These names are usually formed according to some kind of system. Especially in chemistry "new" compounds are often named like that. Even a common word like alcohol gives rise to -ol compounds (like methanol) to indicate to a scientist that the two have certain chemical properties.
The compounds they name may or may not be in common use as nouns, and as such have lost their "name"-feeling.
If you want to capitalize arginine, you should, by rights, also capitalize alcohol, methanol and polypropylene. These are "names" given to substances, but they do not function like proper names.
In extremis, if you want to capitalize them, you should capitalize Water as well. It is, after all, the "proper name" given to dihydrogenoxide.
Of course, when a compound is given a trade mark name, it does get capitalized, even if the name seems to be systematically derived. However, if the name becomes very commonly used, it is possible that the trade mark name loses its "proper name" feel again, and we stop capitalizing it again.
Examples of that are Aspirin and Heroin (trademarks of Bayer), which are now written as aspirin and heroin.
Something similar happened with nylon and rayon (trademark of duPont) - their Teflon seems to be going the same way.
Do we always write 'W' capital in Western society, Western countries, Western culture, Western ethnicity?
Choose a particular style guide and stick with what it says. But be consistent throughout one paper or article or post or blog. But style guides and usage changes over time.
The Chicago Manual of Style prefers the "down style" (8.1, 16th edition) that is, to keep capital letters to a minimum.
It goes on to say:
8.46 Regions of the world and national regions
Terms that denote regions of the world or of a particular country are often capitalized, as are a few of the adjectives and nouns derived from such terms. The following examples illustrate not only the principles sketched in 8.1 but also variations based on context and usage. For terms not included here or for which no suitable analogy can be made, consult Webster’s or an encyclopedia: if an otherwise generic term is not listed there (either capitalized or, for dictionary entries, with the indication capitalized next to the applicable subentry), opt for lowercase. Note that exceptions based on specific regional, political, or historical contexts are inevitable and that an author’s strong preference should usually be respected. [16th edition, emphasis mine]
As you have experienced, consulting "Webster's" (or other dictionaries) and reference works sometimes clouds the issue. So I think you are justified to use whichever, Western or western. Just be consistent and be ready to back up your choice, if asked.
The Chicago Manual of Style gives these specific examples:
the West, western, a westerner (of a country); the West Coast; the West, Western (referring to the culture of the Occident, or Europe and the Western Hemisphere); west, western, westward, to the west (directions) [16th edition, emphasis mine]
And the APA has an article that is "an example of the use of bias-free language in scientific writing."
In it, one finds 'modernism' defined as "Westernized changes involving the adoption of new lifeways that include innovative and culturally different beliefs and behaviors" [my emphasis].
So, 'Western' appears to be in vogue for geographic and, I would add, Socio-Cultural-Politcal(?) entites as in 'the West,' 'Western powers', 'Western decadence'.
I guess the BBC prefers an even greater 'down style" when it says "western countries."
Perhaps this is in contrast to 'Western countries', which refers to countries included in 'the West,' the Socio-Cultural-Politcal(?) Entity that includes Japan.
Also, is it incorrect to write both the first letter capitals? 'Western Countries' in the middle of the sentence?
If you have a phrase that needs both words capitilized (i.e., a proper noun), then do so: 'Western Hemisphere', 'West Coast.'
Best Answer
You are right: Meadow Hall is the proper name of a house or mansion described in the book, and that is why the words are capitalized.
Note also that there is no article before "Meadow Hall": we don't usually use articles with proper nouns. We do have the definite article the before "scullery window", which somewhat attests to the fact that these words are common nouns (with "scullery" used in an adjective role).
In The Lord of the Rings, Bilbo Baggins's house is called Bag End, for instance: the name is also capitalized, and again there's no article before it.
Per PerryW's comment - there are exceptions to this pattern of "no article before the name of a building". The definite article is normally used before the names of pubs and bars: The Royal Oak, The Dover Castle, The Woolshed, etc.
According to BBC ("The" with place names: rules and exceptions),