for which X vs. for the X of which

Question

In each quotation beneath, what happens if I replace with for which determination? Does anything change?

In Current Sailing a resultant has to be found for two simultaneous courses and distances. Oblique Sailing is a term applied to those cases for the determination of which an oblique triangle has to be solved. The above is the accurate use of the term "Plane Sailing", but it is sometimes loosely used as a synonym for the equally ill-used term "Navigation", as contrasted with "Nautical Astronomy".

Glossary of Navigation: A Vade Mecum for Practical Navigators by J. B. Harbord. p 305.

The Supreme Court, reversing the Circuit Court, held 1 that the act was valid and enforceable. The irrigation of really arid lands is a public use, and the question whether any particular land will be benefited is one of fact, for the determination of which the act made suffcient provision.

A Treatise on the Power of Taxation, State and Federal, in the United States by Frederick Newton Judson. p 447.

If Mill were taken literally the whole definition would end up as a mere tautology. For in order to discover how often a certain sum of money changes hands in effecting the sale and purchase of a given quantity of goods, it is neces- sary to know the average price of the goods in question, which is precisely the quantity for the determination of which the (amount and) velocity of circulation of money are to be utilised. In other words, velocity of circulation as defined by Mill could not be regarded as an independent factor in the determination of average price.

Interest and Prices by Knut Wicksell. p 51.

Answer 1

The key difference between the two phrases is the usage of "which."

"For the determination of which" refers to the method (determination) of calculating (determining) X, where X is described after the phrase. There is an emphasis on calculating X, because "which" refers to the X described later in the sentence. In your example:

In Current Sailing a resultant has to be found for two simultaneous courses and distances. Oblique Sailing is a term applied to those cases for the determination of which an oblique triangle has to be solved.

It refers to how to solve an oblique triangle.

"For which determination" instead refers to the selection of which method to choose. The emphasis is on "which determination," because "which" now refers to the "determination" instead of X. This implies that there are multiple different methods (determinations), in a similar style to the example "Which pen are you using?". In the previous example but changed to include this phrase:

In Current Sailing a resultant has to be found for two simultaneous courses and distances. Oblique Sailing is a term applied to those cases for which determination an oblique triangle has to be solved.

It now refers to the choice of the method (determination) with which to solve an oblique triangle, instead of simply solving the oblique triangle. The definition of Oblique sailing in this example is hence different to the original example. The meaning of the phrase will change similarly in your other two examples.

Answer 2

Some of the OP’s examples are drawn from legal writing.

There is plenty of bad legal writing in the world, just as there is bad architecture or bad anything else.

Sometimes, however, a “point” in a contract has to be forced into a single sentence, and this often leads to a lot of qualifications being added as subordinate clauses.

There is a difference in meaning between the OP’s two formulations. Others have pointed this out. However, as the reference below points out, a lack of “precision” in an agreement can open the door to a dispute as to what the contract actually means, which is an obvious defense for someone who has breached the agreement but wishes to deflect the plaintiff and generally delay judgement.

https://www.reedsmith.com/files/uploads/miscellany/A_Guide_to_Contract_Interpretation__July_2014_.pdf

Answer 3

This is legal phraseology, which means it's consciously antique and intended to both confuse and impress its auditor, like all ritual language. However, it's so opaque that no one would ever speak this way unless they were reading aloud.

These three sentences are examples of restrictive relative clauses with pied-piping.
The critical parts are the antecedent noun and its coreferential relative pronoun, both boldfaced:

• those cases for the determination of which
• fact, for the determination of which
• the quantity for the determination of which

In other words, which refers to cases, fact, and quantity, respectively. Each of these things have to be determined, and the methods of determination have to be specified. This construction is one way to handle linking the methods with the things to be determined.

Normally a relative pronoun like which comes right after the noun it refers to (the antecedent noun, from Latin 'going before'). But here the lawyers want a complex clause to specify those methods, and not to explain again that it's for determining stuff. So they pied-pipe the prepositional phrase for the determination and its modifying preposition of, along with the relative pronoun as its object.

You can do that in English, with a preposition that would otherwise be stranded

• the book which he was the editor of (stranded preposition of)
• the book of which he was the editor (pied-piped preposition of)

And you can do it with much heftier constituents, too, like noun phrases

• the books, the lettering on the covers of which is gilded

As for replacing it with for which determination, that would be perfectly grammatical, and should mean the same. But ritual languages like The Law have their own preferred structures and phrases, and their own construals of them. So I'd consult a lawyer before using it in any important document.