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
