tence, it imparted to scientific studies quite a new direction which
has been productive of the most important results. In supporting this
opinion at some length, I shall acquit myself of a task which Fourier
would certainly have imposed upon me, if he could have suspected, that
with just and eloquent eulogiums of his character and his labours there
should mingle within the walls of this apartment, and even emanate from
the mouth of one of his successors, sharp critiques of his beloved
Normal School.

It is to the Normal School that we must inevitably ascend if we would
desire to ascertain the earliest public teaching of _descriptive
Geometry_, that fine creation of the genius of Monge. It is from this
source that it has passed almost without modification to the Polytechnic
School, to foundries, to manufactories, and the most humble workshops.

The establishment of the Normal School accordingly indicates the
commencement of a veritable revolution in the study of pure mathematics;
with it demonstrations, methods, and important theories, buried in
academical collections, appeared for the first time before the pupils,
and encouraged them to recast upon new bases the works destined for
instruction.

With some rare exceptions, the philosophers engaged in the cultivation
of science constituted formerly in France a class totally distinct from
that of the professors. By appointing the first geometers, the first
philosophers, and the first naturalists of the world to be professors,
the Convention threw new lustre upon the profession of teaching, the
advantageous influence of which is felt in the present day. In the
opinion of the public at large a title which a Lagrange, a Laplace, a
Monge, a Berthollet, had borne, became a proper match to the finest
titles. If under the empire, the Polytechnic School counted among its
active professors councillors of state, ministers, and the president of
the senate, you must look for the explanation of this fact in the
impulse given by the Normal School.

You see in the ancient great colleges, professors concealed in some
degree behind their portfolios, reading as from a pulpit, amid the
indifference and inattention of their pupils, discourses prepared
beforehand with great labour, and which reappear every year in the same
form. Nothing of this kind existed at the Normal School; oral lessons
alone were there permitted. The authorities even went so far as to
require of the illustrious savan