TO CALCULATE THE TIME OF NEW OR FULL MOON IN ANY YEAR OF THE CHRISTIAN ERA BEFORE THE 19TH CENTURY. From table I, take the mean time of new moon in March. with the anomalies and distance from the node of a year of the same number in the century with that proposed. Then from table III, take as many centuries of years, with the annexed numbers, as will reduce the year in the 19th century to the year required. Subtract these from the preceding numbers, the remainder will be the mean time of new moon in March, the anomalies and distance from the node for the proposed year. If the time set to March, of the year in the 19th century be less than the time in the centuries of years taken, a lunation from table II, with the annexed numbers must be added to the time in March. Then subtract as before directed. The remaining process is the same, as in calculating the true time of change or full in the 19th century. In most calculations for years before or after the 19th century, the old stile is to be preferred, on account of its uniformity. It may be reduced to the new by the subsequent rules in this work. EXAMPLE. Required the true time of full moon at Plymouth, Mass. in December, 1620, old stile. Time in March at W. 1820. New moon Sun's anom. 's auoma from node 13 11 33 54 5 26 46 13/10 12 3 58 Time in March, 1620 5 Add ten lunations 1295 28 0 17 23 19 0 15 20 7 5 55 56 6 11 19 23 4 24 58 28 1 2 43 26 50 17-4 25 17 28+ 19 이 6 46 13 1 16 1 55 4 25 17 28| + 5 13 431 28 11 59 56 - Hence the true time at Plymouth, by 3 26 the clock old stile, was 28d. 12h. 23m. 28 11 56 30 21s.; in civil calendar, 29th day Oh.23m. 1 25 21s. in the morning. 28 11 57 55 25 26 + t 28 12 23 211 TO CALCULATE THE TRUE TIME OF NEW OR FULL MOON IN ANY YEAR BEFORE THE CHRISTIAN ERA. Find the time of new moon in March, of the year in the 19th century, which added to the year before Christ, diminished by one, will make complete centuries. Subtract the numbers for those centuries, taken from table III, and proceed as in the other precepts. EXAMPLE. Required the true time, in Julian calendar, of new moon in September of the year, that Cadmus brought the letters into Greece, allowing that event to have been in the year before Christ, 1493. TO CALCULATE THE TRUE TIME OF NEW OR FULL MOON IN ANY YEAR AFTER THE 19TH CENTURY. To the mean new moon in March, of the correspondent year in the 19th century, add the requisite numbers for the centuries intervening, from Table III, and proceed as before ; observing to subtract a lunation, should the addition carry the new moon beyond the 31st of March. Except, when the time sought is after March, one lunation less may be added, instead of the subtraction. EXAMPLE. Required the true time of full moon at New Orleans, in July, 1976. New moon 's anom. 's anoma. from nodi D. H. M. SS. O 29 S. 5 39 14:0 4 10 45 Mean new in March, 1876 24 13 22 218 22 21 40 3 Add for one century 4 8 10 520 3 19 6 8 15 1 44 4 19 27 23 21 33 13 8 25 40 4611 21 0 594 23 44 9 118 2 56 12 3 26 25 17 3 13 16 26 0 29 250 22 633 4 17 14 18 22 20 14 33 10 6 12 Mean time in March, 1976+ Deduct lunation Mean full moon Time once equated Time three times equated Time four times equated 11 6 7 230 7 32 53 8 21 - 24 2 40 55 Op 26 25 5 54 300 15 20 7 22 308 11 4 58 12 13 0 31 488 21 10 17 TO CALCULATE THE TRUE PLACE OF THE SUN AT ANY TIME IN THE 18TH CENtury. From Table X, take the mean longitude and anomaly for the year, month, day, hour, minute, and second, required; then equate the longitude by the numbers found in Table XI, having the anomaly as an argument, and it will be the true place of the sun for the time. For any time in the Christian era before the 19th century, find the longitude and anomaly for the corresponding time in the 19th century, and deduct the longitude and anomaly set against the intervening centuries. But for time long past the old stile is to be preferred. Add the longitude and anomaly for 12 days to those of the year sought in the 19th century, the sum will be the longitude and anomaly at the com mencement of the year, old stile. Then proceed as before directed. For any time before the Christian era, find the longitude and anomaly of the year in the 19th century, which added to the year before Christ, minus 1, will make complete centuries. Deduct the longitude and anomaly for the centuries; and proceed as before. For any time after the 19th century; find the longitude and anomaly for the corresponding time in the 19th century, allowing for stile, and add for the intervening centuries, proceed as before. EXAMPLES. Required the sun's longitude and anomaly, July 17, 1860, at 21h. 22m. 9s. Allowing that Alfred's reign closed Oct. 28, old stile, A. D. 900, what was the sun's longitude and anomaly? What was the longitude and anomaly of the sun, March 20, O. S. in the year, that the Children of Israel removed from Egypt, before Christ, 1491 ? Deduct for 3300 0 8 531 0 11 49 40 0 11 49 38 9 21 31 54 6 11 58 31 0 25 11 32'10 28 19 12 Commencement of the yearB.C.1491, 8 26 20 22 7 13 39 19 March Days 20 Mean longitude and anomaly True longitude 1 28 9 11 1 23 9 1 0 19 42 471 0 19 42 43 11 14 12 2010 1 31 3 +1 37 30 Anomaly 11 15 49 50 Required the true longitude and anomaly of the sun, April 12, 1924, at 9h. 42m. 17s. A. M. This and other examples of the 20th century, may be worked by taking the longitude and anomaly for 1900 with the additional time. Table X, ought to be made familiar, mistakes being likely to happen without peculiar care. |