x PREFACE. 
struction? Lie’s analytic method started from the finite form 
of a linear transformation, descended into the infinitesimal re- 
gions where the important analytic work was done, then 
reascended into the regions of the finite where the results 
were exhibited. 
H. B. NEWSON. 
NOTE. 
The above incomplete draft of the preface probably in- 
cludes nearly all, except acknowledgments, that the author 
intended to say. Otherwise the manuscript of this volume 
was complete and the proof had been read and corrected 
through to page 272, when his sudden death on the night of 
February 17, 1910, put an end to his labors. Others, have 
read the remainder of the proof. Doubtless, errors have 
crept in which the author would have corrected if he had 
lived to read the proof himself. It is to be regretted that a 
series of unfortunate circumstances hasso long delayed the 
publication of this work. 
Thanks are due to Dr. Paul Wernicke for assistance ren- 
dered the author both with the manuscript and with the 
proof-reading, also for reading a considerable portion of the 
remaining proof. I also wish to express my thanks to Dr. 
U. G. Mitchell for valuable assistance, without which the 
completion of the publication might not have been possible. 
M. W. NEWSON. 
