Observe in this and every other case of finding equations, that if the signs be at the head of the Table, their degrees are at the left hand, and are reckoned downwards. But if the signs be at the foot of the Table, their degrees are at the right hand, and are counted upwards; the equation being in the body of the Table, under or over the signs, in a collateral line with the degrees. The terms add, or subtract, at the head or the foot of the Tables, where the signs are found, show whether the equation is to be added to the mean time of new or full Moon, or subtracted from it. In Table 7th, the equation is to be subtracted, if the signs of the Sun's anomaly be found at the head of the Table; but it is to be added, if the signs be at the foot. With the signs and degrees of the Sun's anomaly, at the mean time of new or full Moon, enter Table 8th, and take out the equation of the Moon's mean anomaly, subtract this equation from her mean anomaly, if the signs of the Sun's anomaly be at the head of the Table; but add it, if they be at the foot, the result will be the Moon's equated anomaly. With the signs and degrees of the Moon's equated anomaly, enter Table 9th, and take out the second equation, for reducing the mean to the true time of new Moon, adding this equation, if the signs of the Moon's equated anomaly be at the head of the Table; but subtracting it, if they be at the foot, and the result will be the mean time of the new or full Moon, twice equated. Subtract the Moon's equated anomaly from the Sun's mean anomaly, and with the remainder, in signs and degrees; enter Table tenth, and take out the third equation, applying it to the former equated time, as the titles add, or subtract direct, and the result will be the mean time of new, or full Moon thrice equated. With the Sun's mean distance from the ascending node, enter Table 11th, and take out the equation answering to that argument; adding it to, or subtracting it from, the thrice equated time, as the titles direct; to which apply the equation of natural days, from Table 17th, subtracting it, if the clock be faster than the Sun, and adding it, if the Sun be faster than the clock, the result will be the true time of new or full Moon, and consequently of an Eclipse; agreeing with solar time. The method of calculating an Eclipse, for any given year, will be shown further on, and a few examples.compared with the precepts, will render the whole work plain, and easily understood. f The Tables begin the day at noon, and reckon forward to the noon following. They are also calculated for the latitude and longitude of WASHINGTON, excepting Table first, but serve for any place on the surface of the Globe, by subtracting four minutes for every degree that the place lies west of WASHINGTON, from the true solar time of conjunction or opposition, & adding four minutes to the true solar time for every degree that the place lies eastward of WASHINGTON, if Table 16th be used, and the same from LONDON, if Table first be used, the result will be the true solar time of the new or full moon, & consequently of an eclipse corresponding with the place for which the calculations are made. |