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 printed 31, 32, etc., instead of 031, 032, etc.

The selection and arrangement of the thousand headings of the classification cannot be explained in detail for want of space.  In all the work, philosophical theory and accuracy have been made to yield to practical usefulness.  The impossibility of making a satisfactory classification of all knowledge as preserved in books, has been appreciated from the first, and nothing of the kind attempted.  Theoretical harmony and exactness has been repeatedly sacrificed to the practical requirements of the library or to the convenience of the department in the college.  As in every scheme, many minor subjects have been put under general heads to which they do not strictly belong.  In some cases these headings have been printed in a distinctive type, e. g., 429 =Anglo-Saxon=, under =English philology=.  The rule has been to assign these subjects to the most nearly allied heads, or where it was thought they would be most useful.  The only alternative was to omit them altogether.  If any such omission occurs, it is unintentional and will be supplied as soon as discovered.  Wherever practicable the heads have been so arranged that each subject is preceded and followed by the most nearly allied subjects and thus the greatest convenience is secured both in the catalogues and on the shelves.  Theoretically, the division of every subject into just nine heads is absurd.  Practically, it is desirable that the classification be as minute as possible without the use of additional figures, and the decimal principle on which our scheme hinges allows nine divisions as readily as a less number.  This principle has proved wholly satisfactory in practice though it appears to destroy proper co-ordination in some places.