PREFACE 



To make the study of theoretical physics something besides a 

 purely formal mathematical exercise, it is necessary to keep 

 physical things always clearly and vividly in mind. It is com- 

 paratively easy to do this in the study of applied science, but it 

 is extremely difficult to do it in the study of many of the un- 

 familiar topics which are discussed in this book. The character 

 of the treatment in this book has been determined throughout by 

 the desire to keep the student's mind jammed up tight against 

 physical things! The chapter on potential, for example, is 

 kept within severely concrete limits, and the student who 

 wishes to get an insight into the elementary mathematical 

 theory of potential should read chapter IX of Franklin, Mac- 

 Nutt and Charles' Calculus, published by the authors, South 

 Bethlehem, Pa., 1913. 



The authors desire to express their appreciation of the 

 great assistance which Professor R. L. Charles has rendered 

 in the preparation of this book. 

 JANUARY 16, 1915. 



W. S. FRANKLIN 

 BARRY MACNUTT. 



