2d. year, 3 days 13 hrs. &c. and the 7th year, 29 days 4 hrs to which 5hrs 52 mins. or 6 hours for one complete circle being added, the moon's age at 12 o clock in the morning, 1890 is 29 days and to hours. Obf. in counting backwards, 1 tabular difference always to be fubtracted.

III. Required, the fun's distance from the node for any year at the fame time, fuppofe the fame year? This is found by 9th and 10th circle, being one circle in the fame manner.

Defcription of the circle and rule for its ufe.

The 9th and roth circle contains the fun's distance from the node for any year at the fame time, adding or omitting, 30°. (or more exactly, 30, 33′ 4) for every circle, which is alfo 76 years forward or backward from 1769. This itead of counting, may be found in that year of the circle, in which the moon's age was found the fame time and which correfponds to it in the table.

I look, therefore, into the table, and correfponding to 29 days 4 hrs. moon's age, I find 39, 33' to which I add for one complete circle, 30° 33' and the fum is 70° 6' the fon's diftance from the node on New Year's day, at twelve o'clock in the morning, 1890.

IV. Required, where Hydra's heart (which is the ftar for the months of January and February) fouths at night in any year, fuppofe the 6th of January the fame year? This is found by the 8th circle.

Defcription of the circle, and rule for its ufe.

The 8th circle contains the fouthing of fome of the fixed ftars every New Year's day of the week throughout the year, adding one minute for every year for three years after Leap Year, and adding or omitting one minute for every 18 years or 29 minutes every 520 years forward or backward; from which four minutes fubtracted forward every night of the week gives the time of the night. In table the 8th of January, Hydra's heart fouths at 3 minutes after 2 o'clock next morning, and 121 divided by 18 anotes; 6

therefore, according to the rule, adding 6 minutes, and one minute for one year after Leap Year to 3 minutes gives 10 minutes after two o'clock 8th January, adding 28 minutes, for the 1st of January gives the fouthing of Hydra's heart at 38 minutes after 2 o'clock in the morning of New Year's day, 1890.* Obf. The morning hours are in next day.

V. Given the day of the week and the number of the weeks in any month of any year to find the day of the month. Any date or appointment, fuppofe the 2d Wedneíday of October, 1770, required the day of the month? This is found by 7th circle.

Defcription of the circle and its ufe. The 7th circle contains the day of the month at the fame time, which in Leap years after February is one day lefs.

New Year's day of the week, which, as may be found by first example, in 1770, is Monday. Looking therefore into the 7th article, and fecond part of October. I find the 8th of the month is Monday, which is therefore the 2d. Monday, and confequently next Wednefday is the 2d Wednesday and the 1oth of the month,

VI. Required, the time between any two dates in days or in years and days of the year. This is found by 6th circle.

Defcription and ufe of the circle.

The 6th circle contains the days of the year, fame time, from which the time in years and days between any two dates may be found by fubtrac

tion.

1. A draught dated June 1, 1770, payable at 30 days, required when it becomes due.

June 4, 1770, being Monday the 155th day of the year. Friday is therefore the ft of June and 152d day of the year, to which adding 30 days, the fum is 182 days, the day of the year when the draught becomes due, which Monday the 2d of July being the 183d of the year in the table, correfponds to Sunday the rit of July, when the draught is due.

A bond dated March 5, 1739, and

paid June 7, 1770, required the time in years and days to calculate the interett?

March the 5th in table is the 64th day of the year, and June the 7th is the 158th, the 4th being the 155th; fubtracting therefore 1739 years, 94 days from 1770 years, 158 days, the remainder is 31 years and 94 days, the time in years and days of the year between these two dates.

3. A workman is hired by the day to do a piece of work, and begins May 1, 1770, and finishes his work September the 8th, fame year; required the number of days he has worked?

The 7th of May in the table being the 127th of the year, the rft is the 121ft; and the 10th of September being the 253d, the 8th must be the 251ft, from which 121 days being fubtracted there remains 130 days, and fubtracting the number of weeks in the table between them, which is 18 for the Sundays; the remainder is 112 the number of days he has worked.

VII. Required the moon's age for any day in any year? fuppofe September 12, 1770. This is found by 5th circle, and the 11 and 12 already explained.

Defcription of the circle and rule for its ufe.

The 5th circle contains the moon's annual age, fame time, which being added to the age found by 11 and 12 circle for the year, omitting 29 days, 13 hours, when it exceeds them gives the moon's age at that time, and which being fubtracted from 29 days, 13 hours, leaves the time to new

moon.

Moon's age for 1770 (being the 2d year in the table) found by rith and 12th circle is 3 days, 22 hours. Annual age for September the 10th found in 5th circle is 15 days, 18 hours, and confequently on the 12th the moon's annual age is 17 days, 18 hours, which being added together gives 21 days, 16 hours, for the moon's age at 12 o'clock in the morning the 12th of Sepember, 1770. This being fubtracted from 29 days 13 hours, leaves 7 days, 21 hours the time to the next change. Adding therefore 7 days 21 hours to the 12th of September gives the 19th of September and 21 hours, April, 1771.

which is 9 o'clock at night for the time of night new moon.

VIII. Required whether or no, there is an eclipfe at any new or full moon, fuppofe this new moon in September, 1770. This is found by the fourth, ninth, and tenth circles in the fame

manner.

Defcription of the circle and rule for its ufe.

The fourth circle contains the fun's diftance from the node, fame time, which being added to the distance found in the ninth and tenth circle for the year, omitting 360° when it exceeds them, is the fun's distance from the node at twelve o'clock in the morning on new year's day of the week. And adding one degree for every day and three minutes for every hour for any remaining days and hours of the week to new or full moon, gives the fun's distance from the node at that time, which being within 70° or 12° either of 180° or 360° there must be an eclipfe, otherwife not.

Sun's diftance from node for 1770, found by the 9th and 10th circle, is 27° 16'.

Annual distance for September the 17th (being the neareft new year's day of the week to new moon) is 269° 0′. And therefore on the 19th, at twelve o'clock in the morning, the distance is 270° o', and three minutes for every hour to nine o'clock at night, the time of change is 1° 3', all which being added together is 299° 19' the fun's diftance from the node at the time of new moon. This fubtracted from 360° the nearest number, leaves 60° 41'the fun's ditance from the node, which being far above 17° there can be no eclipfe at this new moon.

IX. Required the time of high wa. ter and afpects of the moon at any time ? fuppofe at London the 16th day, 12th hour of the moon's age at twelve o'clock in the morning. There are found by the fecond and third circles.

Defcription of the circles and rule for their ufe.

The fecond circle contains twentyfour hours and the moon's afpects, and the third circle contains the moon's age at the time, in fecond circle of high water, counted from this mar D d

called

called Place's change time of high water, between these times fame day, having added one minute for every half hour of change time of high water. Change time of high water at London is three o'clock: counting the hours therefore from this mark calling it 3, the next 4, and then an half hour, and adding one minute for every half hour in three hours, which is fix minntes, gives 36 minutes after four o'clock in the morning, for the time of high water at London the 16th day and a half of the moon's age found as already explained. And this time must be in the morning; becaufe the table fhews the time between the change times of high water in the fame day, that is, at London between three o'clock in the morning and three o'clock in the afternoon.

In this age the moon is one day eighteen hours påft full, and one day twenty three hours from the fifth octave, as may be feen by infpection in the table.

2. At the fame age of the moon required the time of high water at Leith? Change time of high water at Leith is oor 12 o'clock, counting therefore from the mark gives the time of high water at half an hour paft one o'clock in the morning.

The time given must be between twelve o'clock in the morning and twelve at noon, because the moon's age is at twelve o'clock in the morning. And for the fame reafon no minutes of change time of high water are to be added

A half day's diftance of moon's age, from the time of any tide, found forward or backward, points to the time of the preceding or fucceeding tide, &c. which may be reckoned in the fame manner.

X. 1. Suppofe it ten o'clock at London, required what o'clock it is at Alexandria?

This is found by the first circle.

Defcription and Use of the Circle. The firft circle fhews the distance to any place in degree, &c. or in time in the fecond circle, which being eaft added to, or weft fubtracted from, the prefent time, is prefent time there. And in places east or weft (the meridin of London) proportional times fooner or later lets or more in table are to be allowed..

Alexandria being 30° 22' which correfponds to 2 hours, 2 minutes in 2d circle east the meridian of London. This being added to 10 o'clock, gives the time at Alexandria 2 minutes afternoon.

2. Suppofe new moon 9 o'clock at night at London, required the time at Babylon?

Babylon being 323° 35′ longitude correfponding to 2 hours, 26 minutes, east the meridian. of London in zd circle; adding therefore 2 hours, 26 minutes to 9 o'clock at night, give 26 minutes after 11 o'clock at night for the time of new moon at Babylon.

XI. Required the time of the night by a view of the tabular star for the month by the eye, compafs, or a glass, or perforated dial of the author's invention any night in the year. Sup. pofe therefore Hydra's heart fhews one o'clock the 6th of January, 1771, required what o'clock it is?'

RULE. Tabular time in the morning fubtracted from, or compliment of tabular time at night to 12 o'clock, added to the time fhewn by ftar to the eye or through a dial, adding or omitting 12 hours when neceffary is the time of night.

The 8th of January in table Hydra's heart, fouths at 3 minutes after z o'clock in the morning. But 1771 being 2 complete years after leap year, 2 minutes are added. Therefore the time in the morning to be fubtracted is 2 hours, 5 minutes, from 1 hour, o minutes, fhewn by ftar, which (adding 12 hours) leaves ro hours, 55 minutes, and adding 8 minutes for the 6th of January, gives 3 minutes past 11 o'clock at night, when the ftar fhews one o'clock in the morning.

XII. Required the time of the night by the moon fhining on a fun dial, &c. at any time. Suppofe the moon's age 6 days and a half, and 16 days and a half, and fhews 10 hours and a half upon the dial, required

what o'clock it is?

RULE. First half an annation moon's age in time 2d circle counted from the mark at 29 added to, zd half fun, the distance in time counted from 13 to moon's age the contrary way; fubtracted from time fhewn by moon on a fun dial or year's dial, &c. adding or omitting 12 hours when neceffary is the time of the night.

1. I