said to me, “I could, from this moment, consider the examination at an end.  I will, however, for my own pleasure, ask you two more questions.  What are the relations of a curved line to the straight line that is a tangent to it?” I looked upon this question as a particular case of the theory of osculations which I had studied in Legrange’s “Fonctions Analytiques.”  “Finally,” said the examiner to me, “how do you determine the tension of the various cords of which a funicular machine is composed?” I treated this problem according to the method expounded in the “Mecanique Analytique.”  It was clear that Lagrange had supplied all the resources of my examination.

I had been two hours and a quarter at the board.  M. Monge, going from one extreme to the other, got up, came and embraced me, and solemnly declared that I should occupy the first place on his list.  Shall I confess it?  During the examination of my comrade I had heard the Toulousian candidates uttering not very favourable sarcasms on the pupils from Perpignan; and it was principally for the sake of reparation to my native town that M. Monge’s behaviour and declaration transported me with joy.

Having entered the Polytechnic School, at the end of 1803, I was placed in the excessively boisterous brigade of the Gascons and Britons.  I should have much liked to study thoroughly physics and chemistry, of which I did not even know the first rudiments; but the behaviour of my companions rarely left me any time for it.  As for analysis, I had already, before entering the Polytechnic School, learnt much more than was required for leaving it.

I have just related the strange words which M. Monge, junior, addressed to me at Toulouse in commencing my examination for admission.  Something analogous occurred at the opening of my examination in mathematics for passing from one division of the school to another.  The examiner, this time, was the illustrious geometer Legendre, of whom, a few years after, I had the honour of becoming the colleague and the friend.

I entered his study at the moment when M. T——­, who was to undergo his examination before me, having fainted away, was being carried out in the arms of two servants.  I thought that this circumstance would have moved and softened M. Legendre; but it had no such effect “What is your name,” he said to me sharply.  “Arago,” I answered.  “You are not French then?” “If I was not French I should not be before you; for I have never heard of any one being admitted into the school unless his nationality had been proved.”  “I maintain that he is not French whose name is Arago.”  “I maintain, on my side, that I am French, and a very good Frenchman too, however strange my name may appear to you.”  “Very well; we will not discuss the point farther; go to the board.”