Birmingham.
[The above matter is made the more puzzling to all who are not
astronomers, by the pertinacity with which popular writers persist
in speaking of the moon's motions as if they were regular.
There is no particular beginning to the cycle of nineteen years:
anybody may make it begin when he pleases. What it means is this:
that in any set of nineteen years, the new and full moons
generally (not always) fall on the same days as in the preceding
nineteen years. For instance, in 1831, the 14th of March was a day
of new moon: go on nineteen years, that is, to the 14th of March,
1850; most probably, not certainly, this must be a day of new
moon. It happens, however, otherwise; for in 1850 the new moon is
on the 13th. But in the Aprils of both years, the new moons are on
the 12th; in the Junes, on the 10th. All that can be said is, that
where any day of any year is new moon, most probably _that day
nineteen years_ is new moon also, and certainly either the day
before or the day after. In that cycle of nineteen years, which is
called the cycle of the _golden number_, there is an arbitrary
beginning, which has something to do with the new moon falling
_near_ the 1st of January. The cycle in which we now are, began
(that is, had the year marked 1) in 1843.
To find the last time when the new moon fell on the 1st of January
with certainty, would be no easy problem for any but an
astronomer. The nearest which our correspondent can do is this.
Take Mr. De Morgan's recently published _Book of Almanacs_, and
turn to almanac 37. Take the day in question (Jan. 1), and from
the first of the Roman numbers written opposite (xxx.) subtract
one (xxix.). Look back into the new style index (p. 7.), then any
one year which has the epact 29 is very likely to have the new
moon on the 1st of January; epact 30 may also have it. Now, on
looking, we find that we are not in that period of the world's
existence at which epact 29 makes its appearance; no such thing
has occurred since 1699, nor will occur until 1900. We are then in
a period in which new moons on the 1st of January are
comparatively infrequent. Our best chance is when the epact is 30,
as in 1843: here there is a narrow miss of what we want, for it
was new moon on the day previous, as late as seven in the evening.
Our correspondent's notion that the moon's cycle begins with a new
moon on the 1st of January, is probably derived from this, that
the calendar is so contrived that for a very long period the years
which have 1 for their golden number, have a new moon _near_ the
1st of January, either on it, or within a day of it.]
_Cocker's Arithmetic._--At a sale of books by Messrs. Puttick and
Simpson, a copy of Cocker's _Arithmetic_ was sold for 8_l._ 10_s._, date
1678, said to be one of the only two extant. It is stated Dr. Dibdin had
never seen any edition printed in the seventeenth century, and mentions
the thirty-second as the earliest he had met with. I have in my
possession a copy bearing date 1694, seeming to be one of a further
impression of the first edition, as it gives no edition, but simply has
in the title page:
"This impression is corrected and amended with many additions
throughout the whole."
"London: Printed by J. R. for T. P., and are to be sold by John
Back, at the Black Boy on London Bridge, 1694."
Perhaps you can give me some information on the edition, if you think it
a fit subject for your valuable publication.