Is “down” not meaning “below” (e.g. “down the line”) formally acceptable?

Question

One of my biggest issues when learning the language was when I heard people saying "down there" or "down the line" when referring to a counter or a line in a bank, respectively, for example.

That just didn't make sense to me. Translating the words, it never would, but in informal language, this is one of the most common expressions used in the English language.

Is that usage of the word down formally correct?

Answer 1

Formally, yes - it is correct. Down can be used as a preposition, such that:

• Down can be used to indicate movement from a higher to a lower position

They went down the mountain

• Or at a lower or further level or position on, in, or along:

He ran down the street

She is down the other end of the line.

Down is defined as a preposition in a number of dictionaries, see here and here.

Answer 2

If by “formally correct” you mean “acceptable in formal discourse” — Yes, it’s an ordinary metaphorical extension of down employed as a preposition, and according to the Oxford English Dictionary it’s been perfectly acceptable for over a century and a quarter.

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FOR ADVANCED STUDENTS:
Down derives from an Old English expression meaning “from the hill” and had as its initial sense, according to the OED (the emphases are mine):

 I. Of motion or direction in space.  1.  In a descending direction ; from above, or towards that which is below ; from a higher to a lower place or position ; to the ground.  It is applied to any degree of descent, from a vertical slope to the slightest slope as in a nearly level river valley, and thus passes into sense 2, in which the descent may be entirely imaginary or conventional.
…
 2.  To some place which is conventionally viewed as lower in position ; in the direction of a current, or with the wind ; from the capital to the distant parts of a country ; away from a university ; from the House of Lords to the House of Commons or ‘lower house’ ; to a lower or inferior court of law, etc.

That sense 2 is already documented in 1200. And it’s just the second of 22 senses the original OED (1897) distinguished in the bare adverb, before it got to fixed phrases and to prepositional uses. (There are more senses in the Supplements, and I’d be willing to bet still more in the current online version.)

One of the prepositional definitions and an accompanying citation are relevant here:

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 2.  Often with no implication of actual descent : To (or at) what is regarded as the lowest part of ; along the course or extent of. … … 1878 Mod. Traffic passing up and down the line.

You must not ask English prepositions and adverbs of position or direction to behave strictly literally or logically—they have far too much work to do.

Answer 3

A straightforward way to consider the usage of down you referenced is by considering a log book. Each event that happens is recorded on the next line, creating a linear relationship through time. So down is essentially a term used to refer to an item or event that is farther down some linear progression.

For example:

"Down there" could be interpreted as, "continue moving down the list of counters until you get to that one."

"Down the line" could be restated as, "continue moving from person to person in the line until you get to that one."