The principles set forth in this book, the queries answered, I have so often talked over with the assistants who, at Harvard and Wellesley, have aided me in my work, that I feel the results here given are as much theirs as mine. I owe so much in the past, also, to their enthu siasm and their intelligent devotion to their work, that I cannot refrain from recognizing my indebtedness. For valuable suggestions while this book has been going through the press and for reading of the proofs I wish in particular to thank assistant-professor S. C. Hart of Wellesley College, and Mr. F. G. Caffey, of Montgomery, Alabama. For the classification of definitions used on pp. 54 — 59 I am indebted to Professor Genung in his Practical Elm/tents of R/zetorz'c.