With the general introduction of clocks and watches into use about a century ago this kind of solar time went out of common use, since no well-regulated clock could keep the time correctly. The earth in its orbital motion around the sun goes faster in some parts of its orbit than in others, and in consequence the sun appears to move more rapidly among the stars in winter than in summer; moreover, on account of the convergence of hour circles as we go away from the equator, the same amount of motion along the ecliptic produces more effect in winter and summer when the sun is north or south, than it does in the spring and autumn when the sun is near the equator, and as a combined result of these causes and other minor ones true solar time, as it is called, is itself not uniform, but falls behind the uniform lapse of sidereal time at a variable rate, sometimes quicker, sometimes slower. A true solar day, from noon to noon, is 51 seconds shorter in September than in December. [Illustration: FIG. 30.--The equation of time.] 53. MEAN SOLAR TIME.--To remedy these inconveniences there has been invented and brought into common use what is called _mean solar time_, which is perfectly uniform in its lapse and which, by comparison with sidereal time, loses exactly one day per year. "The time" in this system never differs much from true solar time, and the difference between the two for any particular day may be found in any good almanac, or may be read from the curve in Fig. 30, in which the part of the curve above the line marked _0m_ shows how many minutes mean solar time is faster than true solar time. The correct name for this difference between the two kinds of solar time is the _equation of time_, but in the almanacs it is frequently marked "sun fast" or "sun slow." In sidereal time and true solar time the distinction between A. M. hours (_ante meridiem_ = before the sun reaches the meridian) and P. M. hours (_post meridiem_ = after the sun has passed the meridian) is not observed, "the time" being counted from 0 hours to 24 hours, commencing when the sun or vernal equinox is on the meridian. Occasionally the attempt is made to introduce into common use this mode of reckoning the hours, beginning the day (date) at midnight and counting the hours consecutively up to 24, when the next date is reached and a new start made. Such a system would simplify railway time tables and similar publications; but the American public is slow to adopt it, although the system has come into practical use in Canada and Spain. 54. TO FIND (APPROXIMATELY) THE SIDEREAL TIME AT ANY MOMENT.--RULE I. When the mean solar time is known. Let _W_ represent the time shown by an ordinary watch, and represent by _S_ the corresponding sidereal time and by _D_ the number of days that have elapsed from March 23d to the date in question. Then S = W + 69/70 × D × 4. The last term is expressed in minutes, and should be reduced to hours and minutes. Thus at 4 P. M. on July 4th--