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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 10 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.

Description of the circle and rule for its ufe.

The 9th and 10th circle contains the fun's distance from the node for any year at the same time, adding or omitting, 30°. (or more exactly, 300, 33′ 4) for every circle, which is alfo 76 years forward or backward from 1769. This instead 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 fun'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 use.

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 529 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 1ft 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 Wednesday of October, 1770, required the day of the month? This is found by 7th circle.

Defcription of the circle and its use. 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 10th 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 use 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 fubtraction.

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 1ft of July, when the draught is due.

A bond dated March 5, 1739,

and

The Stars are for January and February Hydra's Heart; March, April and May Virgin's Ops; June, July Eagle's Heart; August, September Markab. Peg. Wing. Odober, November, December Seven Stars.

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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 thefe 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 ft is the ft; and the 10th of September being the 253d, the 8th mult be the ift, from which 121 days being fubacted there remains 130 days, and tracting 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 ercle, 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 aded to the age found by 11 and 12 circle for the year, omitting 29 days, 13 tours, 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

reoon.

Moon's age for 1770 (being the 2d year in the table) found by 11th and 1th circle is 3 days, 22 hours. Anal age for September the 10th found in 5th circle is 15 days, 18 hours, and Confequently on the 12th the moon's raual age is 17 days, 18 hours, which being added together gives 21 days, 15 hours, for the moon's age at 12 clock in the morning the 12th of Sepember, 1779. This being fubtractei from 29 days 13 hours, leaves 7 cay, 21 hours the time to the next Cange. 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 use.

The fourth circle contains the fun's distance 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 thin, 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 distance from node for 1770, found by the 9th and 10th circle, is 27° 16'.

Annual distance for September the 17th (being the nearest 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° 0', 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 distance from the node, which being far above 17° there can be no eclipfe at this new moon.

IX. Required the time of high water 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

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called Place's change time of high water, between thefe 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; because 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 paft full, and one day twenty three hours from the fifth octave, as may be seen 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, becaufe 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 firft circle.

Defcription and Use of the Circle. The first 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 eaft or weft (the me:idian of London) proportional times fooger 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 eat the meridian of London. This being added to 10 o'clock, gives the time at Alexandria z 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, eaft the meridian of London in 2d 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 ftar for the month by the eye, compass, or a glass, or perforated dial of the author's invention any night in the year. Suppofe therefore Hydra's heart thews 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 2 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 10 hours, 55 minutes, and adding 8 minutes for the 6th of January, gives 3 minutes past 11 o'clock at night, when the star 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, 2d half tun, 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 necefiary is the time of the night.

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1. I look into the table and find 6 To the AUTHOR of the LONDON

days and a half moon's age, is 5 hours and a half in 2d circle which added to 10 hours and a half is 16 hours which omitting 12 hours is 4 o'clock.

2. The distance in time between 13 and 16 days, 12 hours. Moon's age is 11 hours, which fubtracted from 22 (adding 12 hours) leaves the time of the night 11 o'clock.

A general Rule to find the intereft of any
Sum of any Money per cent. at any
Intereft, and for any Time.

1. Multiply your principal by the integer and divide it by the fraction of your intereft.

2. Multiply the fum of thefe by your years, and having pointed off two figures in each denomination, divide them by your part of a year, and this quote added to your product is your intereft.

EXAMPLE, I.

6537481. at 3 per cent. per annum for one year, required the interest? 2)653748

3 Integer of interest.

1961244 Product.

326874 Quote by fraction.

22881.18 Sum = 22881/. 35. 7d. Int.

II. 356297. 195. 11d. 2, at 3 years, 5 months, 2 weeks and 1. s. d.

for 9

x 3.8.

day.

35629 19 11 × 3 ÷

or

285039 19 10

106889 19 11

I.

168)365(2.173.

1353-939 019 0 1 x 9

12185.459 011 2 I 623.073 ΟΙ

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SIR,

MAGAZINE.

II Yubmitted my thoughts to the N your Magazine of January laft public, concerning the injuftice done to the memory of King Charles the Firft; and, as I fill apprehend the caufes for it are not well understood, I am defirous of explaining them, and of vindicating his memory from the afperfions, fo induftriously propagated upon republican principles for very fufpicious purposes.

When we look back on paft tranfactions, we are too apt to weigh them by a standard of our own imagination, and not by that ftandard of law and ufage which were in being when the matters in question were done.

Thus it has been, and ftill is, in weighing the actions of King Charles the First in the earliest part of his reign; what was then done was founded on very recent inftances done in a very popular and nearly preceding reign; namely, Queen Eliza beth's; and, if weighed by her standard of laws and ulage (which continued in being till after the time in queftion) it will fall fhort in every degree of weight by the comparison.

The queen's government was completely arbitrary, of which all the hif torians are full; Mr. Hume, in particular, recapitulates the crown prerogatives, which had been tranfmitted to her by her immediate predeceffors, and been exercifed by her with the general confent and approbation of her fubjects.

Among the chief of thofe prerogatives was the court of Star-chamber, which was very antient, and was established by act of parliament in the reign of King Henry the Seventh; it 128087. 105. 7d. poffeffed an unlimited authority of fining, imprisoning, and inflicting corporal punishments; and its jurifdiction extended to all forts of offences, contempts, and diforders; and it fupported and enforced all proclamations, and other royal acts, which lay not

Value of decimals. 12hillings=11pen.

pen. fc.

019 far nearly far. nearly. .co far. nearly. III. 571438 pistoles at 5 for 10 yrs.

190479-33 3)571438 x 53

2857190

380958

within the reach of the common-law: its members confifted of the privycouncil, and judges, who enjoyed their office during pieafure, and could only interpofe with their advice, when the prince was prefent, and fubmit

323814.866 x 10 intereft in pif- to his will when abfent. toles and decimals of a pistole.

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The court of high commiffion took cognizance in all matters of conscience; and was established by act of parliament in Queen Elizabeth's reign; who, in a letter, to the Archbishop of Canterbury, faid exprefsly, that "the was refolved, no man fhould be fuffered" to decline either on the left or on the right hand, from the drawn line limited by authority, and by her laws and injunctions."

66

Martial laws was then occafionally exercifed in civil cafes, and Lord Bacon obferves, that the trial at common law granted to the Earl of Effex and his fellow confpirators was a favour. Among many inftances to confirm this ufage, was Queen Elizabeth's proclamation, which ordered martial law. to be used against all perfons importing bulls, or even forbidden books, and pamphlets from abroad; and forbad the lieutenants or their deputies, to be queftioned for their arbitrary punishment of fuch offenders; any law or ftatute to the contrary in any wife notwithstanding." and in like manner, when the streets of London were much infefted with idle vagabonds, and riotous perfons, fhe gave Sir Thomas Wilsford a commiffion of provolt-marthal; granting him authority, and commanding him, upon fignification given him by the juftices, of fuch offenders as worthy to be speedily executed by martial law, to attach and take fuch perfons, and in the prefence of the faid justices," according to juftice of martial law, to execute them on the gallows, or gibbet, openly, or near to fuch place where the faid rebellious and incorrigible offenders fhould be found to have committed the faid great offences

were

Befides the above prerogatives and jurifdictions, the fecretary of state and the privy-council were used in thofe times familiarly, by warrant, to imprifon perfons during any time they fhould think proper, and, in fufpicious times the go were full of fuch; who were fometimes loaded with irons, and even tortured with the rack, without further authority; and the practice then in ufe, of not confronting the witneffes with the prifoner, gave all imaginable advantage against him; while the timid juries, and judges who held their offices during pleafure,

2

never failed to fecond all the views of the court on such like occafions.

There were divers inferior courts, fuch as of wards and other prerogative exertions, for creating monopolies, and exacting loans, benevolences, purveyances, &c. without number, which greatly exalted the power of the crown ; and if any complaints were made in parliament, touching the legality of thefe exertions, the queen prohibited the house of lords, or commons, in which fuch complaints were made, from meddling with what the called ftate matters, or ecclefiaftical caufes, and openly fent the members to prifon, who dared to tranfgrefs her imperial edicts.

Thefe exertions of power were the more firmly established in the minds of the people, by the homilies enjoined to be read every Sunday in all the churches; thofe homilies inculcated a blind and unlimited paffive obedience to the prince, and which, on no account, and under no pretence, was it lawful for them in the fmalleft article to depart from or infringe.

By thefe, and other fpirited and prudent meafures, the queen fupported her exertion without fcarce a murmur; and her memory is fill defervedly esteemed, notwithstanding her actions were, altogether arbitrary and defpotic.

King Charles, with as great abilities, though fewer faults, afcended the throne on the death of his father (King James the Firft) poffeffed of the fame prerogatives, and fupported by the fame laws as were in the queen's reign, which laws and prerogatives were feelingly expreffed by Sir Walter Raleigh (while in prifon under the difpleafure of King James the Firft) who fpeaking of the prerogative of parliament fays, "The three efiates did but advife the king as the privy-council did, which advice, if the king embraced it, became his own act in the one, and his law in the other."

In the remarkable cafe of fhip moncy in King Charles's reign, the council for the crown infifted plainly and openly on the king's abfolute and fovereign power; which the council for Mr. Hampden did not deny, afferting only, that the fubjects had a fundamental property in their goods

which

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