apogee. At the time of new Moon, she is nearer to the Sun than the earth is at that time, by the whole semidiameter of the Moon's orbit; which, at a mean state, is 240,000 miles; and at the full she is as many miles farther from the Sun, than the earth then is. Consequently, the Sun attracts the Moon more than it attracts the earth, in the former case, and less in the latter. The difference is greatest, when the earth is nearest the Sun; and least when it is farthest from him. The obvious result of this is, that, as the earth is nearest to the Sun in winter, and farthest from him in summer; the Moon's orbit must be dilated in winter, and contracted in Summer. These are the principal causes of the difference of time, that generally happens between the mean and true times of conjunction or opposition of the Sun and Moon. The other two differences, which depend on the differences between the anomalies of the Sun and Moon, and upon the Sun's distance from the lunar nodes in the syzygies, are occasioned by the different degrees of attraction of the Sun and earth upon the Moon, at greater or less distances, according to their respective anomalies, and to the position of the Moon's nodes, with respect to the same. If it should ever happen, that the anomalies of both the Sun and Moon, were either nothing, or six signs at the mean time of new or full Moon; and the Sun should then be in conjunction with either of the Moon's nodes, all the above-mentioned equations would then vanish; and the mean and true time of the syzygy, would coincide; but if ever this circumstance did happen, we cannot expect the like again in many ages afterwards. Every 49th lunation returns very nearly to the same time of the day as before; for 49 mean lunations wants only 1 minute, 30 seconds, 34 thirds of being equal to 1477 days. In 2,953,059,085,108 days, there are 100,000,000,000 lunations, exactly, and this is the smallest number of natural days, in which any exact number of mean lunations are completed. The following tables are calculated for the meridian of WASHINGTON, excepting table first, which is calculated for the meridian of LONDON, but they equally serve for any other place by adding 4 minutes to the tabular time, for every degree that the given place is eastward from WASHINGTON; or subtracting 4 minutes for every degree that the given place is westward from WASH INGTON. These tables also begin the day at noon, and reckon forward to the noon following, for one day. Thus, March 31st, at 22 hours, 30 minutes, and 25 seconds of tabular time, (in common reckoning,) will be April 1st, at 30 minutes, 25 seconds after 10 o'clock in the morning. INTERROGATIONS FOR SECTION THIRTEENΤΗ. Does an object appear at a less angle when far off, than when near? Do the Sun and Moon subtend different angles at different times? Are the angles subtended by the Sun and Moon once at the greatest, and once at the least in one revolution? Are these gradual differences the same as they would be, if those luminaries moved in circular orbits? Do they agree perfectly with elliptical orbits ? Where must the lower focus of each orbit be placed to have them agree? What is meant by the term apogee? What by perigee ? Into how many parts do astronomers divide each orbit? from any point of its orbit? What is the distance at any given point, of the Sun or Moon from its apogee called? What is the anomaly of the Sun or Moon when in apogee? What in perigee? In what part of their orbits are the Sun and Moon con tinually accelerated? In what part retarded? 1 What are the mean motions of the Sun and Moon called? What are the unequable called? In what parts of their orbits are the mean motions forward of the true? In what part are the true forward of the mean? Does the Moon's apogee move forward in the ecliptic? Does it move faster or slower than the Sun's? Does the Moon revolve sooner from any node to the same again, than from any fixed star to the same again? If so, what is the difference? What is meant by a lunation? Why do astronomers begin the year with March? What does table third contain? What table first? Why was table first calculated for Old Style? What is the greatest difference between the mean or true time of new or full Moon, on account of the Sun's motion? Are the lunations longer in winter than in summer? What reason can you advance? What the greatest difference? On what do these differences depend? What are they called? Why is this equation not sufficient to reduce the mean time to the true? Is the Moon's orbit more elliptical than the Sun's? Is the Moon sometimes sooner or later in conjunction or opposition with the Sun, than she would be if her motions were equable in every part of her orbit? If so, what is the greatest difference? On what account does the Moon's orbit become different? When is it the most eccentric? When the least? What is equal to the Sun's distance from the Moon's apogee? On what does the first of these differences depend? On what the second? What is the remotest point of the earth's orbit called? What is the nearest point to the Sun called? Has the attraction of the earth any influence on the motion of the Moon? In what case is the motion continually accelerated? Why is the Moon's orbit dilated in winter? For what place are the following tables calculated? SECTION FOURTEENTH. PRECEPTS RELATIVE TO THE FOLLOWING TABLES. To calculate the true time of New or Full Moon, and Eclipses of the Sun or Moon, by the following Tables. IF the required new or full Moon be between the years 1800 and 1900, take out the mean time of new Moon in March, for the proposed year, from Table 16th, together with the anomalies of the Sun and Moon, and the Sun's mean distance from the Moon's ascending node. But if the time of full Moon be required in March, add the half lunation at the bottom of the page, from Table 3d, with its anomalies, &c. to the former numbers, if the new Moon falls before the 15th of March; but if after the 15th of March, subtract the half lunation before mentioned, with the anomalies, &c. and write down the respective remainders. In these additions and subtractions, observe that 60 seconds make a minute, 60 minutes make a degree, 30 degrees make a sign, and 12 signs a circle. When the number of signs exceed 12 in addition, reject 12, and set down the remainder. When the number of signs to be subtracted is greater than the number you subtract from, add 12 signs to the minuend, you will then have a remainder to set down. When the required new or full Moon is in any month after March, write out as many lunations, with their anomalies, and the Sun's distance from the Moon's ascending node, from Table 3d, as the given month is after March, setting them regularly below the numbers taken out for March; add all these together, and they will give the |