Galileo challenged the foundations of the physics and cosmology taught by the Aristotelian professors and literature of his epoch. He developed a new science of nature in mechanics, with his experiments and mathematical laws of natural free fall, and in cosmography and astronomy, with his use of new methods of parallax, his revolutionary telescopic discoveries, and applications of ideas of relativity of motions. The most important collection of Galileoâ€™s original scientific papers is housed at the Biblioteca Nazionale Centrale of Florence. These autograph manuscripts - his correspondence and books and other papers are bound in many volumes in the extensive Manoscritti Galileiani (Ms. Gal.). This immense collection embraces the works of an epoch in Italian natural philosophy and physics. It also includes original papers of other important authors. The volume Ms. Gal. 72 contains a collection of notes on motion and mechanics by Galileo that is particularly important for the history of mechanics. The majority of the notes are from 1633 and after, while Galileo was under house arrest, but it also contains papers and fragments written as early as 1600-1605. In fact none of these folios were dated by Galileo. Yet some of the passages are very intriguing and it would be very useful to fix their dates of composition.
The general goal is to explore the use of evidence like ink (and paper) as a tool for determining association and orders of the compositions. Specifically, we have been able to determine that physical clues about the ink could be used to solve various grouping problems which are now familiar to specialists in Galileoâ€™s numerous non-dated notes and essays on scientific subjects.
Based on a non-destructive examination, using the so-called PIXE method, of many ink locations on papers in Ms. Gal. 14, 86 (both dated correspondence), 26 (dated financial records), and 72, data are obtained. In a simplified description one obtains for each observed ink location the relative masses XFe, XCu, and XZn in the ink, of iron (Fe), Copper (Cu), and Zinc (Zn), respectively. In particular XFe + XCu + XZn = 1. The three dimensional Dirichlet distribution with unknown shape parameters (λFe, λCu, λZn) є R3+ is used to describe the distribution of (XFe ,XCu ,XZn). Since this statistical model is a full regular exponential family, the theory for such statistical models can be used in the statistical analysis. The likelihood equation in (λFe, λCu, λZn) contains the digamma function. The asymptotic results for exponential families reduce the statistical analysis to one way analysis of variance with known covariance matrix. We shall present some of these results in further details.