The grammar book says:
1) "The" is used as an adverb in such sentences; as,
- The more the merrier.
- The fewer the better.
I tried google bt it is not helping me. so I came here.
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SUPPLEMENTAL to rogermue's ANSWER
Pay no attention to the adverb designation. This is a 'fixed' comparative usage, whose origin rogermue describes. Dictionaries have to call it something, and "adverb" is the wastebasket term where uses that don't fit into any other category get put.
"the + comparative" is not the normal article (nominative/accusative), but an old fifth case form of "that" which was comparable to the Latin ablative.
Here was the underlying idea: in that measure something is better, in that same measure something is more expensive. That was parallel to the way how in Latin the idea of proportionality was expressed.
This old case form changed its shape and got the same form as the normal article. Dictionaries label this form of the article as adverb which is somehow justified, but one should know the story behind "the + comparative". And perhaps it would be better to label "the" as particle or function word.
AHD, American Heritage Dictionary:
[Middle English, from Old English thy:, the:, instrumental of thæt, neuter demonstrative pron (: means long vowel)
See AHD, the no.2, adverb https://www.ahdictionary.com/word/search.html?q=the&submit.x=52&submit.y=37
Over the last 30-40 years, linguistic terminology has changed. If a word expressed manner or degree, it used to be considered "adverbial". The term adverb is slowly being supplanted by new terms: adposition, preposition, postposition, interposition, and circumposition.
This form, the X the Y, means "Y is in proportion to X". The proportion can be direct or inverse.
The slower you walk, the longer it will take to get there.
The faster you paint, the more likely you are to make a mess.
The more, the merrier!
(The more people at the party, or in the party, the more fun it will be.)
I don't think those are very good examples, since technically they're not complete sentences, but more of phrases or "sayings". This would be the expanded version of the saying:
The more (something, typically people there are) the merrier (it will be).
Neither "more" nor "merrier" are verbs here, the subjects and verbs are actually missing from the original phrase (I've included them in parenthesis). "The" is not functioning as an adverb in this phrase or sentence.
I've done some basic searching myself and I cannot think of an example where "the" would function as an adverb.
The fox frantically sprints across the meadow.
Frantically is the adverb here, and replacing it with "the" would obviously make no sense. The whole premise of an adverb is that you're trying to be more descriptive about the action, the verb itself. Even if you were able to find a way to tack on an article like "the" to a verb, I don't know why you would do this, as it wouldn't add anything.
According to M-W:
1: than before : than otherwise —used before a comparative [none the wiser for attending]
2a : to what extent [the sooner the better]
2b : to that extent [the sooner the better]
3: beyond all others
According to Dictionary.com:
- (used to modify an adjective or adverb in the comparative degree and to signify “in or by that,” “on that account,” “in or by so much,” or “in some or any degree”): He's been on vacation and looks the better for it.
- (used in correlative constructions to modify an adjective or adverb in the comparative degree, in one instance with relative force and in the other with demonstrative force, and signifying “by how much … by so much” or “in what degree … in that degree”): the more the merrier; The bigger they are, the harder they fall.