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This article offers suggestions, not for formal lessons on astronomy, but for occasional “raids” into astronomical territory—excursions intended to show how even an elementary knowledge of mathematics may be applied fruitfully to problems of real importance and abiding interest. The mathematical knowledge assumed is acquaintance with the three main trigonometrical ratios and their reciprocals, familiarity with the “natural” trigonometrical tables, and a little practice in changing the subject of a straightforward formula containing the ratios. Values taken to three places generally suffice, and skill in using logarithms, though desirable, is not demanded.
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- Copyright © Mathematical Association 1943
References
Page 45 of note * Star-gazers in the southern hemisphere have no Pole Star, but their Southern Cross is a magnificent substitute for the Plough. In reading this article they must regularly substitute “south” for “north” and “north” for “south”.
Page 46 of note * “Whitaker” is indispensable, but need not be the current issue. The official Nautical Almanac (H.M. Stationery Office) is a desirable luxury. The issue for 1938 includes the late Professor Fotheringham’s masterly article on the Calendar, but much of this matter is in Whitaker.
Page 46 of note † It is assumed that the rectangle represents the cylinder as seen from the point O within it. If the appearance from without is needed, “right” and “left” must be interchanged.
Page 47 of note * Here is a simple proof that the sun does so travel. If a prominent constellation (e.g. Orion, which begins, in Britain, to appear in December) be watched during two or three months, it will be seen to reach the same place in the sky rather less than half an hour earlier every week. Now our clocks keep pace with the “mean” sun; hence the sun must be approaching Orion at a rate which would carry it round the heavens in something over 48 weeks—actually in about 365¼ days.
Page 47 of note † Normally it occupies the point some time before or after reaching the meridian on the day of the equinox.
Page 47 of note ‡ At places on the central meridian of a “time zone”, i.e. in longitude 0°, 15°, 30°, 45°, etc., east or west of Greenwich, local mean noon is just 12 o’clock. At places east or west of the central meridian it occurs earlier or later than 12 o’clock, the difference being 4 min. for every degree of longitude. For instance, mean noon occurs at Bristol (2½° west of Greenwich) at 12.10 p.m., at Stockholm (3° east of the 15th meridian) at 11.48 a.m. by the standard clocks of the city.
The record in Whitaker, taken with the preceding paragraph, makes it easy to train a clock to gain 4 minutes a day and to keep sidereal time. Such a clock is useful as a question-provoking object in a mathematical class-room or a laboratory.
Page 54 of note * The scales of altitude should be marked, say in red ink, just inside the edges of the maps, and there should be no exterior right and left margins. The two sheets can then be laid out, at will, so as to make a single complete map.