What analogies does T. H. Huxley use in his essay "The Method of Scientific Investigation"? How and why does he use those analogies?

T. H. Huxley was an ardent supporter of Charles Darwin and a prominent proponent of scientific thinking among the people of England. Huxley sets out in his essay to show the average person that scientific investigation and reflection are as common among regular people as they are among scientists. Huxley uses an analogy to explain this point, saying,

There is no more difference, but there is just the same kind of difference, between the mental operations of a man of science and those of an ordinary person, as there is between the operations and methods of a baker or of a butcher weighing out his goods in common scales, and the operations of a chemist in performing a difficult and complex analysis by means of his balance and finely graduated weights.

Huxley uses the analogy of the tradesman and the chemist to show that despite doing different types of weighing, the chemist and the butcher think along the same lines. He makes the point that regular modes of thinking and scientific thinking are analogous because they share many of the same elements but differ only in their focus.
A different analogy he uses is to compare the discovery of one of Moliere’s characters to the discovery he expects the reader to make. He says,

There is a well-known incident in one of Moliere's plays, where the author makes the hero express unbounded delight on being told that he had been talking prose during the whole of his life. In the same way, I trust, that you will take comfort, and be delighted with yourselves, on the discovery that you have been acting on the principles of inductive and deductive philosophy during the same period.

Huxley points out, to help the audience understand, that the revelation that one speaks in prose is similar to the discovery that every reader of his essay should make about themselves—that they use inductive and deductive reasoning in their regular lives. The design of this second analogy is similar to the first, to help the audience understand that scientific thinking and processes are not foreign to them. The use of these two analogies illustrates for the audience how clearly, the scientific method is accessible to them—and that they can use it to navigate the questions that face them in everyday life.