EDITORS’ PREFACE. 
The volume called Higher Mathematics, the third edition 
of which was published in 1900, contained eleven chapters by- 
eleven authors, each chapter being independent of the others, 
but all supposing the reader to have at least a mathematical 
training equivalent to that given in classical and engineering 
colleges. The publication of that volume was discontinued in 
1906, and the chapters have since been issued in separate 
Monographs, they being generally enlarged by additional 
articles or appendices which either amplify the former pres 
entation or record recent advances. This plan of publication 
was arranged in order to meet the demand of teachers and 
the convenience of classes, and it was also thought that it 
would prove advantageous to readers in special lines of mathe 
matical literature. 
It is the intention of the publishers and editors to add other 
monographs to the series from time to time, if the demand' 
seems to warrant it. Among the topics which are under con 
sideration are those of elliptic functions, the theory of quantics, 
the group theory, the calculus of variations, and non-Euclidean 
geometry; possibly also monographs on branches of astronomy, 
mechanics, and mathematical physics may be included. It is 
the hope of the editors that this Series of Monographs may 
tend to promote mathematical study and research over a wider 
field than that which the former volume has occupied.