Consequently, computing those Motions according to the equal Time, it is necessary to turn that Time back again into apparent Time, that they may correspond to Observation: On the contrary, any Phenomena being observed, the apparent Time thereof must be added to equal Time, to have it correspond with the Times mark'd in the Astronomical Tables.
As we don't know of any Body in Nature that moves equably; yet such a Motion is alone proper to measure equal Days and Hours: It has been thought fit to imagine some Body, e. gr. a Star, moving in the Equator, East- ward; and never quickening, or Slackening its Pace, but going thro' the Equator, in precisely the same Time, as the Sun finishes his Period in the Ecliptic.
The Motion of such a Star will represent equal Times; and its diurnal Motion in the Equator, will be 59′ 8″; the same as the mean, or equated Motion of the Sun in the Ecliptic. Consequently, the mean or equable Day, is determined by the Arrival of this Star at the Meridian; and is equal to the Time wherein the whole Circumference of the Equator, or 360°, pass the Meridian, and 55′ 8″ more. Which Addition of 55′ 8″ remaining always the same, these mean or equated Days will be constantly equal.
Since then the Sun goes unequally Eastwards with respect to the Equator; it will sometimes arrive at the Meridian sooner than this imaginary Star, and sometimes later: The Difference is the Difference between true and apparent Time : Which Difference is known by having the Place of the imaginary Star in the Equator; and the Point of the Equator which comes to the Meridian with the Sun. For the Arch intercepted between 'em, being converted into Time, shews the Difference between equal and apparent Time; which, as before, is call'd the Equation of Tune.
The Equation of Time then, may be defined the Time that flows while the Arch of the Equator intercepted between the Point determining the right Ascension of the Sun, and the Place of the imaginary Star, passes the Meridian: Or, as Tycho, and, after him, Street, state it, the Difference between the Sun's true Longitude, and his right Ascension.
To Equate Solar Days, that is, to convert apparent into mean Time, and mean into apparent Time.
1o. If the Sun's right Ascension be equal to his mean Motion, the imaginary and true Sun will pass the Meridian at the same Time: Consequently, the true coincides with the apparent Time.
2o. If the right Ascension be greater than the mean Motion, subtract the latter from the former; and turning the Difference into Solar Time, either subtract it from the apparent Time, to find the mean Time : or add it to the mean Time to find the apparent.
3o. Lastly, if the right Ascension be less than she mean Motion, subtract the former from the latter, and turning the Difference into Solar Time, either add it to the apparent Time, to find the mean Time ; or subtract it from the mean to find the apparent.
This Method of Equation obtains, if the Calculus be progressive' if it be Retrograde) that is, if the Time be reckon'd backwards, the Operation must be just the Reverse.
This Doctrine of the Inequality and Equation of natural Days, is not only of Use in Agronomical Computations, but also in the adjusting and directing of Clocks, Watches, and other Time Keepers : Hence we see, why a Pendulum, or other Movement, which measures equal Time, does not keep Pace with the Sun, which measures apparent Time; but is sometimes before, and sometimes later than the same. Whence, such Automata and Sun-Dials, are found almost perpetually at Variance. See Clock and Dial.
The Variations of the two Kinds of Time, are exhibited in the following Table, for every Day throughout the Year. 'Tis borrowed from Mr. Flamsteed; one Part of whose Praise it is, that he was the first who fully demonstrated and clear'd this Inequality of Natural Days: Tho' others, and even Ptolomey, had a partial Notion of it.
The Use of the Table is obvious: A Clock, or Watch, that is to be kept to true or equal Time, must be so many Minutes and Seconds faster or slower than a Sun-Dial, as is assign'd in the Table, for the respective Day: Or, if you would have it go by the Sun-Dial, it goes well, if it gains or loses each Day the Number of Minutes and Seconds in the Table.
A Table of the liquation of Natural Days, with the Regulation of a Movement by the same.
| DAYS | January. | February. | March. | April. | May. | June. | July. | August. | Sept. | Oct. | Nov. | Dec. | |||||||||||||
| W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | W.too fast. | ||||||||||||||
| Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | Min. | Sec. | ||||
| 1 | 8 | 59 | 14 | 48 | 10 | 08 | 0 | 48 | 4 | 07 | 1 | 03 | 4 | 43 | 4 | 30 | 3 | 48 | 13 | 14 | 15 | 23 | 5 | 2 | |
| 2 | 9 | 21 | 14 | 47 | 9 | 51 | 0 | 32 | 4 | 09 | 0 | 51 | 4 | 51 | 4 | 20 | 4 | 08 | 13 | 28 | 15 | 15 | 5 | 13 | |
| 3 | 9 | 43 | 14 | 45 | 9 | 34 | 0 | 16 | 4 | 11 | 0 | 39 | 4 | 58 | 4 | 10 | 4 | 28 | 13 | 42 | 15 | 06 | 4 | 44 | |
| 4 | 10 | 04 | 14 | 42 | 9 | 17 | 0 | *01 | 4 | 12 | 0 | 27 | 5 | 05 | 3 | 59 | 4 | 49 | 13 | 55 | 14 | 56 | 4 | 15 | |
| 5 | 10 | 24 | 14 | 38 | 8 | 59 | 0 | *14 | 4 | 12 | 0 | 15 | 5 | 11 | 3 | 48 | 5 | 10 | 14 | 08 | 14 | 45 | 3 | 46 | |
| 6 | 11 | 44 | 14 | 33 | 8 | 41 | 0 | 29 | 4 | 11 | 0 | *02 | 5 | 17 | 3 | 36 | 5 | 31 | 14 | 20 | 14 | 33 | 3 | 17 | |
| 7 | 11 | 03 | 14 | 28 | 8 | 23 | 0 | 44 | 4 | 10 | 0 | *11 | 5 | 22 | 3 | 24 | 5 | 52 | 14 | 31 | 14 | 20 | 2 | 48 | |
| 8 | 11 | 21 | 14 | 22 | 8 | 05 | 0 | 58 | 4 | 08 | 0 | 24 | 5 | 27 | 3 | 11 | 6 | 13 | 14 | 42 | 14 | 06 | 2 | 18 | |
| 9 | 11 | 39 | 14 | 16 | 7 | 47 | 1 | 12 | 4 | 06 | 0 | 37 | 5 | 31 | 2 | 58 | 6 | 34 | 14 | 52 | 13 | 52 | 1 | 48 | |
| 10 | 11 | 56 | 14 | 09 | 7 | 29 | 1 | 25 | 4 | 04 | 0 | 50 | 5 | 35 | 2 | 44 | 6 | 54 | 15 | 02 | 13 | 37 | 1 | 18 | |
| 11 | 12 | 12 | 14 | 01 | 7 | 11 | 1 | 38 | 4 | 01 | 1 | 03 | 5 | 38 | 2 | 30 | 7 | 14 | 15 | 11 | 13 | 21 | 0 | 48 | |
| 12 | 12 | 28 | 13 | 53 | 6 | 53 | 1 | 50 | 3 | 57 | 1 | 16 | 5 | 41 | 2 | 16 | 7 | 34 | 15 | 19 | 13 | 04 | 0 | 18 | |
| 13 | 12 | 43 | 13 | 44 | 6 | 35 | 2 | 02 | 3 | 52 | 1 | 29 | 5 | 43 | 2 | 01 | 7 | 54 | 15 | 26 | 12 | 40 | 0 | 12 | |
| 14 | 12 | 57 | 13 | 34 | 6 | 16 | 2 | 14 | 3 | 47 | 1 | 42 | 5 | 43 | 1 | 46 | 8 | 14 | 15 | 32 | 12 | 28 | 0 | 42 | |
| 15 | 13 | 10 | 13 | 24 | 5 | 57 | 2 | 25 | 3 | 41 | 1 | 54 | 5 | 46 | 1 | 30 | 8 | 34 | 15 | 38 | 12 | 09 | 1 | 12 | |
| 16 | 13 | 22 | 13 | 13 | 5 | 38 | 2 | 36 | 3 | 35 | 1 | 06 | 5 | 46 | 1 | 34 | 8 | 54 | 15 | 43 | 11 | 59 | 1 | 42 | |
| 17 | 13 | 34 | 13 | 02 | 5 | 19 | 2 | 46 | 3 | 29 | 2 | 18 | 5 | 45 | 0 | 57 | 9 | 14 | 15 | 48 | 11 | 30 | 2 | 11 | |
| 18 | 13 | 45 | 12 | 50 | 5 | 00 | 2 | 56 | 3 | 22 | 2 | 30 | 5 | 44 | 0 | 40 | 9 | 33 | 15 | 52 | 11 | 09 | 2 | 40 | |
| 19 | 13 | 55 | 12 | 38 | 4 | 41 | 3 | 05 | 3 | 15 | 2 | 42 | 5 | 42 | 0 | 25 | 9 | 52 | 15 | 55 | 10 | 47 | 3 | 09 | |
| 20 | 14 | 04 | 12 | 25 | 4 | 22 | 3 | 13 | 3 | 07 | 2 | 54 | 5 | 40 | 0 | 05 | 10 | 11 | 15 | 58 | 10 | 25 | 3 | 38 | |
| 21 | 14 | 12 | 12 | 12 | 4 | 03 | 3 | 21 | 2 | 58 | 3 | 05 | 5 | 38 | 0 | 13 | 10 | 30 | 16 | 00 | 10 | 02 | 4 | 7 | |
| 22 | 14 | 19 | 11 | 58 | 3 | 44 | 3 | 28 | 2 | 49 | 3 | 16 | 5 | 35 | 0 | 31 | 10 | 48 | 16 | 01 | 9 | 38 | 4 | 35 | |
| 23 | 14 | 25 | 11 | 43 | 3 | 25 | 3 | 35 | 2 | 40 | 3 | 27 | 5 | 31 | 0 | 50 | 11 | 06 | 16 | 01 | 9 | 14 | 5 | 3 | |
| 24 | 14 | 31 | 11 | 28 | 3 | 07 | 3 | 41 | 2 | 30 | 3 | 38 | 5 | 27 | 1 | 09 | 11 | 24 | 16 | 00 | 8 | 49 | 5 | 30 | |
| 25 | 14 | 36 | 11 | 13 | 2 | 49 | 3 | 46 | 2 | 20 | 3 | 49 | 5 | 22 | 1 | 28 | 11 | 41 | 15 | 58 | 8 | 24 | 5 | 37 | |
| 26 | 14 | 40 | 10 | 57 | 2 | 31 | 3 | 51 | 2 | 10 | 3 | 59 | 5 | 16 | 1 | 48 | 11 | 58 | 15 | 56 | 7 | 58 | 6 | 24 | |
| 27 | 14 | 43 | 10 | 41 | 2 | 13 | 3 | 55 | 2 | 00 | 4 | 09 | 5 | 10 | 2 | 08 | 12 | 14 | 15 | 53 | 7 | 52 | 6 | 50 | |
| 28 | 14 | 46 | 10 | 25 | 1 | 55 | 3 | 59 | 1 | 49 | 4 | 18 | 5 | 03 | 2 | 28 | 12 | 30 | 15 | 49 | 7 | 05 | 7 | 16 | |
| 29 | 14 | 48 | 1 | 38 | 4 | 02 | 1 | 38 | 4 | 27 | 4 | 56 | 2 | 48 | 12 | 45 | 15 | 44 | 6 | 38 | 7 | 41 | |||
| 30 | 14 | 49 | 1 | 21 | 4 | 05 | 1 | 27 | 4 | 35 | 4 | 48 | 3 | 08 | 13 | 00 | 15 | 38 | 6 | 10 | 8 | 5 | |||
| 31 | 14 | 49 | 1 | 04 | 1 | 15 | 4 | 39 | 3 | 28 | 15 | 31 | 8 | 20 | |||||||||||
Equation of the Centre, call'd also Prostaphæeresis, and total Prostaphæresls; is the Difference between the true and mean Place or Motion of a Planet; or the Angle made by the Lines of the true and mean Place or Mo- tion; or which amounts to the same, between the mean and equated Anomaly. See Prostaphæresis.
The Motions of the Sun and Moon, are affected with various Inequalities; whence arises a Necessity of so many Equations. See Moon, &c.
From these Inequalities, the Moon's Place became exceeding difficult to be determined; to remove which Difficulty, is the great Design of Sir Isaac Newton's newTheory
