R 1 N 



R I N 



Kepler, in his Epitom. Aftron. Copern., and after him 

 Dr. Halley, in his Inquiry into the Caufes of the Variation 

 of the Needle, Phil. Tranf. N° 195, fuppoie our earth may 

 be compofed of feveral crufts or (hells, one within another, 

 and concentric to each other. If this be the cafe, it is pof- 

 fible the ring of Saturn may be the fragment or remaining 

 ruin of his former exterior (hell, the reft of which is broken 

 or fallen down upon the body of the planet. 



Ring is alfo the name of an inftrument ufed in navigation, 

 for taking the altitudes of the fun, &c. 



It is ufually of brafs, about nine inches diameter, fuf- 

 pended by a little fwivel, 45° from the point of which is a 

 perforation, which is the centre of a quadrant of 9C , di- 

 vided in the inner concave furface. 



To ufe it, they hold it up by the fwivel, and turn it 

 to the fun, till the fun-beams, falling through the hole, 

 make a fpot among the degrees, which marks the altitude 

 required. 



This inftrument is preferred to the aftrolabe, becaufe the 

 di virions are here larger than on the altrolable. See As- 

 trolabe. 



Ring is alfo ufed for the found or tone of a bell ; which 

 lee. 



The ringing of bells, though now a recreation chiefly ot 

 the lower clafs of people, is a very curious exercife. As 

 for the tolling of a bell, this is nothing more than the pro- 

 ducing of a found by the ltroke of the clapper againlt the 

 fide of a bell ; the bell itfelf being in a pendant poiition, 

 and at relt. In ringing, the bell, by means of a wheel and 

 rope, is elevated to a perpendicular : in its motion to this 

 fituation, the clapper ftrikes forcibly on one fide, and, in 

 its return downwards, on the other fide of the bell, pro- 

 ducing at each itroke a found. The mufic of bells is alto- 

 gether melody ; but the pleafure ariiing from it confiils in 

 the variety of interchanges, and the various fuccefhon and 

 general predominance of the conionances in the founds pro- 

 duced. 



The practice of ringing bells in change is faid to be pe- 

 culiar to this country, which for this reafon is called the 

 ringing ifland ; but the antiquity of it is not eafily alccr- 

 tained. There are in London feveral focieties of ringers, 

 particularly one known by the name of the College Youths. 

 Merfennus has fud nothing of the ringing of bells in 

 changes ; and Kircher has only calculated the poffible com- 

 binations arifing from a given number. See Alterna- 

 tions. 



In England, the practice of ringing is reduced to a 

 fcience ; and peals have been compofed, which bear the 

 names of the inventors. Some of the moil celebrated peals 

 now known were compofed about fifty years ago, by Mr. 

 Patrick, fo well known as the maker of barometers. 



For the method of ringing in the Low Countries, fee 

 Carillons. 



Ring, or Annulus, in Geometry. See Annulus. 

 The area of the ring included between the circumferences, 

 A B P A, D E Q D, of two concentric circles, ( Plate XII. 

 Geometry, Jig. 12.) is obtained bv the rule given under An- 

 nulus : viz. Multiply the fum of the diameters by their 

 difference, and the product by .7854, and the ultimate 

 product will be the area required : for the ring being equal 

 to the difference of the two circles, if the diameters be called 

 D, d, and -785398, &c. — a, we (hall have the ring = 



aD - ad'- -^ a x DT~d x D - d. Hence if D W 

 be a perpendicular to the radius C D A, DW : will be 



equal tp A D x AC" + CD = D-d x D -r d, and 

 a D W % or the area of a circle whofe radius is D W, will 



be = oD 1 — ad" = the area of the ring. Hence alfo it 

 appears, that the ring is equal to an ellipfe whole axes are 

 D -u- d and D — d. See Ellipse. 



The area of the ring may alfo be had, by multiplying 

 halt the fum of the circumferences by half the difference of 

 the diameters, the produft being the area. For the cir- 

 cumferences are equal to 4aD, q.ad: therefore a x 



D+rf = |C + |r; which, by fubftitution in the laft 



rule, will give a x T) + d-x.~D — d=\C+\c x 



D~-d = I C + ic x |D — i d, as in the rule. The 

 fame rule will ferve alfo for a part of the ring, ABED A, 

 included between the parts, A D, B E, of two radii, 

 uling for C and c the lengths of the intercepted arcs. 



Another rule for finding the area of the ring is as fol- 

 lows : Multiply the perpendicular breadth of the ring, that 

 is, the difference of the radii, by the circumference R S T, 

 (or part RS for the part A BE DA,) having, the fame 

 centre with, and equally diftant from, the bounding arcs. 

 For this circumference, being equally diftant from the other 

 two, will be equal to half their fum. Hence the whole 

 ring, or any part of it ABED A, included between two 

 radii, is equal to a parallelogram on the fame bafc A D, 

 and whofe altitude is equal to R S, the middle circum- 

 ference. 



Ring, Solid, is a folid returning into itfelf; of which 

 every fection perpendicular to the axis, or line palling 

 through the middle, of the folid, is every where the fame 

 figure, and of the fame magnitude. 



To Jind the Surface of a folid Ring. — Multiply the axis by 

 the perimeter of a fedtion perpendicular to it, and the pro- 

 duft will be the furface. E. gr. a workman having made 

 for a jeweller a circular ring, or a ring whofe axis forms the 

 circumference of a circle ; it is required to find the expencc 

 of the gilding, at a penny the fquare inch ; the thicknefs of 

 the ring, or the diameter of a feftion of it, being 2 inches ; 

 and the inner diameter, acrofs from fide to fide, 18 inches. 

 Here 18 4- 2 = 20 = the diameter of the circle formed by 

 the axis; and confequently 20 x 3.14159 = the length of 

 the axis. But 2 x 3.14159 = the circumference of a fec- 

 tion of it ; therefore 20 x 3.14159 X 2 x 3.14159 = 40 

 X 3.14159*= 394.785 fquare inches, nearly, = 394.785 

 pence = 1/. 12s. iold. nearly, the expence required. 



To find the Solidity of a Ring. — Multiply the axis by a 

 feftion perpendicular to it, and the product will be the fo- 

 lidity. E. gr. required the price of a ring of iron, whofe 

 dimenfions are the fame with thofe in the laft example, at 

 four-pence a pound; a cubic inch of iron weighing 4.423 

 ounces avoirdupois. Here the area of a fedtion being 2" x 

 .7S5398 = 3.14159, which expreffes half the circumference, 

 and the axis being the fame as before, the folidity will evi- 

 dently be exprefled by half the furface in the laft example ; 

 /. e. the folidity = 197.3925 cubic inches, which multiplied 

 by 4.423, gives 873.065 ounces = 54.56657 pounds ; 

 which, at 4J. each, will amount to i8.r. z^d., the price re- 

 quired. 



It is needlefs to multiply examples, as the mode of opera- 

 tion is the fame in all forms, with thole tor prifms, both 

 with regard to the furfaces and folidities : for it is evident 

 that any ring is equal to a prifm, whofe altitude and end 

 are refpeflively equal to the axis and feftion of the ring, 

 both as to furface and folidity, and, therefore, the rules for 

 them both muft be the fame ; and, on this account, any de- 

 monftration of the rules for rings is unneceffary. Huiton's 

 Menfuration. 



Rings of Colours, in Optics, a phenomenon firit obferved 

 9 



