# Specifying notation with introductory clauses

When writing technical papers I often write sentences like:

Where m denotes the proper mass of an object and c denotes the speed of light, the object's rest energy is given by E=mc2.

However I recently received a referee report claiming that this is poor and possibly incorrect usage. This surprised me, but it seems to be true that clauses starting with "where" that specify the meaning of notation more commonly appear at the end of a sentence rather than the start.

Is the usage above in fact incorrect? If I wish to retain the basic structure of (introductory clause specifying notation's meaning) followed by (statement in which the notation is used), is there a better way of formulating the introductory clause?

• I think if you insist on defining your variables before citing the equation, it would be more natural to introduce the definitions with If rather than Where. But the fact of the matter is almost all writers put the ...where m = [blah] and c = [blah] clause after the equation, so by deliberately flouting this convention you're effectively making your text unavoidably "awkward" for the average reader. Why not just use English the way everyone else does? – FumbleFingers Sep 12 '15 at 15:10
• You're using an English sentence to express a mathematical relation. This is not always a good idea. While mathematics is a variety of language, it is often not best expressed in syntax, but in tabular or equational form. You've used the equation, but you've turned it into a noun phrase, and the rest of the sentence is just a list of equivalences. This is not exciting prose, to say the least. So why not just use a bulleted equation with a parenthesized list of parameters underneath it; go ahead and use where in that list -- it's traditional. – John Lawler Sep 12 '15 at 15:43
• "Given that m denotes the proper mass..." – Hot Licks Jan 11 '16 at 0:37
• The way you have it sounds fine -- that referee is full of it. But if you want it to be less wordy, try "With/Using m for the proper mass, ...". – Greg Lee Jan 11 '16 at 1:09

Technically, there is nothing wrong with what you wrote.

But as @Barmar indicates, when terms are introduced before their use, a common convention is to use let, not where. And when terms are defined after their use, where, not let is called for.

This question is not so much about whether your phrase is correct English but whether it is as understandable in the context of technical writing. It is less understandable, primarily because of convention.

It can also be the case that defining terms before their use, in a single sentence, can be confusing when there are many terms. It is easy to lose track of things in such a sentence. When there are multiple terms to define, or some of the terms require complex descriptions, the let is often set off in its own (imperative) sentence preceding the text that makes use of the terms that the let introduces.

Mathematicians, and presumably also scientists describing things mathematically, usually use let in a preceding sentence to introduce names.

Let m be the proper mass of an object and c be the speed of light. Then the object's rest energy E is given by the equation E=mc2.

I suppose you could also do this in a single sentence, separating the clauses with a semicolon.