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NOTICES AND ABSTRACTS 
: MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 
MATHEMATICS AND PHYSICS. 
Address by Professor Tynpatt, LL.D., F.R.S., §c., President of the Section. 
THE celebrated Fichte, in his lectures on the “ Vocation of the Scholar,” insisted 
on a culture for the scholar which should not be one-sided, but all-sided. His 
intellectual nature was to expand spherically and not in a single direction. In 
one direction, however, Fichte required that the scholar should apply himself 
directly to nature, become a creator of knowledge, and thus repay by original 
labours of his own the immense debt he owed to the labours of others. It was 
these which enabled him to supplement the knowledge derived from his own re- 
searches, so as to render his culture rounded and not one-sided. 
Fichte’s idea is to some extent illustrated by the constitution and the labours 
of the British Association. We have here a body of men engaged in the pursuit 
of Natural Knowledge, but variously engaged. While sympathizing with each of 
its departments, and supplementing his culture by knowledge drawn from all of 
_ them, each student amongst us selects one subject for the exercise of his own 
original faculty—one line along which he may carry the light of his private intel- 
ligence a little way into the darkness by which all knowledge is surrounded. 
‘Thus, the geologist faces the rocks; the biologist fronts the conditions and pheno- 
mena of life; the astronomer stellar masses and motions; the mathematician the 
properties of space and number; the chemist pursues his atoms, while the physi- 
cal investigator has his own large field in optical, thermal, electrical, acoustical, 
and other phenomena. The British Association, then, faces nature on all sides 
and pushes knowledge centrifugally outwards, while through circumstance or 
natural bent each of its working members takes up a certain line of research in 
which he aspires to be an original producer, being content in all other directions 
to accept instruction from his fellow men. The sum of our labours constitutes 
what Fichte might call the sphere of natural knowledge. In the meetings of the 
Association it is found necessary to resolve this sphere into its component parts, 
which take concrete form under the respective letters of our Sections. 
This Section (A) is called the Mathematical and Physical Section. Mathematics 
and physics have been long accustomed to coalesce, and hence this grouping. For 
while mathematics, as a product of the human mind, is self-sustaining and _nobl 
self-rewarding, while the pure mathematician may never trouble his mind wit 
considerations regarding the phenomena of the material universe, still the form 
of reasoning which he employs, the power which the organization of that reason- 
ing confers, the applicability of his abstract conceptions to actual phenomena, 
render his science one of the most potent instruments in the solution of natural . 
1868, 
