tables of the equation of the centre, and the reduction to the ecliptic, 

 of all the small planets then discovered. In 1804 he undertook the 

 sole charge of calculating the EfFemeridi Astronomiche, pronounced 

 by Lindenau and Bohnenberger, in 181 6, to be the best ephemeris in 

 existence at that time. From 1802 to 1807 he took a share in the 

 geodesic operations required for the construction of a map of Lom- 

 bardy. These were carried on from 1 788 to 1807 by the astronomers 

 of the Brera, and afterwards by the French engineers. 



A careful examination of the solar tables of Delambre, made in 

 order to ascertain their fitness for use in calculating the Eifemeridi, 

 having revealed some serious errors, Carlini was induced to under- 

 take a revision of them. Retaining the constants which Delambre 

 had deduced from the observations of Bradley and Maskelyne, he 

 recalculated the tables by a method of his own. In 1832 he pub- 

 lished a new edition of the tables, based upon newer and more accu- 

 rate elements. These tables were used till very recently for the 

 calculation of the sun's place in the most celebrated Ephemerides. 



Laplace, dissatisfied with the semiempirical basis on which the 

 lunar theory rested, even after the publication of the ' Mecanique 

 Celeste,' suggested to the Institute, as the subject of the prize for 

 1820, the formation of lunar tables, by theory alone, as exact as 

 those which up to that time had been constructed by theory and 

 observation combined. As far back as in 1813 Plana and Carlini 

 had resolved to construct a complete theory of the moon, subjecting 

 all the inequalities to the laws of geometry, and had made consider- 

 able progress in their task, when the announcement of the programme 

 of the Institute induced them to compete for the prize by sending in 

 the results they had already obtained. By the decision of a com- 

 mission, consisting of Laplace, Burkhardt, and Poisson, the prize 

 was divided between Plana and Carlini, and Damoiseau. The prin- 

 ciple on which their joint memoir rested, and which rendered it 

 superior to all researches of earlier and many of later date, was this : 

 never to take from observation any constants that were not indis- 

 pensably necessary for the solution of the problem. They adhered 

 most rigorously to this condition, without which the analytical 

 solution cannot be perfect. In the development of the various 

 expressions in series, they retained the literal notation, giving an 

 algebraical, not a numerical solution. This memoir was not published 



