Transcriber's Note:
Every effort has been made to replicate this text as faithfully aspossible. Some changes have been made. They are listed at the end ofthe text.
DISSERTATION
SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF
PHILOSOPHY IN THE FACULTY OF PURE
SCIENCE OF COLUMBIA UNIVERSITY
BY
YÜ-GWAN CHEN, M. A.
NEW YORK CITY
1922
The following research was undertaken at the suggestion ofProfessor Marston Taylor Bogert to whose interest and advicethis work owes whatever merit it may possess.
Y. G. CHEN.