234 Notices respecting New Boohs. 
was allowed for a time to retain this post ; but by a decree of the 
18th December, 1864, he was deprived of his chair, as he refused 
to take the oath to the Government. Prof. Cremona writes ; — " II 
Chelini amava sinceramente la patria italiana ed era assolutamente 
alieno dall' associarsi a qualsiasi atto ostile al governo nazionale : 
dei quali suoi sentimenti gli amici intimi possono fai*e ampia testi- 
monianza II Chelini sopporto la sua disgrazia con ammi- 
rabile serenita d' animo." After a brief sojourn at Lucca, Chelini 
was called in 1867 to take charge of the chair of Rational Mechanics 
in the University of Rome. His occupancy of this post was short, 
as four years later Rome became the capital of Italy. In the spring 
of 1878 a small yearly pension was voted to him ; but he did not 
long enjoy this, as he died in the same year, in the Collegio Naza- 
reno, where he had resided since his return to Rome in ] 865. 
His was an uneventful life in the eyes of politicians and men of 
the world, but one spent in the production of several valuable ma- 
thematical memoirs and in the acquiring, to a remarkable degree, 
the affection of mathematicians of many nationalities. Hirst, 
amongst our own countrymen, was an especial friend, a friendship 
commenced at Bologua in 1864 having been subsequently renewed 
and increased at Eome. 
Chelini's works range over a space of 44 years, and are 53 in 
number. His first paper was " Sulla teoria delle quantita propor- 
tionali " (read in July 1834) ; his last was a memoir " Sopra alcune 
questioni dinamiche" (presented April 1877). Our own knowledge 
of Chelini's works, prior to our study of the volume before us, was 
confined to the two or three passages in which memoirs of his are 
analyzed in Chasles's Rapport sur les progres de la Geometric Ample 
justice is done to Chelini's labours, we believe, in the exhaustive 
Analytical Sketch prefixed to the Collectanea, which has been 
drawn up by Signor Beltrami : to the biography in this sketch, 
founded upon an address by Prof. Cremona, we are indebted for 
the few details we have recorded. 
We now proceed to a brief examination of the memoirs in the 
order in which they are presented to us ; and here we may state, 
once for all, that some of the " stones " are of such a kind (i. e. so 
mathematically technical) that we can only name them, and not 
examine them in any detail. The " tour les Fonctions 6(.r) et H(x) 
de Jacobi," by M. Hermite, is of this character, though the process 
of solution is a very direct one. " L'Iperboloide centrale nella 
rotazione de' Corpi," P. Siacci. The property discovered may be thus 
stated: — "When a body, not acted on by any external forces, turns 
round a fixed point, a certain hyperboloid connected (legato) with 
the body and such that its axes coincide with the principal axes of 
inertia relatively to the fixed point, rolls without sliding on a right 
circular cylinder whose axis passes through the fixed point and is 
parallel to the axis of the impulsive couple (coppia a" impulso)." 
" On a Differential Equation," by A. Cayley : this is an equation 
considered by Kummer in his memoir on Hypergeometric Series. 
