PREFACE xi 



Special acknowledgment is hereby made to the following 

 for reading the specified portions of the manuscript and sug- 

 gesting valuable improvements: To Dr. P. L. DeLargy for 

 examining Chapter V; to Professor Frank C. Hoyt for 

 reading Chapter XV; to Professor Carl Eckart for many 

 suggestions relevant to Chapters XIV and XVI; and to 

 Professor Raymond W. Rarnard for information pertaining 

 to the definition of "number' in Chapter XIII. None of 

 these men, however, is to be considered as in any way sub- 

 scribing to the ideas presented in the portion of the manu- 

 script which he examined. I wish also to express thanks to 

 Mr. Richard Schlegel who helped in the routine work con- 

 nected with the manuscript and prepared the index. 



A. C. R. 



Chicago, Illinois 

 July, 1937 



