gerund or verbal noun

OK.  I see your point.  There are some examples of the ...-ing of ... among B&S's 'verbal nouns' as well.

In the drawings example, there is obviously another 'verbier' meaning of drawing, which would be the gerund. 

The drawings in this book are more beautiful than the drawings in the other book. [B&S's verbal nouns; inert pictures on paper; not actions.]
The drawing of the man was very difficult since the man would not sit still. Or Drawing the man was ... [B&S's gerund; the action of making the picture was difficult.] [Rare usage of drawing; used only for purposes of illustration.]

Nevertheless in the barking of the dog, barking is an action.  It's 'verby' in nature.  It is the action of making those noises, an action peculiar to dogs, so I still believe that B&S would call it a gerund.  I have no idea what a purely 'nouny' barking could be.  There is no such established noun barking in English (in the way that drawing is established as a noun).  Still, this could be another example that's somewhere near the fuzzy dividing line I described earlier in the thread.

CJ

«The drawing of the man was very difficult since the man would not sit still. [B&S's gerund; the action of making the picture was difficult.»

I accept you explanation, but there's a more formal and less fuzzy criteria: the meaning of "of". Again, here "drawing" subdues "man".

«Nevertheless in the barking of the dog, barking is an action. It's 'verby' in nature.»

Hmmm. From your viewpoint it is a gerund. But there's no subordination according to the B&S's criteria...

To help you understand me from _your_ viewpoint, I repeat this seemingly "verby" example from the book:

"the well-being of her subjects". It is listed as a verbal noun. I thinks, that's due to the lack of subordination, though you may argue there is some subordination here, and the discussion will condescend to a lower level — to prying into the nature of subordination...

IMHO, "well-being" doesn't govern "her", but belongs to it. So does the "barking" belong to the dog. Yes, it is "verby", but either there's no subordination or it has changed it's direction — the noun subdues the V-ing word (whatever it is...).

EDIT:
«I wasn't aware of any discussions like that between you and Bokeh, no!»

Wow, I really was sure... We used the same word "fuzzy" in the same sence and with similar examples...

Just for fun:
http://www.englishforums.com/English/MoreMostCorrect/vpzzz/Post.htm

«I think I have the advantage of being a native speaker!»

Indeed. If you say a phrase is wrong then it's wrong and vice versa. And thanks for sharing your knowledge!

«Maybe you feel a difference on the basis of whether the completing phrase is a subject or an object of the -ing word.»

Exactly. I even wanted to post some explanations that night:

«The drawing of the man was very difficult since the man would not sit still» — here "drawing" is a gerund because one can say (hope I am right about it): «Drawing the man was very difficult...»

However, you can't transform "the rustling of the leaves" in a similar way, which makes "rustling" a verbal noun.

Same goes to your "ambigous" examples:

1. The cooking of the meat took a long time. //gerund
("cooking" governs "meat" because it takes _someone_ a long time to cook it.)

2. The cooking of the meat was a real pain. //gerund
(same, because I _hope_ it can be transformed to "Cooking the meat")

3. The cooking of the meat can be accelerated by preliminary pickling in our secret marinade. //verbal noun
("cooking" belongs to "meat", the meat cooks faster, cannot be said as "cooking the meat")

So I think this is ambiguity comes from lack of context. But once the context is given, it becomes clear whether it is a gerund or a verbal noun.

«In any case, that is not the criteria that I would apply to decide whether an -ing word is a B&S verbal noun or a B&S gerund.»

So why not? I think it's the very criteria that B&S used.

«Besides that, I think it would be more useful to stick to the modern terminology. Huddleston (Introduction to the Grammar of English) gives several gradations of gerunds, from the 'verbiest' to the 'nouniest'...»

I'll look into that book if I find it and study some another modern grammar's approach to it otherwise.

And thank you very much for the discussion. It has helped me to improve my understanding of the gerund!

EDIT:

Forgot about "the shaking of Earth"

"The shaking of Earth was Gods' amusement" — tranforms into "Gods' enjoyed shaking the Earth" // gerund
"The shaking of the Earth causes great deservations in dense towns." — can't tranform. //not gerund

«...well-being sounds like a noun to me, because I hear it so often as a noun, so I would never call it a gerund.
I've never heard barking as a noun, so I call it a gerund. Here I'm going by linguistic intuition alone, of course -- nothing scholarly or rigorous.»

I have nothing against it. But maybe this verb-ness perceived by your intuition doesn't make any difference on the grammar level, while B&S's subordination criteria (or what I think it is) does declare a grammar difference between the gerund and verbal noun, as I have shown.

Not that I want to say your intution has betrayed you, it just doesn't reflect the grammar differece and hence doesn't agree with B&S (be they right or wrong).

Hope, you don't take the above as critics and don't cease to appeal to intuition in our future conversations!

I found it very interesting that you feel "well-being" is more like a noun because it's having originated from "to be" forces me to think of it as as verby as a V-ing can be... Hmmmmmmmm.

Check this out.
A friend of mine was accused (of what?) ^{of stealing food}. So stealing functions as a present participle in adverbial clause here.
A friend of mine was accused (of what?) ^{of being arrogant}- Same for  this one.

Stealing is a crime- Here, stealing is  noun/ gerund