are left unchanged. Diacritical marks are omitted, however, since the
proper key could hardly be furnished in a work of this kind.

With the above exceptions, this study will, it is hoped, be found to be
quite complete; and as the subject here investigated has never before been
treated in any thorough and comprehensive manner, it is hoped that this
book may be found helpful. The collections of numeral systems illustrating
the use of the binary, the quinary, and other number systems, are, taken
together, believed to be the most extensive now existing in any language.
Only the cardinal numerals have been considered. The ordinals present no
marked peculiarities which would, in a work of this kind, render a separate
discussion necessary. Accordingly they have, though with some reluctance,
been omitted entirely.

Sincere thanks are due to those who have assisted the author in the
preparation of his materials. Especial acknowledgment should be made to
Horatio Hale, Dr. D.G. Brinton, Frank Hamilton Cushing, and Dr. A.F.
Chamberlain.

WORCESTER, MASS., Nov. 12, 1895.





CONTENTS.


Chapter I.
Counting 1