HONORED SIR:  You had the kindness to ask me for my views as to the choice of the moment for the beginning of the day.  As I cannot remain longer in Washington, I allow myself thus briefly to write to you.

When, as in the present case, the object is to introduce uniformity in the time-reckoning of the astronomical and the civil world, I am of the opinion that it is the astronomer only that must give way.  For all purposes of civil life one cannot begin the day in the middle of the day-light—­that is to say, in the middle of that interval during which work is prosecuted.  In general it appears to me natural that the middle of the day, and not the beginning of the day, should be indicated by the highest position of the sun which governs all civil life.  In fact, it would in civil life be simply impossible to bring about a change of date in the middle of the daylight.  For the astronomer there certainly exist difficulties.  His activity occurs mostly in the civil night, and he, therefore, has to make the change of date in the midst of his observations; and this difficulty is increased, since he almost exclusively observes according to sidereal time, so that often a computation must be made in order to ascertain whether the observations were made before or after the midnight or moment of change of date.  However, this difficulty can be overcome by habit, and I believe that scarcely any doubt will occur as soon as a uniformnity of expression has established itself through the astronomical world.  As regards the ephemerides, we already employ, in fact, the beginning of the date at midnight, since the places of planets and comets, are generally computed for 12 o’clock midnight of Berlin or Greenwich or other places.  But these are points that have themselves long since been discussed.

I scarcely need to say anything further.  I would not hesitate for a moment to give the preference to making the change of date take place at midnight, according to civil reckoning, in order to establish a uniformity with the customs of civil life.

It, perhaps, may be important to remark that we could not introduce this change immediately, since the ephemerides are already computed and published for three or four years in advance.  It would, therefore, be well to fix the epoch of change of normal dates to some distant time, such as 1890.

     I remain, very respectfully yours,

W. VALENTINER.

I may also mention that the practice that prevails among astronomers at the present time of reckoning the day from noon is by no means without exceptions.  There are very important astronomical tables which reckon the day from midnight; for instance, in Delambre’s Tables of the Sun; in Burg’s, Burckhardt’s and Damoiseau’s Tables of the Moon; in Bouvard’s Tables of Jupiter, Saturn, and Uranus, and in Damoiseau’s Tables of Jupiter’s Satellites, mean midnight is employed as the epoch of the tables.  I may also mention that Laplace, in his Mecanique Celeste, adopts the mean midnight of Paris as the origin from which his day is reckoned.  Hence there are great authorities, even among astronomers, in favor of commencing the day at midnight.