Should I use a comma before a reduced and defining relative clause in this sentence?

Question

A simple linear relationship between force and displacement known as Hooke's Law was discovered in the 1600s.

I wrote this sentence and intended to use a reduced and defining relative clause, "known as Hooke's Law".

Its long form is:

A simple linear relationship between force and displacement that is known as Hooke's Law was discovered in the 1600s.

Basically, "known as Hooke's Law" defines the whole noun phrase "A simple linear relationship between force and displacement".

The question is whether or not I should use a comma before "known", although it is a defining relative clause.

Which one do you think is correct?

A simple linear relationship between force and displacement known as Hooke's Law was discovered in the 1600s.

A simple linear relationship between force and displacement, known as Hooke's Law, was discovered in the 1600s.

I think the first one (without commas) is correct as it is a defining relative clause.

Thank you.

Answer 1

Either is acceptable; you could consider "known as Hooke's Law" to be either a parenthetical comment or a defining clause from which you omitted "that is" for brevity.

When encountering a sentence like this, an editor would consider the context, flow, and possibility of ambiguity. For example, by omitting the commas, is it possible that the reader links "displacement known as Hooke's Law" rather than "relationship...known as Hooke's Law"? In this case, such confusion would be very unlikely; it's obvious to even a beginner physics student that the law refers to the relationship.

How about flow? For example, does omitting the commas produce a long, rambling sentence without helpful signposts, or does adding them produce a choppy, halting sentence? Neither seems the case here. The version with commas reads slightly better to me, and it's how I'd write the sentence, but I'd defer to the author who omitted them.

Answer 2

I would treat "known as Hooke's law" as a parenthetical phrase. It gives additional information about the relationship, specifically its usual name. Thus I would strongly favor using a comma both before and after this phrase, resulting in the sentence:

A simple linear relationship between force and displacement, known as Hooke's Law, was discovered in the 1600s.

Note that the phrase can be omitted and the sentence is both grammatical and factually correct:

A simple linear relationship between force and displacement was discovered in the 1600s.

If the sentence came to me as an editor with either nor both commas omitted, I would pretty much automatically insert them.