of the Sphere, is an Arch of a great Circle inter- cepted between the fame.
SPHEROID, in Geometry, a Solid approaching to the Figure of a Sphere, but not exactly round , but oblong ; as having one of its Diameters bigger than the other; and gene- rated by the Revolution of a Semi-ellipfis about its Axis.
When 'tis generated by the relation of the Semi-ellipfis about its greater Axis, 'tis call'd an Oblong Spheroid ; and when generated by the Revolution of an Ellipfis about its lefs Axis, an oblate Spheroid. See Oblate.
The Contour of a Dome, ^Daviler obferves, fhould be Half a Spheroid. Half a Sphere, he fays, is too low to have a good Effect below. See Dome.
For the Solid Dimenfions of a Spheroid, 'tis 4 of its Circum- fcribing Cylinder : Or it is equal to a Cone, whofe Altitude is equal to the greatet Axis, and the Diameter of the Bafe to four Times the lefs Axis of the generating Ellipfis.
Or a Spheroid is to a Sphere defcribed on its greater Axis, as the Square of the lefs Axis to the Square of the greater : Or 'tis to a Sphere defcribed on the leffer Axis, as the prcater Axis to the Lefs. The Word is form'd from Sph-era-, and Sj 1 ©-, Shape.
SPHINCTER, in Anatomy, a Term applied to a kind of circular Mufcles, or Mufcles in Form of Rings, which ferve to clofe and draw up feveral Orifices in the Body, and prevent the Excretion of the Contents. See Muscle.
The Word is form'd from the Greek wyK7>i%, Stridor, i. e. fomething that binds and conftringes a Thing very clofely ; thefe Mufcles having an Effeft much like that of a Purfe- ftring.
Sphincter. Ani, is a circular Mufcle, ferving tofhut the Anus, and keep the Excrements from coming away involun- tarily. See Anus and Excrements.
'Tis near two Inches broad, and hangs down below the Reclaim, near an Inch. It is faften'd on the Sides to the Bones of the Coxendix, and behind to the Os facrum : Before, in Men, to the Accelerator Urin£, and in Women, to the Vagina Uteri. See Rectum.
Some would have it Two Mufcles, and fome Three ; but without much Reafon.
Sphincter Vejficte, is a Mufclccoijfifting of circular Fibres, placed at the Exit of the Bladder, to prevent the perpetual dripping of the Urine. See Urine and Bladder.
It keeps the Bladder conltantly fhut ; and is only opened, when by the Contraction of the Abdominal Mufcles, the Bladder is comprefs'd, and the Urine forced out.
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Sphincter.
