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public duty, and served bis alloted time with efficiency if without 
special distinction. When, however, his mandate expired, instead 
of seeking re-election, he betook himself once more to the uninter- 
rupted pursuit of the career for which his abilities best fitted him. 
Liouville was as fortunate in his private life as he was successful 
in his public career. He lived to a good old age in the happiest 
domestic circumstances, until a cruel accident deprived him of his 
wife. His son, a councillor in the Court of Haney, died soon after- 
wards, and the aged mathematician never completely recovered from 
the effects of this double bereavement. Although his health gave 
way, his intellect remained unclouded ; and it was only in the 
beginning of 1882 that he gave up his favourite work of lecturing 
at the College de France. He still continued, however, to attend 
the meetings of the Academy, but expressed to his friends his con- 
sciousness that the end was near. He died on the 8th September 
1882, as he himself said, “in his turn”; for, since the death of 
Chasles, he had been the patriarch among European mathema- 
ticians. 
Some idea of the extent of Liouville’s mathematical writings may 
be obtained by consulting The Catalogue of Scientific Memoirs 
published by the Poyal Society of London. The entries under 
Liouville’s name number 379, and cover some twelve pages. Many 
of these are merely remarks made on contributions to his journal, 
or notes appended to works by other mathematicians wdiich he 
edited; yet, brief as they are, they frequently contain matter of 
much importance. As specimens of this part of his work, we may 
mention his “ Hotes on Two Letters of Mr Thomson relative to the 
Employment of a Hew System of Orthogonal Coordinates in certain 
Problems in the Theories of Heat and Electricity, and in the 
Problem of the Distribution of Electricity on the Segment of a 
Spherical Shell of Infinite Thinness” {Jour. cl. Math., xii. 1847), 
in which he draws attention to the analytical and geometrical im- 
portance of the method of Inversion, which had just been brought 
under the notice of mathematicians by the brilliant use that 
Thomson had made of it in his physical researches. 
In another note {Jour. d. Math., xv. 1850) he enunciates the 
important theorem that the equation 
dx 2 + dy 2 + dz 2 = X(da 2 -!- dj3 2 + dy 2 ) , 
