Afterwards, he asked me to determine the centre of gravity of a
spherical sector. "The question is easy," I said to him. "Very well;
since you find it easy, I will complicate it: instead of supposing the
density constant, I will suppose that it varies from the centre to the
surface according to a determined function." I got through this
calculation very happily; and from this moment I had entirely gained the
favour of the examiner. Indeed, on my retiring, he addressed to me these
words, which, coming from him, appeared to my comrades as a very
favourable augury for my chance of promotion: "I see that you have
employed your time well; go on in the same way the second year, and we
shall part very good friends."

In the mode of examination adopted at the Polytechnic School in 1804,
which is always cited as being better than the present organization,
room was allowed for the exercise of some unjustifiable caprices. Would
it be believed, for example, that the old M. Barruel examined two pupils
at a time in physics, and gave them, it is said, the same mark, which
was the mean between the actual merits of the two? For my part, I was
associated with a comrade full of intelligence, but who had not studied
this branch of the course. We agreed that he should leave the answering
to me, and we found the arrangement advantageous to both.

As I have been led to speak of the school as it was in 1804, I will say
that its faults were less those of organization than those of personal
management; for many of the professors were much below their office, a
fact which gave rise to somewhat ridiculous scenes. The pupils, for
instance, having observed the insufficiency of M. Hassenfratz, made a
demonstration of the dimensions of the rainbow, full of errors of
calculation, but in which the one compensated the other so that the