# Popular Science Monthly/Volume 56/February 1900/Forenoon and Afternoon

FORENOON AND AFTERNOON. |

By CHARLES F. DOWD, Ph. D.

IT is a fact of common observation, at different times of the year, that the forenoon and afternoon, as to daylight, are of unequal length. Along in later autumn the shortness of the afternoons is very noticeable, and the shortness of forenoons along in later winter. Whatever makes common facts more intelligible adds to the general intelligence and to the general good. It is to this end that the following brief statements are made.

Nothing is more evident than that the sun requires just as much time to go from the eastern horizon to the midday meridian as to go from that meridian to the western horizon. But, strange to say, there are but four days during the whole year in which the sun reaches the midday meridian at just twelve o'clock. The true noon point varies from about fifteen minutes before to about sixteen minutes after twelve o'clock. These extreme points in one set of variations fall in the first week of November and in the second week of February, not to designate exact days for years in general.

The calendars show that in the latitude of Saratoga (essentially Boston latitude) on November 3, 1898, the sun rose at 6.30 and set at five o'clock, thereby making the forenoon a half hour longer than the afternoon. On that day the sun reached the midday meridian at 11.45. On February 13, 1899, the sun rose at just seven o'clock and set at 5.30, thereby making the afternoon a half hour longer than the forenoon, and on this day the sun reached the midday meridian at 12.15. These are facts plainly open to general view, and therefore need no verifying.

The causes of the foregoing are not so apparent to common observation. It must be borne in mind that the mean or average solar day is the basis for all time measurements, therefore its exact length is of the greatest importance. Yet the general solar day, from which the average one is derived, is a very indefinite term as to its length. Its length in general may be defined, under view of the sun's apparent motion, as the time extending from the instant that the sun's center crosses any given meridian of the earth on one day to the instant that center crosses the same meridian on the following day—i. e., the time intervening between these two instants is the length of a solar day.

The motion of the sun, however, is only apparent; the actual motion is in the earth's revolution upon its axis. We should have one day a year long if the earth did not revolve on its axis at all, since the revolution of the earth around the sun once a year would in the course of the year bring all sides facing the sun. Consequently the earth makes one more revolution upon its axis each year than the number of solar days in that year, and a little consideration of this fact will show that in each solar day the earth makes one full revolution on its axis and about 1365 of another, which fractional addition is occasioned by one day's progress of the earth along its orbit.

Another fact needs to be considered. Since the earth's orbit is in the form of an ellipse, with the sun at one of the foci, the earth must pass nearer the sun in some parts of its orbit than in others. By the laws of gravity, when nearer, the attraction between the earth and sun is greater, and if this were not balanced by increased velocity along its orbit the earth would fall into the sun; and, on the other hand, when farther off this attraction is less, and if this were not balanced by a diminution of velocity along its orbit the earth would fly off into space. This varying velocity, together with other complications too technical for a magazine article, gives varying lengths of orbit to the several solar days of the year. If the earth's orbit were laid out upon paper and, by astronomical calculations, an exact proportionate section were marked off for each solar day of the year, the variable lengths of orbit for the different days of the year would plainly appear to the eye.

But, as before explained, the time of a solar day is the time of one revolution of the earth upon its axis, together with the fractional part of another revolution occasioned by one day's progress of the earth along its orbit. Then it must follow that as the daily sections of the orbit vary in length, the time of the solar day must vary in length. ISTo clock could be made to keep the variable time of true solar days, and if this were possible, the hour, minute, etc., would be variable of length, and hence no standard for time measurements. But by working a simple arithmetical problem of addition and division an average length of day for the year may easily be found. This average day is the mean solar day adopted. Its time is arbitrary and exact, forming a perfect standard for all time measurements. From this the term mean time gains its significance.

By referring to the foregoing earth's orbit laid out on paper, with the true solar days marked off in sections of mathematical exactness" it will be seen that by dividing each section into two equal parts and marking the division point with red ink, the true noon point of each solar day in the year will be conspicuous upon the drawing, and in its proportionate relations in every way. If now we set a pair of dividers or compasses so that the opening shall reach over the exact space on the orbit of one half of the mean solar day, and beginning at the red noon point of one of the four days in the year when the true noon falls at just twelve o'clock—say December 24th—and step the dividers around on the orbit, making a blue point mark at each second step, then as the blue points vary from the red so will the mean time which our clocks keep vary from the true noon of each day of the year. Variation in length of forenoon and afternoon, therefore, may be viewed by common intelligence not only as a fact but as a necessity.