I had scarcely taken up the chalk, when M. Legendre, returning to the first subject of his preoccupations, said to me:  “You were born in one of the departments recently united to France?” “No, sir; I was born in the department of the Eastern Pyrenees, at the foot of the Pyrenees.”  “Oh! why did you not tell me that at once? all is now explained.  You are of Spanish origin, are you not?” “Possibly; but in my humble family there are no authentic documents preserved which could enable me to trace back the civil position of my ancestors; each one there is the child of his own deeds.  I declare to you again that I am French, and that ought to be sufficient for you.”

The vivacity of this last answer had not disposed M. Legendre in my favour.  I saw this very soon; for, having put a question to me which required the use of double integrals, he stopped me, saying:  “The method which you are following was not given to you by the professor.  Whence did you get it?” “From one of your papers.”  “Why did you choose it? was it to bribe me?” “No; nothing was farther from my thoughts.  I only adopted it because it appeared to me preferable.”  “If you are unable to explain to me the reasons for your preference, I declare to you that you shall receive a bad mark, at least as to character.”

I then entered upon the details which established, as I thought, that the method of double integrals was in all points more clear and more rational than that which Lacroix had expounded to us in the amphitheatre.  From this moment Legendre appeared to me to be satisfied, and to relent.

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.