Despite the retroactive acclaim given to Galileo's theory of knowledge, the empirical claims he made in the book—that comets are sublunary and their observed properties the product of optical phenomena—were incorrect.

[1] In 1619, Galileo became embroiled in a controversy with Father Orazio Grassi, professor of mathematics at the Jesuit Collegio Romano.

The debate between Galileo and Grassi started in early 1619, when Father Grassi anonymously published the pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618 (Disputatio astronomica de tribus cometis anni MDCXVIII),[2] which discussed the nature of a comet that had appeared late in November of the previous year.

[6] Galileo and Guiducci offered no definitive theory of their own on the nature of comets,[7][8] although they did present some tentative conjectures that are now known to be mistaken.

In its opening passage, Galileo and Guiducci's Discourse gratuitously insulted the Jesuit Christoph Scheiner,[9][10][11] and various uncomplimentary remarks about the professors of the Collegio Romano were scattered throughout the work.

[9] The Jesuits were offended,[8][9] and Grassi soon replied with a polemical tract of his own, The Astronomical and Philosophical Balance (Libra astronomica ac philosophica),[12] under the pseudonym Lothario Sarsio Sigensano, purporting to be one of his own pupils.

The title page also shows that Urban VIII employed a member of the Lynx, Cesarini, at a high level in the papal service.

In The Assayer Galileo mainly criticized Grassi's method of inquiry, heavily biased by his religious belief and based on ipse dixit, rather than his hypothesis on comets.

It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.Galileo used a sarcastic and witty tone throughout the essay.

He wrote that heat, pressure, smell and other phenomena perceived by our senses are apparent properties only, caused by the movement of particles, which is a real phenomenon.

[26][27] Galileo also theorized that senses such as smell and taste are made possible by the release of tiny particles from their host substances, which was correct but not proven until later.[28]...

[29]Those minute particles ... may enter by our nostrils and strike upon some small protuberances which are the instrument of smelling; here likewise their touch ... is received to our like or dislike according as they have this or that shape, are fast or slow, and are numerous or few.