This book is the result of almost daily discussion for some years with classes of the ideas contained in it, but in that discussion there was a chance to treat with each individual the many exceptions, apparent or real, which he could raise to any principle enunciated. Such full discussion is impossible in a book the size of this one. Therefore I must seem to favor an instruction far more dogmatic than my pupils know from me. No textbook can do away with the value of proper classroom work. The practice of the past provides satisfactory principles for students of ordinary endowment. A person of long experience or unusually endowed, however, after grasping these principles, must at times break from them if he is to do his best work. The classroom permits a teacher such adaptations of existing usage. Such special needs no textbook can forestall. This book, then, is meant, not to replace wise classroom instruction, but to supplement it or to offer what it can when such instruction is impossible.