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confequently thzRbumb fail'd on is had by the Rule of Three. — 4°. Since the Coline is to the whole Sine as the whole Sine to the Secant; the Difference of Latitude GD, is to the Length of the Rhumb-Line AG, as the whole Sine to theSecant of the Angle of the Rhumb.
3 . The Length of the Rhumb-Line, or of the Ship's Way in the fame Rhumb AG, is to the Latus Mecodptamkum, or Mecodina- inic Side AB-f IK-f HF, as the whole Sine to the Sine of the Lexodromic Angle GAP.
Hence, i p . The Rhumb, or Angle of the Rhumb, being given, as alio the Ship's Way in the fame Rhumb-Line AGrj the Meco- dynamc Side is bad by the Rule of Three, in Miles; i. e. in the lame Meafure wherein the Length of the Rhumb is given. — 2°. In like manner, the Mecodynamic Side AB-f-lK-J-HF being given; as alfo the Rhumb Line, or Ships Way AG; the Rhumb fail'd in is found by the Rule of Three.
4 . The Change of Latitude GD, is to the Mecodynamic Side AB-f-iK-fHF; as the whole Sine, to the Tangent of the Loxo- ^m.- Angle PAG or AIB.
Hence, the Rhumb, or Lexodromic Angle PAG, and the change of Latitude CD, being given; the Mecodynamic Side is found by the Rule of Thiee.
5". The MecoAynamfcSi&e AB-j-IK-fHF is a mean Proporti- onal between the Aggregate of the Rhumb AG, and the Change ot Latitude GD and their Difference.
Hence, the Change of Latitude GD, and the Rhumb-Line AG, being given in Miles; the Mecodynamic Side is found in the fameMealure.
6". The Mecodynamic Sid: AE+IK -f-HF being given; to find the Longitude AD.
Multiply the Change or Difference of Latitude GD by fix, which reduces it into parts, of ten Minutes each : Divide the Product, by the Mecodynamic Side; the Quotient gives the Miles of Longitude anfwering to the Difference ot Latitude in ten Mi- nutes. Reduce thefe Miles of Longitude in each Parallel into Differences of Longitude, from a Loxodnmic Table. The Sum of thefe is the Longitude required. See Longitude.
7 . If a Ship fail on a North or South Rhumb, it defcribes a Meridian; if on an Eaft or Weil Rhumb, it defcribes either the Equinoctial, or a Parallel thereto. See Sailing.
8" To find the Rhumb between tvjo Places, by Calculation, or Geometrically. We have two Canons, or Proportions : The firft, —As the Radius, is to the Co-fine of the middle Latitude;- fo is the Difference of Longitude to the whole Departure from the Meridian, in the Courfe between the two Places propofed.
The fecond,— As the Radius is to the half Sum of the Co- fines of both Latitudes; or (rather for Geometrical Schemes) as the Diameter, is to the Sum of the Co-fines of both Latitudes; fo is the Difference of Longitude, to the Departute from the Meridian.
For en Example of the former Proportion.— Let the Rhumb be required between Cape Finifier, Latitude 43°, Longitude 7° 20'; and St. Nicholas Ijle, Latitude 38', Longitude 352 . The middle Latitude is 40" 30', the Complement 49" Degrees 30'; and the Difference of Longitude 15" 20'. Out of thefe leffer equal Parts, prick down 15" from C to L, (Fig. 20.) and de- fcribe the Arch BD with <5o° of the Chords, and make it equal to 40 30', and draw CD continued farther to A.— From L take the nearcft Diftance to AC which is equal to LM, and make it one Leg of a Right-angled Triangle; make the other Leg the Difference of Latitude 5 , which prick from the equal Parts from L to F.— Then, the extent MF meafured on the faid Parts, ihews the Diftance to be >3° 24'; which, allowing 20 Leagues to a Degree, is almoft 2(58 Leagues.— Then, with the Radius CB letting one Foot at M, crofs the Rhumb Triangle at GH; which extent meafurbd on the greater Chord is almoit 22°, the Complement whereof is 68°; and fo much is the Rhumb from the Meridian between the two Places, amounting to 6 Points, and upwards of 80 Minutes.
For an Iultance of the latter Proportion.— Let it be required to find the Rhumb and Diftance between the Lizard and Bermu- das. 1 he Lititude of the Lizard being 56°, and that of Ber- mudas 32°, 20', or 32", 41 Centefms, and their Difference of Longitude, 55" Degrees; draw the Lines AC and CD (Fig. 21.J at Right Angles, and with 60" of the leffer Chords defcribe the Quadrant HI, and prick the Radius from I to D; fo is CD the Diameter; then count both Latitudes iron) H to F and G, the nearer! Diftance from F to CI, is the Co-line of Bermudas Latitude, which prick from C to E: Again, the neareft Diftance from G to CI, is the Co-fine of the Lizard's Latitude, which place from Cro S, fo is CS the Sum of both Co-lines; draw DS, and prick down 55 Degrees, the Difference of Longitude from C to V, out of the grcateft equal Parts, and draw VB Pa- rallel to DS, fo is CB the Departute from the Meridian in the Courfe between both Places.— Making that, therefore, one Leg of a Right-angled Triangle, prick down 17°, 59 Centefms, the Difference of Latitude between thofe Places, out of the fame e- quol Parts from C to L, and draw BL._ This reprefents the Courfe and Diftance between the LfeWand Bermudas; and the extent LB meafured on the fame equal Parts, fliews the Diftance to be 44°, 3 1 Centefms, which allowing 20 Leagues to a Degree, is 886 Leagues. & 5
Then, to find the Courfe.-With 60° of the Chotds, fating one Foot in L, with the other make Marks at Y and Z; then the Extent ZY, meafured on the Chords, (hews the Rhumb to be 66 , 37 Minutes from the Meriuian. This Proportion in the prefent Example, holds very juft, according to Mercator's Chart; whereas the former Proportion, by the middle Latitude, would have given the Rhumb 6 7 °, 2', from the Meridian, and the Di- ftance 902 Leagues.
Again, making CA equal to CV, a Line joining LA would be the Courfe and Diftance according to the fame Longitudes] and Latitudes laid down on the Plain Chart; whereby the Courfe fhould be 72 Degrees 17 Minutes from the Meridian, and the Diftance 1155 Leagues. See Sailing, Chart, &c.
RHTAS, in Medicine, a Diminution or Confumption of the Caruncula Lachrymalis, fituate in the great Canthus or Angle of the Eye. See Caruncula.
The Rhyas is ufed in oppofition to the Encanthis, which is an excelHve Augmentation of the fame Caruncle. See Encan- this.
The Caufe of the Rhyas is a fharp Humour falling on this Part; and gnawing and confuming it by Degrees; though it is rometimes alfo pioduced by the too great Ufe of Cathereticks in the Fifcula Laclirpnalis —It is cured by Incarnatives.
The Word is form'd from the Greet p«t, to Sow.
RHYME, Rhlme, Ryme, or Rime, in Poetty, &c. the fi- milar Sound, or Cadence and Termination of two Words which end two Verfes, &c. See Verse.
Or Rhyme is a Similitude of Sound between the lift Syllable or Syllables of one Verfe, and the laft Syllable or Syllables of a Verfe fuccecding either immediatiy or at the Diftance of two or three Lines.
Rhyme is a modern Invention, the Product of a Gothici Age : Milton calls it the Modern Bondage. Yet fome Authors will have it, the Englijb. French, Sec. borrow rheir Rhyme from the Greeks and Latins. — The Greek Orators, fay they, who endeavour'd to tickle the Ears of the People, affeacd a certain Cadence of Pe- riods, ending in a Confbnance, and cail'd th.m i/Mtir&ttmt. The Latins, who imitated them, cail'd thefe meafur'd Phrales, fimili- ter d'fmentia.
This Affectation increas'd as the Latin Tongue declin'd; fothat in the later Latin Writers, fcarce any tiling is more common than rhyming Periods.
The French, and from them the Exglifj, &c. retain'al this Ca- dence of Rhyme, which feem'd to them mote pretty, and even more agreeable than the meafured Verfes of the Greek and Roman Poets.— This kind of latin Poetry in Rhyme was much in Vogue in the Xllth Century; and the Verfes thus running were call d leonine Verfes; for what Reafon Cambden owns he does not know; (for a Lions-Tail, fays he, does not anfwer to the mid- dle Parts as thefe Verfes do) but doubtlefs they had their Name, from a Canon cail'd Leminus, who firft comp~ftd them with Succefs, and of whom we have feveral Pieces remaining, ad- drefs'd to Pope Adrian IV. and Alexander III. See Leonine Verfes.
Cambden has given us a Collection of Latin Rhymes of our an- tient Engliib Writers; among whom Walter de Mapes Archdea- con of Oxford, in the Time of" King Henry II. makes a princi- pal Figure : Efpccially for two Pieces, the one in Praife of Wine, beginning,
Mihi eft prcpofittim in Totem* mori, Vmum fit appofitxm morientis ori; Ut dicant, cum Venerint, Angelorum Chori, Deus fit propitius huic potatori.
The other aga'».,ft the Pope, for forbidding the Cler,:y their Wives; beginning,
Frificiani Regula pe-R^s cafifatur, Sacerdos per hie & haic ,//w d-ciir/atur; Sed per flic folummodo, nu>« a rticulatur, Cum per Nofirum prmjulem ha* amo-ccatur.
Since the Reftoration of Learning "1, the 16th Century, At- tempts have made to banifh Rhyme out ot the modern Poetrv and to fettle the Englijb and French Verfes on j, e footin" of the antient Greek and Latin ones; by fixing the Quannj cS f t| ie s y i_ lables, and tiufting wholly to thofe, and the Nurab^ or f4 ea _ fure. See Quantity, Numbers, e?r.
This, Milton has done with great Succefs, in his Farad^Lr.ff, and other Pieces; and after htm Philips, Addifon, and fome otiiv s> ' — Verfes of this Kind we call Blank Verfes. See Blank.
The French have attempted the fame, but not with the fame Succefs. — Jodelet made the firft Eflay; and after him Pafauier; but they fail'd. Pa/Jerat and Rapin follow'd them, and fail'd like them. Their Hexameter and Sapphic Verfes were neither imi- tated nor approved; and the Cadence of Rhyme was prefer'd to Quantity, or to long and fhort Syllables. Des Partes likewife made fome Effays of Verfes conftructed of long and fhort Verfes without Rhyme, but the Attempt only ferv'd to convince the World that this Kind of Meafure is inconfiiter.r with the Genius of the French Tongue.
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