In 1820 Mossotti published two papers, one as an appendix to the ephemerides
for 1821, concerning the shape and time of revolution of the sun
, and one engineering
paper on the movement of a spring. The inspiration of the latter, says Mossotti in the introduction to
his paper, comes from a memoire by Jean and Jacques Bernoulli, Usage et
Théorie d'une Machine qu'on peut nommer Instrument Ballistique. The goal of
Mossotti's paper is to supply to some theoretical imperfections in the
Bernoulli's memoire. His contributions to the problem must have been
significant and very original, as some Italian scientists wrote to Carlini
after reading Mossotti's paper asking for explanations. It
may seem funny that an Astronomer should explain some of his Pupil's work, but
we have to keep in mind that Mossotti was probably regarded as a sort of
Enfant prodige in the Observatoire: some of his works were translated by
famous German astronomers such as Enke; the level of his mathematical ability
was such that he was able to correct some theoretical imperfections in the
work of the Bernoulli brothers; Gauss, who published reviews of the main
astronomical European publications of the time, usually devoted half a page to
the Milan ephemerides compiled by Carlini, but when Mossotti published his
appendices in 1816 and 1817 Gauss' review dedicated one paragraph to the
actual ephemerides and two full pages to the appendices. Mossotti was an
exceptional theoretician for his times, and some of the notation he
established was to be taken as a standard by Italian scientists like Enrico
Betti.
In 1821 he published a paper on the motion of an ellipsoidal aerostatic
balloon, in which he analyses the possibility of success of such a project,
and concludes that the theoretical possibility exists, but the available
construction materials have to be perfected before attempting such a task.
He also published an appendix for that year's ephemerides, called
Opposizione di Giove nell'anno 1820 osservata al quadrante murale.
On 31 August 1822 Mossotti was accepted as a member of the
Società Italiana delle Scienze residente in Modena, also known as
``The Society of 40" from the number of its members, in the Mathematics class,
receiveing 9 votes, the relative majority over 33 voters (the closest
competitor was Frullani, with 8 votes). Among the other members there were
Legendre and Poisson.
Figure 4: Mossotti elected member of the Società dei 40 (M20).
In 1823 three of his letters to the Baron de Zach are published in his
Correspondance, and the paper concerning the motion of water in canals (
Sul moto dell'acqua nei canali) is published in the Memorie della
Società Italiana delle Scienze, Tomo XIX, Parte contenente le memorie di
matematica; fascicolo secondo, pgg. 616-658. This paper begins with an
interesting account of the history of hydraulics from Galileo to Mossotti's
times, and goes on discussing general theory and particular examples.