Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ...

CHAP. 1. Of the year Civil and Astronomical.

THe Altitudes of the Planets being given to find their places in the Zodiack, hath been already shewed in the Doctrine of the Sphere, & thence their annual or periodical revolutions, toge∣ther with their middle motiōs must be sought, but how to state them so exactly as that we may thereby find their true or appa∣rent places for any time required, is that which many have endevoured, but none have as yet found out, at least not so, as that their places computed by their rules, shall exactly agree with observation, nor was Astronomy brought to that perfection in which it now stands but by degrees, and al∣though there hath been very much done of late towards the perfecting thereof, yet shall it not perhaps come to its full Acme in this our age. That which we intend, is not to shew you from what small beginnings it hath been increased, or by whose labours, it hath from time to time been still corrected and amended, but to shew you how to compute the places of heavenly Bodies, by the plainest, speediest, and exactest ways that are as yet made publike. And in order hereunto we will shew you first the usual way of finding out the time in which the Planets make their Annual or Periodical revolutions, and how from thence to compute their middle Motions, that their annual revolutions may be known, the time of their entrance into one and the same point of the Zodiack, taken in divers years by observation must be given, with a considerable interval of time between these Observations.

And because the Observations taken in any one Meridian (that are as yet published) are not sufficient for our present purpose we must of necessi∣ty,

use the observations made in diverse places, but the intervall of time between those observations cannot be had, unlesse we can reduce the time of an observation made in one account to the like time in another; Al∣though the periodicall revolutions therefore of the planets are the onely proper yeares and first in nature; yet since the civil yeare in every nati∣on is somewhat different from them, we will first shew the quantity of that in most nations, and how to reduce the day of the moneth given in one accont, to the correspondent time in another.

The Civil yeare then, though it doth not exactly agree, yet hath it some proportion with the motions of the Sunne or Moone in every nation; Twelve Moones or Moneths is the common measure of the year in Turkey, in every moneth they have 29 or 30 dayes, in the whole yeare 354, and in every third yeare 355 dayes. The Persians and Egyp∣tians do also account 12 Months to their yeare, but their months are pro∣portioned to the time of the Suns continuance in every of the 12 signes; in their year therefore which is Solar, there are alwayes 365 dayes. And the Julian yeare, which is the account of all Christendome doth dif∣fer from the other onely in this, (that by reason of the Suns excesse in mo∣tion above 365 dayes, which is about 5 hours 49 minutes) it hath a day intercalated once in 4 yeares, and by reason of this intercalation it is more agreeable with the motion of the Sun then the former, and yet here is a considerable difference between them, which hath occasioned the Church of Rome to make some further amendment of the Solar year, but hath not brought it to that exactness which is desired, nor will (as is to be feared) be over-hastily brought to that exactnes which it might; taking these accounts therefore as they now stand, if we will reconcile that discrepancy that is between them, there must be some beginning appointed to every of these accounts, and that beginning must be referred to some one, as to the common measure of the rest.

The most natural beginning of all accounts, is the time of the Worlds Creation, but they who could not attain the Worlds beginning, have rec∣koned from their own, as the Romanes, ab urbe condita, or from some great name or notable event; so the Greeks account from their Olympicks, and the Assyrians from Nabonasser, and all Christians from the birth of Christ, the beginning of which and all other the most notable Epochaes, as others formerly, so we now have also ascertained to their correspondent times in the Julian Period, which Scaliger contrived by the continual mul∣tiplication of three circles all in former times of good use, & two of them do

yet remain; the Circles yet in use are those of the Sun and Moon, the one to wit the Sun is a Circle of 28 years, in which time the Sunday Letter makes all the varieties that it can have by reason of the Bisextile or Leap∣year, and the Circle of the Moon is the revolution of 19 years, in which time, though not precisely, the Lunations do recur; it is called the Golden Number, and was made Christian by the Fathers of the Nicene Council, as being altogether necessaay to the finding out of the Neomenia Pascha∣lis, upon which the Feast of Easter, and the rest of the moveable Feasts de∣pend. The third Circle which now serves for no other use, then the constitu∣ting of the Julian Period, is the Roman Indiction, or a Circle of 15 years, for if you multiply 28 the Cycle of the Sun, by 19 the Cycle of the Moon, the product will be 532, & this by 15, the product will be 7980 the number of years in the Julian Period; whose admirable condition is to distinguish every year within the whole Circle, by a several certain character, the year of the Sun, Moon, and Indiction, being never the same again until the revo∣lution of 7980 years be gon about: this Period, the Authour fixed in the Tohu, or eternal Chaos of the World, 764 Julian years before the most re∣puted time of Creation; which being, premised, we will now by example shew you how to reduce the years of Forreigners to our Julian years, and the contrary.

1 Example.

I desire to know at what time in the Turkish account, the 5 of June 1649, falls. The work is this

The years compleat are 1648, and are thus turned into Dayes, by the table of Dayes, and Decimals of Dayes in Julian Years.

1000 Julian yeares give dayes

365250

600 years give

219150

40 years give

14610

8 years give

292••

May Compleat

151

Dayes

5

The Summe

602088

Now because the Turkish account began July the 16. Anno Christi 622, convert these yeares into dayes also thus

600 Julian years give

219150

20 years give

7305

1 year gives

365

June Compleat

181

Dayes

15

The Summe subtract

227016

From

602088

There rests

375072

56142

2987

152

4

900 Turkish years gives

318930

There rests

375072

56142

2987

152

4

150 years gives

53155

There rests

375072

56142

2987

152

4

8 years give

2835

There rests

375072

56142

2987

152

4

Giumadi I. gives

148

There rests

375072

56142

2987

152

4

Therefore the 5th. of June 1649, in our English accompt, falls in the Turkish accompt, in the year of Mahomet, or their Hegira, 1058, the 4th. day of Giumadi II.

2 Example.

I desire to know upon what day of our Julian year, the 23 day of the moneth Pharmuthi in the 1912 year currant of the Aegyptian accompt from the death of Alexanders fall.

The beginning of this Epoch•• is from the beginning of the Julian Pe∣riod in compleat dayes.

 

1603397

1000 Egyptian years give

365000

900 yeares give

328500

10 years give

3650

1 yeare gives

365

Phamenoth compleat

2••0

Dayes

23

The summe

2301145

6000 Julian yeares

2191500

There rests

109645

70

11

300 yeares give

109575

There rests

109645

70

11

April compleat

59

There rests

109645

70

11

It therefore fell out in the yeare of the Iulian period 6300 the 11 of March, that is subtracting from that period, 4712 in the yeare of Christ 1588. He that understands this may by like method convert the yeare, of other Epochaes into our Julian yeares and the contrary.

Next to the tables which concern the reduction of years in general, we annexed tables for the perpetual finding of the Sunday letter, Golden number and Epact in both the Old Julian, and New Gregorian accompt, with the fixed and moveable Feasts, and a Catalogue of some famous places with their latitude and distance in longitude from the meridian of Lon∣don, whose use is so obvious that it needs but little explanation; yet to take away all difficulty we have added these directions.

The Cycle of Sun, Sunday Letter, Golden Number and the Epact in both accounts are set against the yeare of our Lord, and when those years are out, they may be renewed againe as oft as you please, thus for the yeare 1656 the Cycle of the Sun 1513, the Sunday letters in the English account are F E, in the Gregorian B A the prime or Golden number in both is 4, the Epact in the English accompt is 14 in the Gregorian 4.

And now to find the movable Feast, seek the English Epact, in the first Columne of that Table towards the left hand, and the first F that follows▪ will shew you that the 3d. of February is L X X Sunday, the 17 of Fe∣bruary▪

L Sunday, & the 20th of February Ashwednesday, & the first E that follows will shew that Easter day is the 6th. of April, Ascension day the 15th. day of May, Whitsunday the 25 of May, Corpus Christi the fifth of June, Advent Sunday, November the 30th.

But in the Gregorian, the Epact and Sunday Letters must be sought in the first Columne towards the right hand, so shall the Sunday Letters B A shew the Feast of Easter to be on the 9th of their April, and the rest as in that line they are set down.

The fixed Feasts, together with the Week-day Letters, are set against their proper dayes in every moneth of the Julian year, knowing therefore the Sunday Letter, you may easily know upon what day of the Week any Feast or day of the moneth shall be.

The Catalogue of places doth serve to shew the height of the Pole in those places, and the Difference of the Meridians of any place in the Ca∣talogue from that of London. The Letter S notes that the distance is West∣ward, A that it is Eastward, the figures under the title of Time are Hours and Decimal parts of an houre, the Earth or any Starre comes sooner or later to the Meridian of that place then that of London.

If the time of a Lunar Eclipse then or other appearance be given at London, afternoon 8 hours, 23 parts, and the time when this happens at Uraniburge be inquired, there is found in the Catalogue for Uraniburge 0 hour 83 parts A, if therefore according to the letter A, 83 parts be added to the time given it makes 9 houres 06 parts for the time at Uraniburge. But if the time of another place be to be reduced to the time at London, the diffe∣rence is to be applied with the contrary title.

And that these Reductions whether in time or motion may be the bet∣ter compared with those bookes that are written in the old Sexagenary forme, we have added tables for the ready converting of Sexagenary parts into Decimall and the contrary, the first of these tables is for the con∣verting of the Minutes and Seconds, &c. of a Degree in motion; and the other of the parts of a day in time, an example in each will be a sufficient explanation.

Let it be required to find the Decimall answering to 37′ 25″ 16‴ 5'''' 29''''' in motion.

In the first page of the table I find 37′ 12″ which is the nearest lesse, and 62 answering thereunto, and in the third columne of the second page in the top of the page I find 12″, in which columne I find 25 seconds, and in the sixt and last columne of that page right against 25″, I find this num∣ber 36111111, which being annexed to 62.

The Decimall of 37 minutes 25 seconds is

6236111111

And the Decimall of 16 thuds

0000740741

The Decimall of 5 fourths

0000003858

The Decimall of 29 fifths

0000000373

Their summe

6236856083

is the Decimall sought

2. Example

Again, if it be required to find the Decimall of 8 hours, 17 minutes, 8 seconds, 5 thirds, 12 fourths, 9 fifts. In the first columne of the table en∣tituled, A Table to convert the hours and minutes of a day into Deci∣malls, I find 7 hours 12 minutes, and in the second columne the figure 3, then looking the 12 minutes in the top of the pages, I cast mine eye down∣ward in that column till I come to 8 hours 17 minutes, and in the last co∣lumne of the page against 8 houres 17 minutes, I find this number 451388889 and therefore,

The Decimall of 8 hours 17 minutes is

3451388889

The Decimall of 8 seconds

925926

The Decimall of 5 thirds

009645

The Decimall of 12 fourths

0387

The Decimal of 9 fifths

0005

Their aggregate

3452324852

Is the decimall sought.

To find the parts of a degree in motion, or of a day in time answering to any Decimal given, is but the contrary worke to the former;

Example.

As if it were required to find the parts of a degree answering to 6236856083, the 2 first figures of this Decimall are 62 which being sought in the first page of the table give me 37′. 12 and 62 being subtract▪ from 6236856083, the remainder will be 36856083 which being sought in the last columne, my nearest number is 36111111, and right a∣gainst that number under 12 in the top of the page I find 25, therefore 37′ 25″ are the parts of a degree answering to the Decimall given, but if you would find the thirds, fourths and fifths, from 36856083

Subtract

36111111

The remainder is

749972

Which being sought amongst the Decimals of the thirds, gives me 16

thirds, and this number to be subtracted from it 740741; and the remain∣der 004231 being sought amongst the Decimals of the fourths gives me 5 fourths, and this number to be subtracted from it 3858, and the remain∣der 373 sought amongst the Decimals of the fifths gives me 29 fifths, and so the parts of a degree answering to the Decimall given are 37 minutes, 25 seconds, 16 thirds, 11 fourths, and 29 fifths. Thus may you also find the parts of a day in time answering to any Decimall given.

The next thing to be done towards the finding of the annuall revolu∣tions of the planets is to find their entrance into any point of the Zodiack desired, and that may be done thus. Having the place of the planet taken by observation before and after its entrance into the point desired, sub∣tract the observed place next before from the observed place next after, and the remainder shall shew you the apparent motion answerable to the time between those observation, subtract also the former place, from the place in the point desired, and note their difference: for as the former remainder, that is the apparent motion between the observations, is to the time between those observations: so is this difference, to the time between the first observation, and the planets entrance into the point desired: thus we are to deal with those observations that we our selves shall make, but one mans age not being distance enough between the observations from whence the middle motions may be rightly stated, we must take some observations upon trust; and find the middle motions by comparing the observations made in former ages with those of our owne, of the Sun or Earth, take this Example following.

The vernal Equinox observed by Hypparchus in the year from the death of Alexander 178, was Mechir the 26 day, and 95833333, that is at London 86746111. And the vernal Equinox observed at Uraniburge by Tycho 1588 was March the 9th. 86458333, that is at London 82986111. And that the intervall of time between these two vernall Equinoctialls may be known, the 9 of March 1588 must be reduced to the correspon∣dent time in Egyptian yeares from the death of Alexander, which accor∣ding to the former directions is thus.

The Christian Aera began in the 4713 complete yeare of Julian peri∣od, to which 1587 being added, it makes 6••00 from the beginning of the Julian period therefore to the 11 of March 1588, there are dayes as followeth.

6000 Julia•• yeares give

2191500

300 years give

109575

February

59

Dayes

08

The Summe

2301142

The Aera Alexandri began in the 12 of November in 4390 yeare of the Julian period in which there are dayes,

4000

1461000

300

109575

80

29226

9

3287

October

304

Dayes

11

Which being subtracted

1603397

From

2301142

There rests

697745

332745

4246

596

231

21

1000 Egyptian yeares give

365000

There rests

697745

332745

4246

596

231

21

900 yeares give

328500

There rests

697745

332745

4246

596

231

21

10 years give

3650

There rests

697745

332745

4246

596

231

21

1 yeare gives

365

There rests

697745

332745

4246

596

231

21

Phamenoth compleate

210

There rests

697745

332745

4246

596

231

21

Therefore the 11 of March 2588 in our English account, falls in the 1912 yeare of the Aera Alexandri the ••1 day of Pharmuthi. In which space of time

There are dayes

697746

And from the death of Alexander to the 26 of Mechir 178, there are

64781

There rests

632965

From days

697746. 829••6111

Subtract

64781. 86746111

There rests

632964. 96240000

And in this time the Earth or Sun hath gone 1733 circles, 〈◊〉〈◊〉 623880 degrees. Hence to find the mean motion for a year or 365 days I say▪ If 632964. 9624 d▪ Give 623880 degrees; How many degrees shall 365 dayes give?

And the answer is 359 deg. 7611456036. That is in Sexagenary numbers 359 deg. 45 minutes, 41 seconds, 1 third, 27 fourths. Again, to find the mean motion for a day I say, If 365 dayes gives 359 degrees, 7611456036, what shall one day give?

And the answer is 0. 9856469743. That is in Sexagenary numbers 0 deg, 59 minutes, 8 seconds, 19 thirds, 44 fourths.

And what is here done for the middle motion of the Earth or Sun, may be done for the other planets.