Page images
PDF
EPUB

Fig. XXIX.

PROB. III.

The Latitude of the Place, 51 d. 30 m. and the Sun's Place in the Ecliptick, 29 d. of Taurus, given, to find,

1. The Sun's Declination.

2. The Sun's Amplitude.

3. The Hour from Midnight or Afcenfion all Difference. 4. The Time of the Sun's Rifing and Setting.

5. The Length of the Day and Night.

6. The Angle of the Sun's Pofition at the time of his Rifing or Setting.

I. By the Coeleftial Globe.

Ring the 29 d. of Taurus to the Brafs Meridian, and you B will find 29 of Taurus to lye under 20 d. of the Meridi an, and that is the Sun's Declination North, the Sun being in a Northern Sign. Then, fet the Index of the Hour-Circle to the South 12, and turn the Body of the Globe Eaftward, till 29 d. of Taurus do juft touch the Horizon, and there fix it. Then fhall you find 29 d. of Taurus to cut the Horizon in 33 d. 18 m. counted from the Eaft, which is the Amplitude of the Sun's Rifing from the true Eaft Point of the Horizon Northward: And alfo, the Index of the Hour-Wheel, will point out 11 m. after 4 in the Morning, at which time the Sun Rifeth. -And if you turn the Body of the Globe about Weftward, till 29 d. of Taurus doth touch the Weft Side of the Horizon; then fhall the Index point at 49 m. after 7 at Night, at which Time the Sun Setteth.

Again, Turn the Globe about, till 29 d. of Taurus touch the East Side of the Horizon (as before) and fet the Index of the Hour-Circle to the North (or undermoft) 12: And then turning it Weftward till 29 d. of Taurus touch the Horizon on the Weft Side; and then (hall the Index point at 3 ho. 38 m. more than 12 Hours, from the South 12: Which Thews that the Day is then 15 ho. and 38 m. Long. And if you count the Hours between the North 12 and the Index, you fhall find them to be 8 ho. and 22 m. and that is the Length of the Night.

And then, for the Angle of the Sun's Pofition, that is to be found, as is directed in the 24th Element, and in the Problem to this Second Part, and will be found to be 56 d. 23 m.

The

Fig.

The Globe being in this Pofition, there is reprefented upon the Superficies of it a Spherical Triangle PO O, as in Fig. XXIX. compounded of the Arches of fuch Great Circles of the Sphere, as are ingredient in the Propofition, viz. Of P O, an Arch of the Brass Meridian; of O, an Arch of the Horizon; and of PO, an Arch of that Meridian, which cutteth the Ecliptick in that Point in which the Sun is. And in this Triangle, the Angle PO is a Right Angle: PO, is the Hour from Midnight: And the Angle P O O, is the Angle of Pofition made by the Meridian and Horizon, at the time of the Sun's Rifing. II. By Trigonometrical Calculation.

In the Triangle POO, you have given, (befides the Right Angle at O). (1.) The Hypotenufe P, the Complement of the Sun's Declination, (70 d.) (2.) The Perpendicular PO, the Latitude 51 d. 30 m. To find, (1.) The Bafe O O, the Sun's Amplitude at his Rifing. (2.) The Angle o PO, the Hour from Midnight: And, (3.) The Angle P O Ŏ; the Angle of the Sun's Pofition at his Rifing.

The Canons for Calculation.

1. For the Amplitude,

O. By Cafe VI. of R. A. S. T. As the Co-fine of P O, (the Latitude) 38 d. 30 m.

Is to the Radius, 90 d.

So is the Co-fine of Po, (the Sun's Declination) 20 d.
To the Co-fine of O O, (the Amplitude) 33 d. 20 m.
Which is equal to the Arch of the Horizon. Or O, which
is the Amplitude of his Rifing from the Eaft North-
ward, because the Sun was in a Northern Sign: For if
he had been in a Southern Sign, as in 59 d. of Scorpio,
the Amplitude would have been the fame, but from the
Eaft Southward.

2. For the Hour from Midnight PO. By Cafe V. of R. A. S. T. As the Radius,

Is to the Tangent of PO (the Latitude) 51 d. 30 m.

So is the Co-tangent of PO (the Sun's Distance from the Pole) 20 d.

To the Co-fine of PO (the Hour from Six) 27 d. 14 m. Whofe Complement, 62 d:46 m. is the Hour from Midnight; which turned into Time, (by allowing 15 d. for 1 h. and 4 d. for 1 m. of Time) makes 4 h. and 11 m. Which is the Hour from Midnight.

I i

3. For

Fig. XXIX.

3. For the Afcenfional Difference.

The Hours from Midnight, 4 h. 11 min. fubftracted from 6 h.. there remains 1 h. 49 m. which is the Afcenfional Difference.. Or, The Time that the Sun Rifes before Six in the Summer, or after Six in the Winter.

4. and 5. For the Time of the Sun's Rifing and Setting, and (confequently) the Length of the Day and Night.

The Afcenfional Difference, 1 h. 49 m. being added to 6 h. gives 7 h. 49 m. for the Semidiurnal Ark in Summer; or fubtracted from 6 h. gives 4 h. 11 m. for the Semidiurnal Ark in Win

ter.

The Semidiurnal Ark, 7 h. 49m. fubftracted from 12 h. there remains 4 h. 11 m. for the time of the Sun's Rifing: And that fubftracted from 12 h. leaves 7 h. 49 m. for the time of the Sun's Setting. And,

The Semidiurnal Ark, 7 h. 49 m. doubled, gives 15 h. 38m. for the Length of the Day: And 15 h. 38 m. fubftracted from 24 h. there will remain 8 h. 22 m. for the Length of the Night. 6. For the Angle POO, of the Sun's Pofition, at the time of his Rifing. By Cafe IV. of R. A.Š. T.

As the Sine of Po (the Co-Declination) 70 d.
Is to the Radius:

So is the Sine of PO (the Latitude) 51 d. 30 m.

To the Sine of POO (the Angle of Pofition at the Sun's Ri fing) 56 d. 23 m.

PRO B. IV.

To find the Sun's Meridian Altitude, and his Depreffion at Mid-
night, he being in any Point of the Ecliptick.

ET the Place of the Sun be the fame, as in the former
Problem, viz. in 29 d. of Taurus. Then,

I. By the Cœleftial Globe.

Turn the Globe about, till the 29 d. of Taurus be just under: the Meridian, then fhall you find the Number of Degrees of the Meridian, which are comprehended between that Point and the Horizon to be 58 d. 30m. which is the Meridian Altitude. And îf you bring the 29 d. of Scorpio, which is the oppofite. Point of

the

the Ecliptick in which the Sun is, to the Meridian, the Number Fig. of the Degrees of the Meridian between that Point and the Hori XXIX. zon will be found to be 18 d. 30 m. which is the Sun's Depreffion at Midnight.

D. M.

16 00

In like manner,

[blocks in formation]

When the 25 00 m

[blocks in formation]

find the19 25
Meridian 26 38
Altitude. C43 39)

And the

57 25

Depref.

Depres.

50 22

33 21

PROB. V.

To know when Twilight Begins and Ends.

Tilight begins, when the Sun is 18 d. below the Horizon before its Rifing: And endeth, when the Sun cometh to be 18 d. below the Horizon, after its Setting.

The Globe Rectified, and the Sun in 29 d. of Taurus, find the oppofite Point thereunto, which is the 29 d. of Scorpio, and bring that Point, as alfo the Quadrant of Altitude, both of them on the Weft-fide of the Meridian; and then move both the Body of the Globe, and the Quadrant of Altitude alfo, till the 29 d. of Scorpio lye directly under 18 d. of the Quadrant of Altitude: Which done, keep them both together, and then fee how many Hours the Index is removed from 12, which you shall find to be 1 h. and 8 m. So that Twilight begins at 8 m. after I in the Morning. And this being taken from 4 h.. 11 m. the time of the Sun's Rifing that Day, there will remain 3 h. 3 m. which is the Length or Continuance of the Twilight. Alfo if you double the time of the beginning of Twilight 1 h. 8 m. you fhall have the length of dark Night, which will be but 2 h. 16 m.

In like manner, if you would know when the Twilight endeth after Sun-fetting, you must bring the 29 d. of Scorpio (the Point oppofite to the Sun) on the Eaft-fide of the Meridian, making it, and 18 d. of the Quadrant of Altitude, to meet, then the Index will fhew 10 h. 52 m. and till that time of Night doth Twilight continue.

[blocks in formation]
[blocks in formation]

And if you go about to find the time of the beginning and end of Twilight, all the Time that Sun is paffing from 2 d. of Gemini to 30d. of Cancer, which is from about the 12th of May to the 12th of July, you fhall find that there will be no Twilight at all, but all that Time continual Day: For all that Space of Time the Sun never defcendeth fo much as 18 d. under the Ho-rizon, in the Latitude of 51 d. 30 m.

The former of thefe Two laft Problems needeth no Trigonometrical Calculation: But, if to the Sun's Declination for the Day (or Place of the Sum) given, 20 d. you add the Complement of the Latitude given, 38 d. 30 m. the Sum of them 58 d.. 30 m. is the Meridian Altitude for that Day that the Sun is in 58 d. of Taurus.

But if the Sun had been in 29 d. of Scorpio, a Southern Sign, then the Declination 20 d. fubftracted from 38 d. 30 m. the Complement of the Latitude, the Remainder 18 d. 30 m. will be the Meridian Altitude.

For the Depreffion of the Sun, he being upon the Meridian at Midnight, it is the fame with the Meridian Altitude, when the Sun is in the oppofite Sign.

So the Depreffion at Midnight when the Sun is in

29 d. of Taurus, 2
29 d. of Scorpio. is 18 d. 30 m.

1558 d. 30 m.

PROB.

« PreviousContinue »