The determination of the equation of time is a mathematical pro blem of some complexity : what we have here to notice is, that owing to the joint action of the two sources of difference, it presents a I very irregular series of phenomena in the course of the year. If the sun moved regularly, but in the ecliptic, there would be no equation of time at tho equinoxes and solstices : if the sun moved with its elliptic irregularity, but in the equator instead of the ecliptic, there would he no equation of time at the apogee and perigee. Between the two the equation of time Vanishes only when the effect of one cause of irregularity is equal and opposite to that of the other; and this takes place four times a year. In this present year (1861) the state of the equation of time is as follows :—January 1, the clock is before the sundial 3" 58', and continues to gain upon the dial until February 11, I when there is 14" 32' of difference. This then begins to diminish, and I continues diminishing until April 15, when the two agree, and there is no equation. The dial then is before the clock until May 14, when the equation is 3' 53', which diminishes until June 14, when there is again no equation. The clock is now before the dial, and the equation increases till July 26, when the equation is 6' 12', which diminishes until the let of September, when there is no equation, for the third time. The dial is now again before the clock ; and by November 3,
the equation has become 16' 18', from which time it falls off until December 24, when it is nothing for the fourth and last time. The clock then gets gradually before the dial till the end of the year. The phenomena of the next year present a repetition of the same circum stances, with some trivial variations of magnitude. There are several slight disturbing causes to which we have not thought it worth while to advert in a popular explanation : in particular, the slow motion of the solar perigee [YEAR ; Susi], which will in time wholly alter the phenomena. For instance, when the perigee comes to coincide with the equinox, there will be only two periods at which the equation of time vanishes, namely, when the sun is at either equinox.
The sidereal day is 23" 56' of a mean solar day, and the mean solar day is 24" 3" 56'•55 of a sidereal day. We have in this article only to do with the mode of obtaining a uniform measure of time, or of intervals of time ; this being premised, the subject will be taken up again in the article YEAR.