- Having perfectly learned the Compass, the next necessary thing for a Seaman to know is the alteration or shifting of Tydes, that thereby he may with the greater safety bring his ship into any barred Port, Haven, Creek, or other place, where Tydes are to be regarded.
- And this difference of Tydes in the alteration of flowing and reflowing, is by long experience found to be governed by the Moons motion, for in such proportion of time as the Moon doth separate herself from the Sun by the swiftness of her natural motion: in the like proportion of time both one Tyde differ from another, therefore to understand this difference of the Moons motion is the only mean whereby the time of Tyde is most precisely known.
Of the Moons Motion.
- You must understand the Moon hath two kinds of Motions: a natural motion, and a violent motion:
- Her violent motion is from the East toward the West, caused by the violent swiftness of the diurnal motion of Primum Mobile, in which motion the Moon is carried about the Earth in 24 hours and 48 minutes nearest one day with another, for although the diurnal period of the First Mover be performed in 24 hours, yet because the Moon every day in her slowest natural motion moveth 12 degrees, therefore she is not carried about the Earth until that her motion be also carried about, which is in 24 hours and 48 minutes nearest.
- Her natural Motion is from the West toward the East, contrary to the motion of the First Mover, wherein the Moon hath three differences of moving, a swift motion, a mean motion, and a slow motion: all which is performed by the Divine Ordinance of the Creater in 27 daies and 8 hours nearest, through all the Degrees of the Zodiac.
- Her slow Motion is the in the point of Auge or Apogeo, being then farthest distant from the Earth, and then she moveth in every day 12 degrees.
- Her swift motion is in the opposite of Auge or Perigeo, being nearest onto the Earth at which times she moveth 14 degrees, with small difference of minutes in every 24 hours.
- Between those two Points is her mean Motion, and then she moveth 13 degrees nearest:
- all which differences are caused by the eccentricity of her Orbe wherein she moveth and are only performed in the Zodiack, but the Seamen for their better ease in knowledge of the Tydes, have applied this the Moons motion to the points, degrees, and minutes of the Compass, whereby they have framed it to be an Horizontal motion, which hath by long practice is found to be a rule of such certainty, as that the error thereof bringeth no danger to the expert Seaman, therfore it is not amiss to follow their practised precepts therein.
- In every 29 dayes 12 hours 44 minutes, with another through the year, the Sun and Moon are in conjunction and therefore that is the quantity of time between Change and Change, for although the Moon in 27 days and 8 hours, performing her natural motion, doth return to the same minute of the Zodiack from whence she departed, yet being so returned, she doth not find the Sun in that part of the Ecliptic where she left him, for the Sun in his natural motion moving every day 1 degree toward the East, is moved so far from the place where the Moon left him, as that the moon cannot overtake the Sun to come in Conjunction with him, until she have performed the motion of 2 days 4 hours, and 44 minutes (nearest) more than her natural revolution,
- and that is the Cause wherefore there are 29 days 12 hours, 44 minutes between Change and Change one with another through the whole year: but the Seaman accompteth the Moons motion to be uniform in all places of the Zodiac alike, limiting her general separation from the Sun to be such as is her slowest natural motion, which is 12 degrees, or 48 minutes of time, in every 24 hours.
By which accompt there are 30 dayes reckoned between the Change and Change, being 11 hours, 16 minutes more than in truth there is: but because this difference breedeth but small error in their accompt of Tydes, therefore to alter practised Rules where there is no urgent cause were a matter frivolous, which considered I think it not amiss that we proceed therein by the same method that commonly is exercised
Allowing the Moon in every 24 hours to depart from the Sun 12 degrees, or 48 minutes of time, and in this separation, the Moon moveth from the Sun Eastward, until she be at the Full: for between the Change and the Full, it is called the Moons separation from the Sun: for after the Full, she doth apply towards the Sun, so that between the Full and the Change, it is called the Moons Application to the Sun, in which time of Application she is to the Westward of the Sun, as in her separation she is to the Eastward, or I may say in the Seamans phrase all the time of her application is before the Sun, and in the time of her separation she is abaft the Sun.
Then if the Moon do move 48 minutes of time in 24 hours, it followeth that she doth move 24 minutes in 12 hours, and in 6 hours she moveth 12 minutes: therefore every hour she moveth 2 minutes, and such as is the difference of her motion such is the alteration of the Tydes, and therefore every Tyde differeth from the other 12 minutes, because there is 6 hours between Tyde and Tyde: and in every hour the course of flowing or reflowing altereth 2 minutes, whereby it appeareth that in 24 hours the four Tydes of flowing and reflowing do differ 48 min. of time. And as the whole knowledge of this difference or alteration of Tydes, as also the quantity of the Moons Separation and Application to, and from the Sun, dependeth upon the knowledge of the Moons age, it is therefore necessary, that next you learn how the Sun may be known.
For the performance whereof, there are two Numbers especially required named the Prime and the Epact, for by the Prime the Epact is found, and by help of the Epact the Moons age is known.
Of the Prime, or Golden Number.
The Prime is the space of 19 years in which the Moon performeth all the varities of her motion with the Sun, at the end of 19 years beginneth the same Revolution again, therefore the prime never exceedeth the number of 19 and this Prime both always begin in January, and thus the Prime is found:
Unto the year of the Lord wherein you desire to know the Prime, (excepting in January and February) add 1, then divide that number by 19, and the remaining number which commeth not into the quotient is the Prime.
- Example: In July in the year of our Lord 1590, I desire to know the Prime, therefore I added 1 unto that year, and then it is 1591, which I divided by 19, and it yieldeth in the Quotient 83, and there remaineth 14 upon the division, which cometh not into the Quotient, which 14 is the Prime in the year of our Lord 1590.
The Epact is a number proceeding from the over-plus of the Solar and Lunar year, which number never exceedith 30, because the Moons age never exceedith 30, for the finding whereof this number only serveth: and thus the Epact is known, which Epact doth always begin in March, multiply the prime by 11 (being the nearest difference between the Solar and Lunar year) divide the product by 30 and the remainder is the Epact.
- Example : In the year of our Lord 1590 I would know the Epact, first I seek the Prime of that year, and find it to be 14, I therefore multiply, 14 by 11 and that yieldeth 154, which being divided by 30, it giveth the quotient 5, and there remaineth 4 upon the division, which 4 is the Epact in the year 1590, which beginning in March, doth continue until the next March of the year 1591.
Of the Solar and Lunar Year.
The Solar year, or the Suns year, consisteth of 12 months, being 365 days and about 6 hours, the Lunar year or the Moons year, containeth 12 moons, and every moon hath 29 days, 12 hours, 44 minutes nearest, which amount unto 354 days, 5 hours, 28 minutes, the content of the Lunar year, which being subracted from 365 days, 6 hours, there resteth 11 days and 23 minutes, the difference between the said years, from which difference the Epact commeth.
By this Table the Prime and Epact may forever be found, for when the year
be expired, you may begin again and continue it forever at your pleasure.
The first Circle containeth Years of our Lord, the second the Prime, and the
third and inner Circle sheweth the Epact: under every year you shall find
his Prime and Epact, the Prime beginneth in January, and the Epact in March.
How to find out the Moons Age:
- First, Consider the day of the Month wherein you seek the Moons age, then note how many Months there are between the said Month and March, including both Months, unto those Numbers adde the Epact of that year, that is, you must adde into the one sum the day of the Month, between March and your Month, (reckoning both Months) and the Epact, all which numbers joyned together, if they exceed not 30 is the Moons age, if they be more than 30, cast away 30 as often as you can, and the remainder is the Moons age, if it be just 30 it is then New Moon, if 7 the first Quarter day, if 15 it is Full Moon, if 22 it is then the last Quarter day, and thus the Moons age is found forever. (Readers after the year of our Lord 1754 will need to subtract eleven days from the result, due to the change from the Julian to Gregorian Calendar)
And now being able for all times either past, present, or to come, to give the Moons age, I think it good by a few Questions convenient for the Seamans practice, to make you understand the necessary rule thereof.