e found in the _Transactions of the Royal Society of Edinburgh_ and
of the _Royal Irish Academy_, in the _Bulletin de l'Academie de
St-Petersbourg_ for 1862 (under the name G. Boldt, vol. iv. pp.
198-215), and in _Crelle's Journal_. To these lists should be added a
paper on the mathematical basis of logic, published in the _Mechanic's
Magazine_ for 1848. The works of Boole are thus contained in about fifty
scattered articles and a few separate publications.

Only two systematic treatises on mathematical subjects were completed by
Boole during his lifetime. The well-known _Treatise on Differential
Equations_ appeared in 1859, and was followed, the next year, by a
_Treatise on the Calculus of Finite Differences_, designed to serve as a
sequel to the former work. These treatises are valuable contributions to
the important branches of mathematics in question, and Boole, in
composing them, seems to have combined elementary exposition with the
profound investigation of the philosophy of the subject in a manner
hardly admitting of improvement. To a certain extent these works embody
the more important discoveries of their author. In the 16th and 17th
chapters of the _Differential Equations_ we find, for instance, a lucid
account of the general symbolic method, the bold and skilful employment
of which led to Boole's chief discoveries, and of a general method in
analysis, originally described in his famous memoir printed in the
_Philosophical Transactions_ for 1844. Boole was one of the most eminent
of those who perceived that the symbols of operation could be separated
from those of quantity and treated as distinct objects of calculation.
His principal characteristic was perfect confidence in any result
obtained by the treatment of symbols in accordance with their primary
laws and conditions, and an almost unrivalled skill and power in tracing
out these results.

During the last few years of his life Boole was constantly engaged in
extending his researches with the object of producing a second edition
of his _Differential Equations_ much more complete than the first
edition; and part of his last vacation was spent in the libraries of the
Royal Society and the British Museum. But this new edition was never
completed. Even the manuscripts left at his death were so incomplete
that Todhunter, into whose hands they were put, found it impossible to
use them in the publication of a second edition of the original
treatise, and wisely p