Popular Science Monthly/Volume 80/March 1912/Time and Space
|TIME AND SPACE|
By CHARLES W. SUPER
IT requires but a moment's reflection on the part of any one in the least familiar with modern affairs to realize that the time element has come to be the most important factor in business. Railroad trains and steam vessels are run according to time schedules. Offices are opened and closed at certain hours. Employees of all classes are required to report for duty according to the clock, and their task is not completed until they have put in a fixed number of hours. New devices are constantly being placed on the market the purpose of which is to "save time" as the phrase goes. The importance that our day attaches to time is strikingly shown by the fact that for a decade Switzerland has manufactured from six to eight millions of clocks and watches annually; yet this is but a small part of the world's output. It is safe to say that on the average every adult in the United States and in the most civilized countries of Europe is the possessor of a time-piece of some sort. Time may be conceived under two aspects: it may mean a continuous current of duration flowing past a point which we call the present; or it may signify some fixed point or points in that current and the period between them. Remote time either in the past or in the future is usually designated by the term eternity. Any one who reflects soon comes to realize that he can form no concept of duration without beginning or end because it lies out of the range of experience and observation. The popular use of the word time refers exclusively to shorter and longer divisions or units within endless duration, as when we say: "I have not time to talk of this now"; "that never happened in my time"; "the train is on time." The same statement may be made of space. Although it extends in every direction to inconceivable distances, in practical affairs only that part of it is important which can be measured. What is generally called "nature" furnishes us with no accurate standard of measurement of either time or space. For the former the rotation of the earth on its axis gives us an almost uniform period which from time immemorial has been divided into twenty-four hours. No one has ever been able to explain why this number was chosen rather than some other, but it is wholly artificial. Not only this period, but its smaller units, had to be marked by some technical means. For this purpose water-clocks were invented in a remote period of antiquity. The oldest of which any information has been transmitted to us were in use in Egypt as early as 300 B.C. They consisted of a wooden frame in which was fastened a perpendicular cylinder closed at the bottom and open at the top. In it was placed a piston and rod, and on the rod a number of cogs. These cogs were geared into the cogs of a pulley. At the end of the axle on which the pulley was fastened was a hand behind which was attached the dial-plate to a wooden frame. On the dial, each numeral from I. to XII. was marked twice, and the hand moved round the whole face once in twenty-four hours. The contrivance was set in motion by starting a flow of water from a tank into the space between the bottom of the cylinder and the piston. As the piston-rod rose it turned the pulley and the shaft, and of course with it the hand at the end. By regulating the pressure of the water in the tank, the hand could be made to move faster or slower when it was desired to lengthen or shorten the hours to conform to the relative proportion of daylight and darkness in the twenty-four. Water-clocks were formerly much in vogue in the east and were sometimes very artistically constructed. Haroun al Raschid presented one to [[w:Charlemagne|Charlemagne] that was provided with a striking mechanism and adorned with movable figures such as are now quite common. The ancient Greek designations for the time of both the day and of the night were very vague: "the full market," "candle-lighting," "the first sleep," and so on. Herodotus says the troops that were dispatched by Xerxes to get in the rear of Leonidas left the camp "about the time of the lighting of the candles." It would have been more rational to say "about dark," but he evidently used the common phraseology. Cock-crowing was accepted as an indication of time. A well-known example is given in the story of Christ's trial. It is still much relied on by the peasants in some parts of Europe. In the nature of the case the Greek designations did not indicate the same actual time at all seasons of the year, as candle-lighting would be much earlier in the winter than in the summer. Soldiers divided the night into five watches, the length of which also varied with the seasons. It is not probable that they were accurately measured. This division of time is doubtless the oldest; it is several times referred to in the old testament. Sun-dials were a good deal used by the ancients. The Greeks seem to have received them from the Babylonians. Only the astronomers regarded the hours as of equal length. So far as can be known they depended upon water-clocks. But they were of much simpler construction than the one described above, usually consisting merely of two vessels each of which had a small orifice in or near the bottom. One of these vessels was placed above the other and the water which had been poured into it allowed to trickle slowly into the one underneath. When the lower vessel was full the orifice in the upper was closed, that in the lower opened and placed uppermost, when the same process would be repeated. The speakers in the assembly were timed by these clepsydræ, as they were called; they are several times referred to in extant orations. While they could be used at any time of the day or night, they required constant attention, and were by no means accurate. Generally the sun and the stars were depended on when they could be seen; for in the climate of Greece and the adjoining lands there are fewer cloudy days and nights than in the more northerly regions. In modern Athens about one half the days of the year are entirely cloudless, and only thirty are noted as cloudy. The Greeks used daylight almost entirely for business and rose very early. A decree of Solon is often referred to which forbids teachers to open school before daylight. For longer divisions of time the Greeks, like most of the people of antiquity, depended on the moon, but they never got the lunar months to correspond exactly with the facts. They reckoned the month at twenty-nine and a half days, or one twenty-nine, the next thirty. Their months, however, were not divided like ours and the method of counting them so as to make them correspond with the year was very complex, and the result unsatisfactory; there had to be frequent corrections to make the seasons come at the same time of the year. Yet nowhere in Greece was there ever discovered any way to obviate the inherent defect of their clumsy system. In different parts the months had different names, but were not divided like ours. There is a passage in the "Clouds" of Aristophanes in which the moon is represented as complaining of ill treatment because the Athenians had allowed their calendar to fall into confusion to such an extent that the gods were disappointed in their feasts. This made them angry with the moon—very unjustly, since the confusion in their reckoning was the people's fault. The case is very much as if we allowed our fourth of July to drift about until it ultimately came in cold weather. The lack of a fixed date for determining events gradually became generally recognized; consequently, as is generally supposed, Timæus, a Sicilian Greek, proposed the Olympiads as an era. The Olympiads, however, do not correspond with the era employed in Christian countries. Hence we have to use a rule like the following: "Multiply the complete Olympiads by four, and deduct the total from 776 for events of the autumn and winter, or from 775 for events of spring and summer." Although Timæus flourished as late as 300 b.c., earlier dates were made to correspond to his method of reckoning as well as it could be done. It is probable that much of the older chronology is erroneous. By means of observations taken on the star Sirius, both in Egypt and Babylon as early as the fourteenth prechristian century, the year was' found to be about 3651 days in length. Those old-time astronomers also reckoned by a lunar year of twelve months of 29 and 30 days alternately. This was merely a concession to custom. The moon is such a convenience for measuring periods longer than a day and shorter than a year that the incongruity between its phases and the sun's motions was left out of account. The more intelligent people have become, the less attention they have paid to it. The defective year was brought a little nearer to the actual year by adding an intercalary month every three. The Babylonian year is supposed to have been introduced in Athens about 600 B.C. Half a century later the calendar was further improved by Cleostratus, but in all the Greek states the method of reckoning by days and months always remained a good deal wide of the mark. That the Roman year originally contained ten months is evident from the names of the last four called by them seventh, eighth, ninth and tenth (September, October, etc.), although they are in fact the ninth, tenth, and so on. July was named Quintilis, the fifth, August, Sextilis, the sixth; they were afterwards renamed in honor of Julius and Augustus Cæsar. The Roman calendar had, by the year 67 B.C. gone astray to the number of sixty-seven days, that is the civil and the solar year differed from each other to this extent. Julius Cæsar, with the aid of Sosigenes and M. Flavins, brought about the reform in the calendar which has remained substantially unchanged to the present.
The current arrangement of our calendar is a very stupid one. The seasons are not of the same length and the red-letter days fall on all the days of the week in different years. There are 186 days in the spring and summer seasons and 179 in the other two. It would be more rational to divide the year into four seasons each with 91 days and leave out of the count New Year's day and once in four years the extra day, calling it by some appropriate name, leap-year day, for example. The year should not begin where it now does, but either at one of the equinoxes or at one of the solstices. As the date, in the nature of the case, must be arbitrarily chosen it would thus at least have a scientific foundation. The calendar adopted by the French revolutionary junta was based on a scientific principle. The year began with the autumnal equinox of 1792 and consisted of twelve months of thirty days each with five complementary days, to which was added every six years an intercalary day. The months of the year with their names succeeded each other in the following order: Vendemiaire, Brumaire, Frimaire, Nivôse, Pluviôse, Ventôse, Germinal, Floréal, Prairial, Messidor, Thermidor, Fructidor. The month was divided into three decades. The days were named numerically, Primidi, Duodi, and so on. The fifth (Quintidi) and the tenth (Decadi) were designated as days of rest. The five or six complementary days were named Fête de la vertu. Fête du genie. Fête du travail. Fête de l'opinion, Fête des recompenses and Fête de la revolution. This calendar remained in force until January first, 1806, when that of Pope Gregory was restored by decree of Napoleon. Three Roman emperors after Augustus tried to substitute their own names for months instead of those in current use, but they were not permanently successful. Charlemagne also proposed to displace the heathen names of the months by others that he considered more appropriate, but in this he also was unsuccessful. Christian Europe still clings to the names of the months as they were named by the Romans. It may be said, however, that in some parts of Germany February is known by the title given to it by Charlemagne. The change from old style to new was made by all the governments of western Europe except England and Sweden before the middle of the eighteenth century. In the former country, antipathy to the Pope and the natural conservatism of Parliament resisted a change until dates were eleven days out of the way. It was finally brought about under the Pelham ministry on the motion of Lord Chesterfield, who was, however, merely the "big-wig" put forward to give the measure prestige. He knew very little about the subject, but he knew his audience. Some time afterward he wrote to his son:
I consulted the ablest lawyers and the most skillful astronomers and we cooked up a bill for the purpose. But then my difficulties began. I was to bring in this bill which was necessarily composed of law-jargon and astronomical calculation, to both of which I am an utter stranger. However, it was absolutely necessary to make the House of Lords think that I knew something of the matter; and also to make them believe that they knew something of it themselves, which they do not. For my part, I could just as soon have talked Celtic or Sclavonian to them, as astronomy, and they would have understood me fully as well; so I resolved to do better than to speak to the purpose, and to please them instead of informing them.
The change was, however, not so simple an affair as it might seem. A number of matters had to be regulated by law, especially rent-days, annuities and salaries. The year was henceforth to begin on the first of January instead of March 25, and September 2, 1752, was to be called the fourteenth. The populace was much disturbed by the shifting of the saint-days and immovable feasts. Lord Chesterfield's chief advisers were the mathematicians Macclesfield and Bradley. When some time subsequently a son of the former was a candidate for parliament one of the popular cries against him was: "Give us back our eleven days"; and when a number of years later Mr. Bradley died of a lingering disease, many persons attributed his sufferings to the part he had taken in changing the calendar. Verily, "Genius has its limitations, but stupidity has not." The ancient Romans, like the modern English gained the reputation of being an eminently practical people. But just as the latter cling to an awkward system of coinage, so the former adhered for centuries to a method of reckoning time that hardly passed beyond the stage of puerility. There is no evidence that they even divided the day into hours until the third century B.C. In the year 263 Valerius Messala is said to have carried away, among other trophies captured at the taking of Catania in Sicily, a sun-dial, which he set up in Rome. It was in use an entire century before even the officials became aware that it was not correct for the meridian of Rome, although the latitude of Catania differs from that of the capital by more than four degrees. From that time forward sun-dials came into general use; and since many have been recovered their construction is well known. The most common form is that of a concave hemisphere cut in two. Within one of these quarters the hours were marked. A stylus or hand fastened in the top indicated the time of day, when the sun shone. Pliny says the first water-clock was set up in Rome 159 B.C. These water-clocks appear to have differed from the clepsydræ that had long been in use in the countries farther east. They consisted of an earthen vessel tapering downward to a point, in the bottom of which there was a small hole through which the water flowed in a given time. It was comparatively easy to ascertain when the sun was on the meridian; but not so easy to determine the exact period of midnight. This was moreover, an affair of small practical importance. In the larger cities, the periods or hours were announced by the sound of a trumpet; in the country few persons cared how the hours of the night passed. The custom of proclaiming the hours of the night prevailed in some countries of Europe, especially in Germany, long after clocks had come into almost universal use. It is not known when the Romans began to divide the day into twenty-four hours. At any rate there were two kinds of days in vogue: the astronomical day, the hours of which were all of the same length, and the civil or ordinary day which corresponded with the former at the equinoxes only. The popular day was a matter of latitude. In Rome the longest contains somewhat more than fifteen hours according to mathematical calculation, but owing to the Appennines which lie east of it the fact does not quite correspond with the figures. The hour in Rome was therefore at one time of the year about seventy-five minutes in length, while the hours of the night were correspondingly shorter, and vice versa.
Every schoolboy is taught that twelve inches make a foot, but not one in a million thinks to ask what is the basis of this measurement. It must at once occur to the occasional inquirer that the average human foot is not twelve inches long. When, however, a unit of measurement has been once fixed, the rest is easy. The metric system was the first attempt to establish an invariable standard to which recourse could always be had in cases of doubt. A table before me gives twenty-six different lengths for the foot in the German empire, twenty-five for the rest of Europe, eight for America and four for Asia. Of these the longest is that of Lombardy, which contains a little more than 435 millimeters, the shortest the foot of Siam, which is only 245.6 mm. Even in Germany the foot varies from 429.5 to 250 mm. There is of course the same divergence between the square and the cubic foot. The English foot contains 304 mm., which is usually held to differ slightly from that in vogue in the United States. Until there was a great deal of national and international intercourse the need of some uniform standard of weights and measures was not seriously felt; consequently the efforts of physicists in the seventeenth and eighteenth centuries did not receive much encouragement. Absolute accuracy in matters of this kind is unattainable, but in practical affairs it is not particularly difficult. What the term "accuracy" means to a maker of instruments of precision is forcibly illustrated by an anecdote told of John A. Brashear, of Pittsburgh. A prospective customer once asked him what it would cost to have a bar of glass made that was absolutely straight. Mr. Brashear would not promise absolute straightness, but was willing to come as near as he could for two hundred thousand dollars. After listening to a lecture on absolute accuracy by the renowned mechanician the customer concluded that his needs would be supplied by a ruler that would be correct to the one sixty-fourth of an inch and costing about forty dollars.
Physicists became convinced long ago that the only fixed standard of linear measure is some portion of the earth's circumference. No intelligent Greek or Roman from the time of Plato had any doubts about the shape of the earth. But after the Bible had come to be recognized as an authority in science as well as in doctrine the belief was gradually abandoned and various theories took the place of the true one until the time of Copernicus. Archimedes, about 200 b.c. used an ingenious argument to prove the sphericity of our planet. As water always seeks the lowest level the ocean must be equally deep everywhere and the bottom equally distant from a central point. As this is possible only in the case of a sphere, the earth must be spheroidal in form. The first attempt to calculate the circumference of the earth was made by the celebrated savant Eratosthenes in the third century B.C. Observing that the difference of latitude between two points in Egypt, Alexandria and Syene, was 7° 12′ and supposing them to be on the same meridian, and having ascertained as best he could that they were about five thousand stades apart, he reckoned this to be the fiftieth part of the earth's circumference, which would accordingly be 250,000 stades. More than a century later Poseidonius estimated the distance between Rhodes and Alexandria, on the testimony of seamen, to be five thousand stades, or one forty-eighth part of the circumference. Putting the value of the stade at six hundred feet—authorities vary considerably on this point—both estimates must be considered a remarkably close approximation to the truth.
In 1525 Fernel measured the distance between Paris and Amiens with a wheel. Almost a century later Snellius discovered, or rather rediscovered, trigonometry, which greatly simplified geodesy. By this method he measured the distance between Alkmaar and Bergen-op-Zoom, using thirty-three triangles. He obtained nearly the same results with Fernel as to the circumference of the earth. Since that time similar work has been going on almost uninterruptedly. In 1669 Picard measured the meridian Amiens—Malvoisine, and from it estimated the circumference of the earth to be 20,541,500 toises or fathoms. Picard's figures were used by Newton in the studies which led to the discovery of the universal law of gravitation. At this point in the investigations the question arose whether the earth is a perfect sphere or a spheroid. In order to solve this problem two expeditions were fitted out, the one to operate in Peru, the other in Lapland. Both occupied several years, completing their labors about 1740. The results obtained settled for all time the relation of the polar to the equatorial axis. Geodetic surveys are, however, still in progress. The most extensive of the older projects was completed by Arago and Biot in 1808, based on the labors of Mechain and Delambre. The meridian measured was that between Dunkirk and Formentera, an island near the Mediterranean coast of Spain. This arc extended over twelve degrees and twenty-two minutes. The principal object of this survey was to establish a fixed unit of linear measure for the meter, which was to be the one ten-millionth part of the earth's meridian quadrant. This is the so-called métre des Archives, a platinum rod deposited in Paris. Although it is now known that it is not strictly correct there is no probability that it will ever be changed, as it has become the foundation of the metric system. In 1861 general Baeyer proposed the measurement of the meridian Christiania-Palermo. The work was to be carried out by the European governments conjointly. The proposal led to a general conference of savants in Berlin in 1862. A permanent commission was organized under the presidency of General Baeyer. Another conference was held in Berlin in 1867, all the governments of Europe, except Turkey, having in the interval promised cooperation. Since then meetings of the commission have been held every two or three years, their object being the continuation and revision of the French measurements to Algiers, a complete triangulation of the Mediterranean Sea, the measurement of a parallel through Central Africa from Cape Town to Upper Egypt, and to take such other observations as usually fall within the scope of a geodetic survey. For many years the United States government has been engaged in measuring the ninety-eighth parallel which extends from the southern point of Texas to the Canadian border. Strange as it may seem in view of what they accomplished in several directions, the ancients had almost no knowledge of machinery. Water power was called into requisition to a limited extent, but the main reliance was on the muscular force of man and beast. In the East and in Egypt, the potentates tried to impress their contemporaries and posterity by the vastness of their structures; the artistic sense of the Greeks led them to make only such objects as were beautiful. But even the Romans who were intensely practical in most things never constructed labor-saving machinery. It is no explanation of the fact to say that actual or virtual slavery was the cause of this lack of enterprise. The same conditions prevailed throughout the Middle Age after slavery had been to a considerable extent abolished. Machinery can hardly be said to antedate the era of steam. Although time-pieces can not properly be called machines, their construction requires a knowledge and appreciation of the mechanical powers. It is in strict conformity to the law of progress that water-power which had been in use for purposes of propulsion for thousands of years should also be employed in the manufacture of timepieces.
We need to be often reminded that the phrase "to save time" is one of the most frequently misapplied in our language. If we can cross an ocean or a continent in five days instead of the fifty formerly required, where have we saved any time, if we make no good use of the forty-five we are supposed to have saved? If we can converse with a person ten miles or a hundred or even a thousand miles distant without stepping out of doors, where is anything gained if we have nothing to say that is worth saying? If by means of so-called labor-saving machinery we are provided with a thousand pages to read for every one that was within easy reach of our grandfathers, how are we better off if very little of it is worth reading? We are losing rather than saving time in the operation. The truth is that nothing worth doing has ever been done in a hurry. Almost all the great discoveries and inventions that have really benefited mankind are the result of much patient thought and investigation and experiment. The same is true of every work of art, whether pictorial or plastic. After they have become public property their use is a mere matter of routine and imitation. The more time we "save" the less we seem to have. The more we rely on machinery to do our work, the more nearly we become machines ourselves. Even our educational processes have largely degenerated into mere mechanical routine. Each pupil and student is taught to do what he has seen others do. Most of our young people are advised to transform themselves into living cash-registers as early as possible, although the coins they handle are for the most part either counterfeit or of small value. .
- The Prussian general Baeyer, who died in 1885 at the age of ninety-one, probably devoted more years to geodesy than any other man of modern times. He began his practical studies in 1816 and published his last work in 1881. He cooperated with Bessel in many of his measurements and astronomical observations.