EQUATOR

EQUATION OF TIME, in Astronomy, denotes the difference, expre ed in mean solar time, between the true or apparent right ascension of the sun and its mean right ascension. It may be popularly defined as the difference between the times indicated by an accurately constructed sun-dial and a well-regulated clock. The equation of time arises from the combined operation of all the causes which tend to produce inequalities of the sun's motion in right ascension. The first of these is the eccentricity of the solar orbit, in consequence of which the sun's motion in longitude is unequal. The second is the obliquity of the ecliptic, in consequence of which the arcs of the ecliptic and equator, counting from the intersection of these circles to the meridian, are in general unequal. The third cause of the equation of time arises from the perturbations of the moon and planets, which sensibly affect the sun's motion in longitude. The different parts of the equation of time are collected and computed in the following manner: — Let N P represent the ecliptic, N Q the equator; and let N be the intersection of these circles, or the first point of Aries. Take N A to represent the p mean motion of the sun in any given time T, reckoning from the vernal equinox; then, if the sun advanced equably in the ecliptic, his place at the time T would be at the point A. But suppose that in consequence of the eccentricity of the orbit he would have advanced to B; then A B is what is called the equation of the centre. Suppose, further, that by the combined action of the planets during the time T he is carried forward to C; then the true arc of the ecliptic described by the sun is N C. Now, if we put; = N C, the sun's true longitude, 7W = N A, the sun's mean longitude, e = A B, the equation of the centre, /> = B C, the effect o^the perturbations, there will result the equation i = w + c + p. Through C let the arc C D be drawn perpendicular to the equator; the point D will be that point of the equator which pa es the meridian at the same time with the sun. If we now make >-=N C— N D; then r is the reductimi to the ecliptic, and the sun's true right ascension is/— r = ND. Let N F = N A = w^; then F is the point of the equator which the sun would occupy at the instant he occupies the point A in the ecliptic if he moved uniformly in the equator, and N F is the sun's mean right ascension. The me as sun would consequently pa the meridian with the point F, whereas the true sun pa es it with the point D; therefore at the instant of true noon, when the points C and D are on the meridian, the mean sun is at the distance D F from the meridian. But DF = ND — NF = Z — »- —?w = e + ju — r, which is the equation of time expre ed in an arc of a circle. To convert it into mean solar time, we must multiply by 24 hours (corresponding to 360 degrees); therefore, representing the equation of time by t, we have t^^{e-\-p-r). This equation still requires to be corrected for the effect of nutation. The variation of the mean longitude resulting from the nutation is expre ed by the formula 18" sin. (360°— moon's node) =18" sin. N; and this reduced to the equator is 18" sin. N cos.4» (a being the obliquity of the ecliptic). Consequently the effect on the equation of time, being the difference of the variations on the ecliptic and equator, becomes 18" sin. N (1 —cos. a). But 18" (I— COS. m) being reduced to time, becomes 0 09925 seconds; therefore, including the correction for nutation, the equation of time becomes finally <= ^ (e + p - r) + sin. N y. 009925 sec. The last term of this expre ion is very small, amounting when greatest to le than the tenth of a second, and is therefore scarcely sensible. The part depending on the perturbations is also very small, and can scarcely exceed two seconds. The principal parts, therefore, are the two depending upon the eccentricity and obliquity; and these were known in the time of Ptolemy. The equation of time is at its maximum about the beginning of November, when it amounts to about 16 m in. 16 sec.; and is subtractive, that is to say, the clock is faster than the dial by that quantity. At four times in the year the equation vanishes, or the clock time and dial time agree. This happens about the 25th of December, the 16th of April, the 16th of June, and the 1st of September. But these epochs, depending on the longitude of the sun's perigee, are subject to some variation. The equation is given in the Nautical Ahnanac for every day of each year. [s. 423]