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:s BC = 61° 46′ = 1° 46'. The Sun's Place. Then

As R ctBt ACs BA = 59° 39', the Right Afcenfion. This Problem being the Reverse of the two laft, needs no Example in Numbers.

PROBLEM VII.

Given the Sun's Place 1° 46′ and greatest Declination 23° 29'; to find the Angle of the Sun's Pofition, or that Angle which the Ecliptic makes with the Meridian, viz. AC B.

Practice.

Use the Analogy in the Synopfis Cafe 2, Var. 3; faying,

As the Co-fine of B C = 61° 46′

Is to Radius

-

9.6749194

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So is the Co-tangent of B = 23° 29′ 10.3620437

---

To the Tang. of the Ang. C — 78° 23′ 10.6871243

Or thus; Rcs BC::tB:ct C = 78° 23'.

Note, If the Sun's Place and prefent Declination be given, that is, BC and AC; then the Angle C is found thus ;

R:ct BC::tAC:cs C = 78° 23'

Also if the prefent Declination A C, and Right Afcenfion B A, be given, the Angle C is found by this Analogy.

=

SCA:R::tBA::1 C 78° 23'.
Varied thus,

Rct BASCA: ct C = 78° 23'.

PROBLEM VIII.

Given the Latitude of the Place, and the Sun's Declination, to find its Amplitude of Rifing and Setting.

Practice.

Practice.

Suppofe at Chichester it be required to find the Sun's Amplitude, May the 1ft, 1735, when the Declinanation is 20° 34'; by Prob. 4.

In the Scheme annexed, there are formed two Right-angled Triangles A B C, and CP H, by either of which this Problem may be fatisfied. For in the Triangle ABC, befides the Right-angle at A, there is given the Side A C, which is the present Declination, and the Angle at B the Com

H

P

A

To answer this,

B

S

N

plement of the Latitude; to find the Amplitude B C. Alfo in the Triangle CPH, Right-angled at H, there is given the Side HP the Latitude, and C P the Complement of Declination, to find HC, the Complement of the Amplitude.

In the Triangle ABC, the Analogy is this,

As the Sine of B = 39° 04'
Is to the Sine of AC=20° 34'
So is Radius

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9.7994951 9.5456896

10.0000000

To the Sine of the Amplit. BC=33° 52′ 9.7461945

In the Triangle CP H, this is the Analogy; As cs PH: R::cs PC:cs HC = 56° 08'. Hence we see on that Day the Sun will rife and fet 33° 52' from the Eaft and Weft Points of the Hori

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zon towards the North; or 568 08' from the North towards the Eaft or Weft Points of the Horizon; that is on the Points NE by E, and NW by W, very nearly.

PROBLEM IX.

Given the Latitude and prefent Declination, to find the Afcenfional Difference; and fo the true Time of the Sun's Rifing and Seting, and the Length of Days and Nights.

Practice.

Example. Let the Latitude be that of Chichester, viz. 50° 56', and the Sun's Declination 20° 34', as on May 12th, 1735; I demand the Afcenfional Difference?

In the foregoing Scheme, by either of the two Right-angled Triangles ABC, or CPH, this Problem alo is to be answered.

For in the Triangle ABC, the Side AC, and Angle B, are given to find AB, the Afcenfional Difference.

Alfo in the Triangle CPH, there is given HP, and CP, to the Angle at P the Complement of the Afcenfional Difference.

'Tis moft directly found by the Triangle A B C, whofe Analogy runs thus,

As Radius

Is to Co-tangent of B = 39° 04'

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10.0905978

So is the Tangent of AC= 20° 34' 9.5742761

To the Sine of AB = 27° 32′

9.6648739

The

The Analogy for finding the fame in the Triangle CPH, is this; As t PC:R::tPH: cs P= 62 28'.

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Now the Afcenfional Difference A B being found 27 32, this Motion in the Equinoctial is performed by the Sun in 1 Hour, 50 Minutes, 8 Seconds of Time; and this being the Time the Sun riseth before, and fetteth after, 6 a-Clock, 'tis evident the Sun will then rife at 4 H. 9 M. 52" in the Morning; and fet at 7 H. 50' 8" at Night.

Confequently the Length of that Day will be 15 H. 40' 16"; and the Length of the Night 8 H. 19' 44", as was required.

PROBLEM X.

Having given the Right Afcenfion, and Afcenfional Difference; to find the Oblique Afcenfion, and Defcenfion.

Practice.

1. If the Sun be in Northern Signs, fubftract the Afcenfional Difference from the Right Afcenfion, the Remainder is the Oblique Afcenfion.

Thus on May 12th, 1735. The Afc. Diffe. is 27 32 The Right Afc. is 59 39

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3. But if the Sun be in the Southern Signs, the Sum of the Right Afcenfion and Afcenfional Difference gives the Oblique Afcenfion; and their Difference, the Oblique Defcenfion.

PROBLEM XI.

The Latitude and Declination given, to find the Time (Morning and Evening) when the Sun will be due Eaft and West.

Practice.

In the adjacent Diagram, there are formed two Right-angled A Triangles A B C and CP Z, in either of which this Problem may be answered. For in the Triangle ABC, H there is given the Side A C, the Declination; and the Angle at B the Latitude; to find the Side A B, the Timebefore and after fix a

S

N

P

Clock, wherein the Sun will be in the Azimuth of East and West Z N, in the Point C.

Alfo in the Triangle C P Z, there is known, the Side CP the Co-Declination; the Side Z P the Co-latitude; to find the Angle P, the Time from Noon, &c.

Example. I demand what Time the Sun will be due Eaft or Weft on May the 12th, 1735, when the Declination of the Sun will be 20° 34', at Chichester, whofe Latitude is 50° 56/?

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