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lectures given at the Sorbonne by E. Picard. 
Mathematics is not only for the young and 
those who make a living therefrom, but its 
study leads to an intellectual penetration with 
unlimited room for growth. Our interest in 
this subject naturally grows with our knowl- 
edge thereof and the former is apt to grow 
much more rapidly than the latter. 
In view of these facts it seems to me that 
all the larger city libraries should contain a 
considerable collection of modern mathemat- 
ical works, including current parts of the best 
modern mathematical reference work, viz., 
“Eneyclopédie des Sciences Mathématiques,” 
so that new parts of this important work may 
become available soon after their publication. 
High school teachers of mathematics can 
render great assistance in this direction by 
familiarizing themselves with suitable mathe- 
matical collections and the needs-of their local 
libraries, and suggesting improvements to the 
proper authorities. 
Above all let us try to instil in our students 
a desire for more mathematical knowledge, 
and encourage them to utilize the facilities of 
local libraries along mathematical lines. Our 
large general dictionaries and encyciopedias 
contain much that can be used to advantage 
during mathematical recitation periods. It is 
searcely necessary to say that such outside 
contact should not take the place of penetra- 
tion into the subject in hand, but this penetra- 
tion is more likely to become attractive if 
broad contact is kept in mind. 
It should be noted that many of our best 
general works of reference are weak along 
mathematical lines. As an illustration we 
may note an entirely senseless definition of 
regular group appearing under the word group 
in the 1917 edition of the “New Standard 
Dictionary.” This definition is as follows: 
“a transitive group whose order is the same 
as that of the letter on which it is made.” 
Such weaknesses are, however, not always 
harmful to the young student since they may 
serve to promote the important attitude of 
mind of not accepting statements without 
study and verification. As another instance 
SCIENCE 
[N. S. Vou. XLVIII. No. 1249 
of an unreasonable statement which appeared 
on the first page of a recent publication of the 
Department of Commerce, U. S. Coast and 
Geodetic Survey, No. 92, 1918, we cite the 
following: “It was his regular custom to 
spend 17 hours per day in study and writing.” 
An almost equivalent statement appears under 
the name of J. H. Lambert in the ninth 
edition of the “ Encyclopedia Britannica,” but 
fortunately it is not found in the later edition. 
As mathematics teachers, and perhaps as 
teachers in general, our attitude towards sal- 
aries is often inconsistent. In choosing this 
profession we practically say that we are more 
interested in intellectual matters than in the 
making of money. On the other hand, many 
of our members sacrifice intellectual opportu- 
nities for a little increase in salary. Positions 
which offer a reasonable income together with 
sufficient time and proper facilities for study 
should not be abandoned in favor of those 
offering poorer facilities for intellectual growth 
but a little more salary. School officials 
should be impressed by the fact that their 
teachers appreciate advantages for develop- 
ment and that the best teachers can be secured 
and held only by furnishing advantages for 
their development, especially in the form of 
good library facilities. 
The great war for justice and democracy 
should tend to dignify our high calling since 
it directs so forcibly attention to the facts that 
it is sometimes necessary to make great sacri- 
fices for the opportunities for higher develop- 
ment and the rights of nations and of indi- 
viduals do not depend upon their sizes. We 
as teachers should be especially impressed by 
the fact that curtailments of rights must be 
based on other considerations. With the im- 
provement in world ideals as a result of this 
war there should come a keener appreciation 
of thorough preparation for the various duties 
of life. The appointment of an athlete to a 
chemical position in Washington for which he 
was wholly unprepared should be regarded as 
close to treason even if it may have been due 
to the ignorance of politicians. Thorough 
preparation for our various duties should be 
