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. E. K. JUTT. Frome, Somerset.