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Proceedings of the Royal Society 
left in an unfinished state, hut taken up some twelve years later in the 
first volume of the Memoirs of the National Academy of Sciences. 
Among all of Peirce’s contributions to science, that which he 
himself seemed to value most highly was his Linear Associative 
Algebra, which, however, was only published by lithographing and 
privately distributing a few copies. It essayed a general theory of 
the multiplication of units of different classes, subject to the law of 
association and distribution, but not of commutation. 
In 1867 he was appointed Superintendent of the Coast Survey, 
to succeed Professor Bache ; hut finding administrative duties little 
to his taste, he resigned in 1874. 
During the last few years of his life a tendency towards specula- 
tion, partly of a philosophic and partly of a cosmological character, 
which he had exhibited during most of his life, showed itself yet 
more strongly. He delivered before the Lowell Institute a course 
of lectures on Ideality in Science which have been published in 
book form, and afford an interesting view of the speculative 
operations of his mind. 
The influence exercised by Peirce on the progress of mathematical 
science in his own country, is at least equal in importance with his 
scientific work. He was an ardent and euthusiastic friend, ever 
ready to encourage younger men and promote their work. He had 
an especial fondness for seeking out comparatively unknown men 
whose ability had been overlooked. As a teacher, he was very 
generally considered a failure. The general view he took was that 
it was useless for any one to study mathematics without a special 
aptitude for them ; he therefore gave inapt pupils no encouragement, 
and made no attempt to bring his instruction within their com- 
prehension. His extreme generality and terseness of expression, and 
his fondness for brevity of notation, sometimes made it difficult even 
for an expert to follow him • while a certain imaginative and poetic 
vein, in which his fundamental principles are laid down, was unsuited 
to most minds. The most characteristic as well as the most exten- 
sive of his works is his System of Analytic Mechanics. The exposi- 
tion of dynamical concepts in the first forty pages is pleasant read- 
ing for one already acquainted with the subject, hut that a student 
beginning the subject could understand it without a clearer distinc- 
tion between definitions, axioms, and theorems seems hardly possible. 
