Time and longitude are complementary
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Time and longitude are complementary. Longitude may be expressed in hours, minutes and seconds of time, as well as in degrees, minutes and seconds of arc. The relationship is simple. One hour equals fifteen degrees of arc. The two are complementary in the sense that when either is known the other can be determined; but in the ordinary way it is not possible to tell one without the other.
The altitude observation of a heavenly body off the meridian leads up to the determination of its hour angle at the point of observation, and from that the local mean time of the observation can be found. But here a difficulty arises. Either the longitude or the time must be known. They are mutually dependent.
A striking (literally) example occurred on the occasion of the farewell speech of King Edward VIII. The broadcast was scheduled for 3:00 P.M. and the occasion seemed so historical that we made a special effort to hear it. The clocks in our home are, needless to say, kept very close to Mountain Mean Time. At a few minutes before three o'clock we turned on the radio and the first thing we heard was the announcer in London telling us that we would hear Big Ben strike. At that moment the clock in our hall started to chime and strike three times. Before it was through striking, we could hear Big Ben giving the first of its ten repeated booms.
One of two conclusions can be drawn from this coincidence. If our clock had been set precisely to local mean time we could decide that we were exactly seven hours west of Greenwich (which we were within about eight seconds), or, if we knew our longitude to be seven hours west, we could then deduce that our clock was about right by Mountain Mean Time. If we had not known one premise or the other, we could not have drawn these conclusions.
This is all very well, and for practical purposes nothing more is required; but there is something about an interdependent system like this which bothers the more theoretical mind and for many centuries astronomers have desired an absolute means of finding time--one which could be used irrespective of geographical knowledge; or conversely a method of determining positions upon the Earth without knowing the time. The difficulty which at first seemed to have no practical consequences has become more acute with the increased rate of travel by air, and with the explorations around the North and South Poles where the longitudes converge. On one occasion a polar explorer allowed his watch to run down, and he was left almost helplessly lost. He had no knowledge of his longitude and he might be wandering about there yet, had he not had the luck to meet another more careful explorer who helped him to reset his watch to Greenwich Mean Time.
As long ago as 1540, Apian recognized this problem. In his day its necessity seemed less likely, and his argument is rather quaint:
"To find the longitude of a place with speed and facility . . . it is appropriate that the reader should learn what we attempt here and study this chapter. . . . For, if by some chance you should not observe the sky for several years and do not know (which would not be unusual) where among the peoples or parts of the Earth you are, and you can not find out by inquiring, nevertheless you can find your position by relying on your own skill and ability, as is expressed in the old adage, 'The whole world nourishes you; for yourself you should want to know it.'"
Lest our readers should ever find themselves in such dire predicaments, we might mention that Apian offered a solution. He took advantage of the relatively rapid movement of the Moon among the stars; and measured it by an instrument of his own invention, which he called a "torquetum." The torquetum was the predecessor of the equatorial telescope.
Apian's method was not very exact and any error was multiplied about thirty times in the result. Besides, the chance of finding yourself in an unknown country with a torquetum seems considerably less than the chance of finding yourself anywhere else without one.
There are, however, other methods of determining longitude or time by aid of the Moon. One consists in measuring lunar distances and another in observing the occultations of stars as the Moon passes across them. Both these methods suffer from lack of accuracy; and call for a sextant or a telescope and, of course, a Nautical Almanac. You should never consider misplacing yourself without these valuable aids.
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