10 AUTOBIOGRAPHY OF FRANCIS ARAGO. 
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 sat- 
isfied, 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 con- 
stant, 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 ex- 
aminer. 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 gaye them, it is said, 
