SYNODIC, SYNODIC REVOLUTION' (o6vobos, conjunction of paths). The synodic revolution of two bodice which move round a common centre is that portion of one or more actual revolutions in which they go through all their possible relative positions. The simplest instance which can be given is that of the two hands of a watch : the absolute revolution of the minute hand is made in one hour, that of the hour hand in twelve hours • but the synodic revolu tion of the two hands is the interval which elapses between any time at which they are together, and the next time at which the same thing takes place.
Every phenomenon which depends upon the relative position of two revolving bodies cannot complete all its phases in less than a synodic revolution. Thus, in the case of the sun and moon, the total dis appearance of the latter which takes place when they are nearest in the heavens, cannot take place again until they are again at their nearest, that is, until the moon has not only completed the circuit of the heavens, but has further progressed until she overtakes the sun. The actual revolution of the moon is not an object of interest, except to those who watch her progress among the fixed stars : the phases which are visible to all the world depend solely on her motion relatively to that of the sun. Those who would make a common watch tell time in a manner resembling the indications of luni-solar phenomena must rub out the marks of minutes and hours from the dial-plate, and choose for an interval of measurement that which elapses between successive con junctions of the minute and hour hands.
If the two revolutions be made in the same direction, and if a` and t be their respective times, T being the greater, the time of the synodic revolution is T t For, if x be the time of a synodic revolution, the portion of an actual revolution which the quicker has gained upon the slower is xx _ _ t but by hypothesis this is a whole revolution, since the synodic period is nothing but the time in which the quicker gains a whole revolution upon the slower. Equate the last formula to unity, and the resulting value of x is the first formula. But if the two revolutions be made in opposite directions, the synodic revolution is made in the time T T T Thus in the ease of the hands of a watch, T t=1"; and 1? of an hour, or lb 5' is the interval of two conjunctions of the two hands.
To find roughly the synodic period of the sun and moon, let us take the sun's actual revolution at 3651 days, and moon's at 271 days. We have then 3651 x 271 days nearly.