87 
considered as Functions of their Amplitude.” Jour. Pc. Polytech., 
xiv., 1834, and Jour, de Math., v., 1840. 
“On the Integration of a Class of Transcendent Functions.” 
Jour, de Math., xiii., 1835. 
“On a Flew Use of Elliptic Functions in Celestial Mechanics.” 
Jour, de Math., i., 1836. 
“ On the Classification of Transcendents, and on the Impossibility 
of Expressing the Eoots of certain Equations as a Finite Function 
of their Coefficients.” Jour, de Math., ii., 1837. 
“ On a very Extensive Class of Quantities whose value is neither 
Algebraic nor reducible to Algebraic Irrationals.” Jour, de Math., 
xvi., 1851. 
Relating to the theory of differential equations, we have the 
following : — - 
“On the Equation of Riccati.” Jour, de VPc. Polytech ,, xiv., 
1833. 
“ On a Question in the Calculus of Partial Differences.” Jour, 
de Math., i., 1836. 
“On the Development of Functions or Parts of Functions in 
Series, whose various terms satisfy the same Differential Equation 
of the Second Order containing a Variable Parameter.” Three 
Memoirs. Jour, de Math., i. and ii., 1836-37. 
“ On the Integration of the Equation ^ .” Jour, de VPc. 
CLC CvJu 
Polytech., xv., 1837. 
“ On the Theory of Linear Differential Equations, and on the 
Development of Functions in Series.” Jour, de Math., iii., 1838. 
“ On the Integration of a Class of Differential Equations of the 
Second Order explicitly Infinite Terms.” Jour, de Math., iv., 
1839. 
Some of Liouville’s most important work was in the department 
of applied mathematics. When, in 1834, Jacobi enunciated his 
theorem that an ellipsoid with three unequal axes is a possible 
figure of equilibrium for a mass of rotating fluid, and challenged the 
French mathematicians to give a proof, Liouville at once published 
one in the Journal de VPcole Polytechnique, xiv., 1834. He after- 
wards returned to the problem, and, in continuation of the work of 
Meyer on the same subject, showed that Jacobi’s form is not possible 
