library, all the books on any given subject bear the number of that
subject in the scheme. Where a 0 occurs in a class number, it has its
normal zero power. Thus, a book numbered 510, is Class 5, Division 1,
but _no_ Section. This signifies that the book treats of the Division 51
(Mathematics) in general, and is not limited to any one Section, as is
the Geometry, marked 513. If marked 500, it would indicate a treatise on
Science in general, limited to _no_ Division. A zero occurring in the
first place would in the same way show that the book is limited to
_no_ Class. The classification is mainly made by subjects or content
regardless of _form_; but it is found practically useful to make an
additional distinction in these general treatises, according to the form
of treatment adopted. Thus, in Science we have a large number of books
treating of Science in general, and so having a 0 for the Division
number. These books are then divided into Sections, as are those of the
other Classes according to the form they have taken on. We have the
Philosophy and History of Science, Scientific Compends, Dictionaries,
Essays, Periodicals, Societies, Education, and Travels,--all having the
common subject, =NATURAL SCIENCE=, but treating it in these varied forms.
These form distinctions are introduced here because the number of general
works is large, and the numerals allow of this division, without extra
labor for the numbers from 501 to 509 would otherwise be unused. They
apply _only_ to the general treatises, which, without them, would have a
class number ending with two zeros. A Dictionary of Mathematics is 510,
not 503, for every book is assigned to the _most specific head that will
contain it_, so that 503 is limited to Dictionaries or Cyclopedias of
Science _in general_. In the same way a General Cyclopedia or Periodical
treats of no one class, and so is assigned to the Class 0. These books
treating of no special class, but general in their character, are divided
into Cyclopedias, Periodicals, etc. No difficulty is found in following
the arithmetical law and omitting the initial zero, so these numbers are