whswhs (whswhs) wrote in linguaphiles,

English grammar: definite article with ordinals

One of my clients for copy editing asked me a question about English grammar: When is the definite article required with ordinals? My first approximation to an answer was that you use it when the ordinal refers to an entity, either concrete or abstract: The last to depart should turn off the lights or I stopped after the fourth martini. If it's being used adverbially it doesn't need and shouldn't have an article: I left last, so I turned off the lights.

But what about this sentence: We approximate the temperature change over the past century to third order/the third order? The word "order" seems to be a noun (if an abstract one) and by the general rule I came up with ought to have a definite article. But it seems to be common for mathematicians just to write "to Nth order" with no article. Is there some grammatical principle that explains this difference of usage? Or is it just an idiomatic usage that doesn't fit the standard pattern and has to be taken as a separate thing? I can't see any rule that obviously fits, and I'm not sure how to search for one.

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