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When I am comparing a numeric value to a numeric limit, as in a maximum value, should I say the value is "below the limit" or "less than the limit"?

Specifically, I am saying, "the maximum concentration limit (MCL) is 5 mg/L," and then "the measured concentration was (below/less than) the MCL," but I am not sure which is correct (below or less than).

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Which one you use depends on the metaphor you're using.

Less than is a measure of quantity, typically volume, which implies a Container metaphor.

Below, on the other hand, implies an Up/Down metaphor.

Saying that something is less than the maximum means there is still room in the metaphoric container for more; i.e, v(t) < Vᵐ.

Saying that something is below the maximum means that some effort is still needed to metaphorically move it up to the maximum, against gravity; i.e, f = mG.

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The sentence is stating compliance, as if to say, "as long as we do not exceed this value, no further discussion is needed." – Melody Cornelius Dec 11 '12 at 16:12
Yeah, that seems to be the pragmatic reason for it. – John Lawler Dec 11 '12 at 16:21

Given those two choices, I'd use below, probably reasoning intuitively along the lines John Lawler mentioned in his answer. However, if other choices are allowed, I'd instead say

The measured concentration did not exceed the MCL.

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Agreed. Though that's not metaphoric and also more formal. Which may be bonus points. – John Lawler Dec 4 '12 at 14:22

Within limits works well. If you're wedded to your options, it would really depend on the exact turn of phrase you're going to use and intentions. With regard to blood alcohol limit, as an example, the word "below" is frequently used. There's no reason why you couldn't use either proposed word to talk about quantity limits

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below the limit
The preferred term is below the limit.

Google nGrams confirm the instinctive choice of below in the context.

Google nGram *below the limit*, *under the limit*, *less than the limit*

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On a different note, there seems to be another issue with the terminology. Maximum limit is not a preferred term, maximum itself implying upper limit. It's better to say upper limit of concentration or maximum concentration in this context. (The abbreviation 'MCL' will not longer work.) – Kris Dec 4 '12 at 5:21
Oh yes, you're right. MCL stands for Maximum Contaminant Level. On the state level, we call them Protective Concentration Limit. So, if I am reporting conditions that are environmentally compliant, especially concerning contaminants that are not naturally occurring and should not be present, the correct, or at least most popular, phrasing is below. I like that. – Melody Cornelius Dec 11 '12 at 16:08

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