Learn English – Meaning of “the field in which I grow the [expletive]”

The essential part of the question is in the interrogative.

Whence (adverb) : From what source

The author is saying that though he believed he had accomplished all that he could at his current position, he was still routinely plagued by a question regarding the source of life.

Considering he's discussing natural philosophy I would assume he's referring the source of life from abiotic material. In this case I would consider "principle" to not mean belief, but rather the foundation of something. The question, in my mind, is something like:

What is the foundational source of life?

Unfortunately, the word is used in a number of ways in the era in question. As a noun, it refers to decorative detail work (1). As a verb, it might be slang for drinking (2), clapping silently with the fingertips (3, 4), or weakly shaking hands (5).

The "drinking" usage is tenuous: the phrase to tip the little finger was apparently Australian slang for to drink, while the usage here is by a British author and the word "little" is not mentioned.

The decorative detail work option is a possibility, especially if the man is elsewhere said to have an interest in decorating ornaments.

Of the remaining two verb options, the first would not be a literal usage unless the man is a poet or music teacher. The second, however, indicates weakness and effeminacy.

These last three usages all have similar connotations that might be captured by ideas like "effeminacy" and "not wanting to get his hands dirty." Based on this, I'd interpret the passage to be communicating that the man is a dandy, one who is seen as relatively effeminate and weak.