What kind of structure with a relative pronoun is this?

As Lord Esher once noted, ‘Any proposition the result of which would be to show that the common law of England is wholly unreasonable and unjust cannot be part of the common law of England.’

Would someone please help unravel the bolded relative clause, step-by-step? Please explain your steps. I've never seen this construct before.

Does the bolded clause = 'whose result'?

Moreover, is it equivalent to 'the result of any proposition which would be to show ...' ?

Source: P101, How the Law Works, Gary Slapper

Solution 1:

The technical term for this construction is Pied-Piping.
  (I don't make up these names, honest; this one, like many others, is due to Haj Ross)
Here's how it works:

Relative clauses modify nouns; these nouns are called antecedents (because they "go before").
Every relative clause contains an anaphor of its antecedent, which becomes a relative pronoun,
and, under certain circumstances, may simply be deleted.

• [the man [the man came to dinner]] --> [the man [who/that came to dinner]]
• [the man [I saw the man]] --> [the man [who/that I saw]] --> [the man [I saw]]

In the first example above, the relative pronoun is the subject and must not be deleted.
In the second example, the relative pronoun is the direct object and may be deleted.
That accounts for the majority of relative clauses.

However, subject and object do not exhaust the roles or positions of nouns.
Other roles are called Oblique, as a class, and include objects of prepositions, of all sorts.
In the following examples, I'll leave out the who/that version, which is always possible,

• [the man [I looked at the man]] --> [the man [who/that I looked at]]

because oblique relative pronouns are always deletable.
(Note that these all end up stranding a preposition at the end, just like the one above does):

• [the man [I looked at the man]] --> [the man [I looked at]]
• [the man [I talked to the man]] --> [the man [I talked to]]
• [the man [I came with the man]] --> [the man [I came with]]
• [the room [I live in the room]] --> [the room [I live in]]

In effect, moving or deleting the relative pronoun breaks up the prepositional phrase.
However, prepositional phrases are constituents, and may optionally be moved as one unit:

• [the man [I looked [at the man]]] --> [the man [[at whom] I looked]]
• [the room [I live [in the room]]] --> [the room [[in which] I live]]

This process, of moving the whole prepositional phrase instead of only its object,
is what Pied-Piping means. The preposition gets piped away to the front, marking its object.

Moreover, prepositional phrases can modify nouns that are objects of other prepositional phrases, and they, too, are constituents, and can be moved as a unit. So are, and so can, the noun phrases. Again, only optionally. Which leads to such mind-numbing spectra of nonrestrictive relatives as:

• The government prescribes the height of the lettering on the covers of the reports.
• the reports, which the government prescribes the height of the lettering on the covers of
• the reports, of which the government prescribes the height of the lettering on the covers
• the reports, the covers of which the government prescribes the height of the lettering on
• the reports, on the covers of which the government prescribes the height of the lettering
• the reports, the lettering on the covers of which the government prescribes the height of
• the reports, of the lettering on the covers of which the government prescribes the height
• the reports, the height of the lettering on the covers of which the government prescribes

This kind of syntax seems especially common in pedantic, bureaucratic, or legal contexts.
Opinions vary as to the grammaticality of various portions of the spectrum; pied-piping seems to be a syntactic habit one picks up, if at all, later in one's education, and individually. I.e, YMMV.

Solution 2:

Did anyone answer the last question: "Moreover, is it equivalent to 'the result of any proposition which would be to show ...' ?" Assuming "it" refers to the quote:

‘Any proposition the result of which would be to show that the common law of England is wholly unreasonable and unjust cannot be part of the common law of England.’

then, no, I don't see a way of filling in the dots to make "the result ..." equivalent. Instead, the original quote is equivalent to:

If any proposition has the result that the common law of England is wholly unreasonable and unjust, then that proposition cannot be part of the common law of England.

Part of the derivation of the original is to convert the antecedent of the if-then construction to a relative clause, which is then attached to the subject of the consequent of the if-then clause.

It's all a fancified way of saying that, in law, the common law is assumed to be consistent with itself.