One

nroach the Truth. Jf we »ffumc, as- Mr. m$i did, the Arch of oM'wnte to be Unity, and ane Minute to be the common Difference of aRank of Arches: It will be in all Cafes, as the Arch of one Minute ; to itsCbord • So the Secant of the Middle Latitude , to the First Step of our Se-ries This by Reaton of the ncar Equality betwecn n and 2 s, which are toone another inthe Rfitie of Unity to 1—0, 0000000035256645771 3,&fc.iH not Bister front the Secant /, but in the 9 th Figure; bemg less thun it

in that Proportion.

The next.Step being -+• b!_

3 a r r

will be Equal to the

— o,o-

Cube of the Secant of the Middle Latitude Multiplied into -V * 1

3 * r, r

000000070513290X715 ; which therefore unlcss the Secant exceed rentimcs Radius, can ncvcr aniount to 1 ifi the hsih Pl aC e. These two Steps

---- - . _ - — - —- —— * x ncLc two bteps

suffice to make the Meridian Line., or Legar it hm Tangent , to far more Places

thanany 'Fahles of Natural Secams yet extant, are computcd to; but ifihe

ThirdStepbe required it will be found to be -+/1 into ---il— — 0 00000 .

5 /1 r+ ’

OOÖ0Ö060000S949S by all which It appears that MrJVright’s Table doesno where excecd the true Meridian Parts by fully half a Minute ; which EmailDifference arifcs by hishaving added continuaily the Secams of C, 7/,instead of oE, 1F, 2v, 3-j 7 , Ö'c. But as it is, it is abundantly sufficient for, Nautical Ules. That in Sir Jenas Moores New Sjsicme of the Mathematicis Rrriueh neaier the Truth, but the Difference from fVrigh't isscarce (eniible, tillyou exceed thoie Latitudes where Navigation ceales to be. Practicable, theone excceding the Truth about half a Minute, the other being a very sinallmatter Deficient therefrom.

For an Example easie to be Imitated by whofo pleases, I have added thetrue Meridional Parts to the First and Last Minutes of the Quadrant.

The Firfi Minute. 1, 00000001410265862178..

The Second, —-2, 0000000 5641063 806707.

The Last , or 89° 59'. 30374,9634311414228643, and not 32348,<279 as Mr. Wright has it, by the Addition of the Secams of every wholeMinute: Nor 30249, 8 as Mr. Oughtred's Rule makes it, by adding the Se-cams of every half Minute. Nor 30364, 3 as Sir ‘jonas Moor had conclu-ded it by I know not what Method, though in the rest of his Table he fol-lows Oughtred.

The läme niay be Deduced independently, from the Arch it seif. For if theLatitude from the Equator be estimatcd by the length of its Arch A, Radiusbeing Unity, and the Arch put for an Integer be rt , asbefore; the Meridional

Parts anfwering to that Latitude will be — into A -+• -b AA -i- — A 5 -+.0 A 6 24