etique suivant laquelle Newton a presente ses
decouvertes, j'ai reconnu l'indispensable necessite de l'analyse pour
approfondir les questions tres difficiles que Newton n'a pu qu'effleurer
par la synthese. Je vois avec un grand plaisir vos mathematiciens se
livrer maintenant a l'analyse et je ne doute point qu'en suivant cette
methode avec la sagacite propre a votre nation ils ne seront conduits a
d'importantes decouvertes."

Newton himself was aware that by the law of gravitation the stability of
the solar system was endangered. The power of analysis alone enabled La
Grange to prove that all the disturbances arising from the reciprocal
attraction of the planets and satellites are periodical, whatever the
length of the periods may be, so that the stability of the solar system
is insured for unlimited ages. The perturbations are only the
oscillations of that immense pendulum of Eternity which beats centuries
as ours beats seconds.

La Place, and all the great mathematicians of that period, had scarcely
passed away when the more powerful Quaternion system began to dawn.

FOOTNOTES:

[Footnote 10: Professor Sedgwick died shortly after my mother.]

CHAPTER XII.

PARIS--ARAGO, LAFAYETTE, MM. BOUVARD, POISSON, LACROIX, &c., MARQUISE DE
LA PLACE, DUPIN, F. COOPER--LEGITIMISTE SOCIETY--MAJENDIE--VISIT BARON
LOUIS--LETTER FROM LAFAYETTE.

My health was never good at Chelsea, and as I had been working too hard,
I became so ill, that change of air and scene were thought absolutely
necessary for me. We went accordingly to Paris; partly, because it was
near home, as Somerville could not remain long with us at a time, and,
partly, because we thought it a good opportunity to give masters to the
girls, which we could not afford to do in London. When we arrived, I was
so weak, that I always remained in bed writing till one o'clock, and
then, either went to sit in the Tuileries gardens, or else received
visits. All my old friends came to see me, Arago, the first. He was more
engaged in politics than science, and as party spirit ran very high at
that time, he said he would send tickets of admission to the Chambers
every time there was likely to be an "orage." When I told him what I was
writing, he gave me some interesting memoirs, and lent me a mass of
manuscripts, with leave to make extracts, which were very useful to me.
General de La Fayette came to town on purpose to invite Somerville and
me to visit him at La Grange,