Imágenes de páginas
PDF
EPUB

PROBLEM VIII.

To exhibit or point out the general Uses of this Projection.

The more notable Ufes of this Projection are as follows.

1. It manifeftly appears, that when the Sun is in either Aries, or Libra, it is alfo in the Equinoctial ER, and confequently that then the Days and Nights are equal all over the World; that is, the Diurnal Arch Ev = √ R the Nocturnal Arch; and this happens twice in the Year, viz. March the Tenth, and September the Twelfth; as is plain from the Calendar. II. When the Sun is in the Sign Cancer, 'tis plain the Days are then longeft, and the Nights the shortest they can be to us in the Latitude of London; that is the Semidiurnal Arch, a, is then the longest, and the Seminocturnal Arch, a T, is then the shortest it ever can be; and this happens about June the Eleventh.

III. It appears that on the longest Day, the Height of the Sun at Noon is H = 62 Degrees; its Height when due Eaft or Weft, Sv= and its Height at the Hour of 6, Morning and Evening, is AK- The Sun's greatest Declination then is E = 23° 30'; its greatest Amplitude is ra= its greatest afcenfional Difference is Aa= it is alfo evident there is then no dark Night, for the Almacanter Ww, which bounds the Twilight and total Darknefs, doth not touch the Tropic ST, or parallel of the Sun's Motion for that Day.

The

[merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small]

IV. When the Sun is in the Sign Capricorn VS, juft
the Contrary will happen to what did when the
Sun was in Cancer; the Semidiurnal Arch KX is
now the shortest, and the Seminocturnal Arch
VOL. II.

E 2

X Wa

Xvs, is the longest it can be; the Amplitude XV, is equal, but on oppofite Points, to Vas fo the Declination is now E K E = 23° 30', but South; the Meridian Altitude is now but HK = 15° 00'; the Length of Twilight is the Arch X. The afcenfional Difference is much about equal to the Twilight in this Cafe.

PROBLEM IX.

To exhibit in one. View a Synopfis of the Aftronomical Affections and Pofitions of the Heavens, for any particular Time, as May the firft, for Example.

[ocr errors][merged small]

From the first of May, parallel to the Equinoctial ER

draw the Parallel of Declination ƒ I,

cutting the Ecliptic in O,

through which draw the Almacanther gb:

Let fall the Perpendiculars fe,

m, bi.

Suppofe the Time of the Day, be Nine a-Clock in

the Morning.

Then draw the Hour Circle of 9 P L QM,

and the Azimuth Circle Zp Nq.

Then for May the firft, 9 Hour, A M.

The Sun's Place will be, o,

His Longitude in the Ecliptic, vo.

Declination North, E f.

Meridian Altitude, Hf.

Altitude at 9 a-Clock, m.

Altitude at 6 a-Clock, bi.

Altitude when Eaft or Weft, s V.

Rifing and Setting, C.

Right Afcenfion, L.

Afcenfional Difference, bc,

Amplitude of Rifing and Setting, V c.
Azimuth at 9 a-Clock, V p.
Semidiurnal Arch, fc.

Seminocturnal Arch, c I.

The Arch of Twilight, ct.

Note, The Time of the Motion in any of those Arches is easily known. For fince the Sun, or Earth, moves 360° in 24 Hours, that is at the Rate of 15° in one Hour, and 15′ in one Minute of Time.

PROBLEM X.

To reprefent the fixed Stars in the Analemma.

Practice.

I. Find the Star's Declination from the Equinoctial. II. Alfo its Latitude from the Ecliptic.

III. Draw the Parallel of the Star's Declination, to the Equinoctial.

IV. Draw the Parallel of its Latitude alfo to the Ecliptic.

V. Then in the Point where thefe two Parellels do interfect each other, will the Star be projected.

Thus I fuppofe the young Learner hath by this time a fufficient Notion of the Nature, Manner, and Ufe of the Orthographical Projection. And I do advife every one that is ftudious this way, to make for his Use a very large one, with the Calendar annexed, and it will serve him as a perpetual Almanack; and fave him the trouble of Calculation in many Aftronomical Problems; as is evident from what I have already fhewn, and will hereafter further appear.

СНА Р.

CHA P. IV.

Theorems ferving to the Stereographic Projection of the Sphere in Plano.

THEOREM I.

A Point is there projected into a Point in the Plane of the Projection, where a Ray of Light, paffing thro' the Eye and the given Point, meets the Plane of the Projection.

Demonftration.

[blocks in formation]

and the Point B

will be projected in b,

which is the Plane infinitely continued. 2, E. D.

THEOREM II.

A ftraight Line in the remote Hemifphere, or Semicircle, is projected into a Right Line lefs than it felf but in that Hemisphere, or Semicircle, which is contiguous

« AnteriorContinuar »