journal; he gives frequent notes upon the best modes of teaching
the elementary branches, and proposes to publish in a serial form
treatises adapted to use in the school-room. Every number of the
"Monthly" contains five prize problems for students. Nor are its pages
confined to topics strictly mathematical. The number for February
introduces a problem by a quotation from Longfellow's "Hiawatha";
another gives a list of fifty-five of the Asteroid group, with their
orbits, and the circumstances of their discovery. The March number
explains an ingenious holocryptic cipher, written with the English
alphabet, with no more letters than would be required for ordinary
writing, yet so curiously complicated, that, while with the key easy to
understand, it is without the key absolutely undecipherible, even to the
inventor of the plan; and the key is capable of so many variations, that
every pair of correspondents in Christendom may have their own cipher
practically different from all others. In the November and December
numbers, a popular account of Donati's Comet was given by Geo. P. Bond,
then assistant, now chief director of the Observatory at Cambridge. This
paper has been issued separately, very finely illustrated by twenty-one
cuts, and by two beautiful engravings. No papers, readily accessible to
the public, contain, in a form so entirely devoid of technicalities, and
so clearly illustrated to the eye, so much information relative to the
nature of cornels in general, and in particular to the phenomena of this
most beautiful comet of the present century.

The purely mathematical articles are all original, many are of great
value, and some are, to those who understand their secret meaning,
peculiarly interesting. A note of Peirce's, for example, in the number
for February, proposes two new symbols, one for the mystic ratio of
the circumference to the diameter, a second for the base of Napier's
logarithms,--and then, by joining them in an equation with the imaginary
symbol, expresses in a single sentence the mutual relation of the three
great talismans in the magic of modern science. Another article, in the
April number, by Chauncey Wright, contains a new view of the law of
Phyllotaxis, approaching it from an _a priori_ stand-point, and showing
that the natural arrangement of leaves about the stems of plants is
precisely that which will keep the leaves most perfectly distributed for
the reception of light and air.

We are gla