os, those
between ten and twelve inches as quartos, those from seven to ten inches
as octavos, and all measuring seven inches or under as 12mos. Mr. H. B.
Wheatley, in his work, "How to Catalogue a Library," 1889, proposed to
call all books small octavos which measure below the ordinary octavo
size. As all sizes "run into each other," and the former classification
by the fold of the sheets is quite obsolete, people appear to be left to
their own devices in describing the sizes of books. While the metric
notation would be exact, if the size of every book were expressed in
centimetres, the size-notation in the table given is wholly wanting in
precision, and has no more claim to be adopted than any other arbitrary
plan. Still, it will serve ordinary wants, and the fact that we cannot
reach an exact standard is no reason for refusing to be as nearly exact
as we can.

And while we are upon the subject of notation may be added a brief
explanation of the method adopted in earlier ages, (and especially the
years reckoned from the Christian era) to express numbers by Roman
numerals. The one simple principle was, that each letter placed after a
figure of greater equal value adds to it just the value which itself has;
and, on the other hand, a letter of less value placed before (or on the
left of) a larger figure, diminishes the value of that figure in the same
proportion. For example:

These letters--VI represent six; which is the same as saying V+I. On the
contrary, these same letters reversed represent four; thus--IV: that is
V-I=4. Nine is represented by IX, _i. e._, X-I, ten minus one. On the
same principle, LX represents 60--or L+N: whereas XL means 40--being L-X.
Proceeding on the same basis, we find that LXX=L+XX=70; and LXXX or L+XXX
is 80. But when we come to ninety, instead of adding four X's to the L,
they took a shorter method, and expressed it in two figures instead of
five, thus, XC, _i. e._ 100 or C-X=90.

The remarkable thing about this Roman notation is that only six letters
sufficed to express all numbers up to one thousand, and even beyond, by
skilful and simple combinations: namely the I, the V, the X, the L, the
C, and the M, and by adding or subtracting some of these letters, when
placed before or after another letter, they had a whole succession of
numbers done to their hand--thus:

I, 1 XX, 20 CC, 200
II, 2 XXX, 3