ASTRONOMY AT THE FRONT: A LUNAR CALENDAR IN THE MEMORY.
(To Tar •Eorros or THE " erserma.,
Sm,—Mr. Maunder's mention of the use of the moon for bearings (Spec. tator, August 19th, p. 215) is a reminder of the unusual importance of moonlight during the war. In old days moon-dials were occasionally used for getting the time from the moon, the inverse problem to Mr. Maunder's, but they cannot be recommended for the trenches. On'the other hand, how long after sunset the moon would rise might be vital knowledge to a partially disabled man lying in a shell crater waiting to crawl back to his lines, while air raids and driving after dark may interest
ethers in moonlight. Pocket calendars are apt not to be there when wanted, and the writer devised some years ago a simple method of carrying in effect a complete lunar calendar in the memory and regrets that in the pressure of war work the possible value at the front of the method did not occur to him earlier. All that has to be remembered for the whole year is the date of new moon in March. The number of the month is used as the basis, 1 standing for January, 2 for February, &c., as usuaL Those unaccustomed to scientific matters may be assured that it is so simple that, once understood, they can work it out mentally in a few seconds without knowledge of astronomy, though to begin with they may require more explanation than there is room for here.
(1) The date of new moon is the same in January as in March, and in other months is earlier than the March date by the difference between the month number and 3. The previous new moon having been thus found, the moon's age in days at the required date is got at once by subtraction. In leap years the dates in January and February are of course earlier than this by one day.
(2) The time of " southing " (i.e., moon due south or midway between rising and setting) is later than noon by the same number of hours as the age in days less ten times as many minutes, or (nearly the same) decimal eight times the age. Adding the " establishment " of any port gives roughly the time of high tide.
(3) The number of the month denoting the moon's ecliptic position (position among the stars) is found by adding to the required date half as many calendar months as the number of hours just found by (2). The method is based on this :—The sun and moon being close together at each new moon, the moon takes in each lunar month nearly the same ecliptic journey as the sun will take in the year (really 13 months) following each new moon. Thus the moon's height in the sky and the length of the lunar day on the required date are obtained by (3) because they are nearly the same as the sun's in the corresponding position, viz., in the calendar month found by (3). That is why the ecliptic position is here expressed in terms of months instead of in degrees of longitude. The length of the day and the sun's height at the different seasons are familiar, and so (1) to (3) give a fair idea of what the moon will do ; but while familiar they are apt to be remembered indefinitely, hence it is better to use (4). This, the number of hours by which rising is earlier and setting is later than southing, is obtained by adding 3 to the month number previously found by (3). In English and Flemish latitudes this is true about the end of the third week of each month from January to May, while in June hours are reached. From July to October (also about their third weeks) subtract the month number from 15, noting that 4 hours is not reached till December. Except at the solstices —June and December—the change is about a quarter of an hour a week. (4) applies also to the sun and gives the times of sun rise and set, but only roughly, as the sun may south as much as 15 minutes before or after noon by the clock. (1), (2), and (3) apply all over the world, and the almanac shows the alterations required in (4) for different latitudes. Owing to the many irregularities in the moon's motion, a short method like this can give the times only within an hour or so. As the difference between Greenwich and local time in Flanders and in the West of England is only a few minutes it can be ignored here.
Taking as an example the night of September 10th-11th, 1916, we have only to remember for the whole year that in March new moon was on the 4th. By (1) for month 9 the previous new moon is 9 less 3, i.e., 6 days earlier than the March date, the 4th, i.e., it is on August 29th. Hence on September 10 the age is nearly 13 days. (It is best to reckon the date of the night as that of the following day, here September 11th.) By (2), it souths at 13 hours less 10 x 13 minutes say 10.45 p.m. By (3)— ignoring odd quarters, half of 101 is nearly 51, thus the moon when 13 days old has already got 51 months in the sun's annual path in advance of the sun and is where the sun will be 5} months after September 10th, i.e., near the end of February, and so her height and length of day are about those of a February sun. This may be all the information we require. If we proceed we have by (4)—to 2, the month number of February, add 3, giving 5 hours as the length of the half lunar day. Hence as southing is by (2) about 10.4.5 p.m., rising is about 5.45 p.m. and setting 3.45 p.m. For the sun about the third week of September (4) shows that the month number 9 must be subtracted from 15, giving 6 hours and, two weeks earlier, say 61 hours as the length of the half- day ; thus the sun will rise about 5.30 a.m. and set about 6.30 p.m., and if not cloudy the night will be well lit by the moon up to a couple of hours before sunrise. For rough purposes we may ignore the fact that for half of each lunation the moon is higher and for the other half lower than the sun when in the same ecliptic position. It is, however, easily included, though lack of space prevents an explanation here.— I am, Sir, &a., W. J. BsEman Davis, A.M.I.C.E.
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