In the third example, “towards” does not refer to anything which comes after the end of the story. However, in the second example, is it possible that it really stopped raining a while after noon? Does the first example mean “around” the middle of the 19th century?
In all of these examples, towards means before or shortly before.
Thank you, Elric.
I read all the sentences to mean “approximately” or “around”. Maybe there is a literally meaning of before or of a little before but I would never think that.
There is a vector/movement component of the word indicating an approach to the time specified but I think that really just adds some rhetorical flare. I don’t think you can really go wrong thinking approximately.
Thank you, Davidked.
This may be nitpicking, and I’m not a native so I feel kinda like an impostor here, but it seems to me that “around” a certain time can be either before or after, whereas towards, at least in my perception, can only be before. If someone’s moving towards a certain place, for example, he/she has not really gotten there yet.
It is an interesting question so I asked some friends, “What years would would be included if I said an event occurred toward the middle of the century?” Everyone answered 45-55 or 40-60. No one answered that it could only be before. There may be an official meaning of “before” but native speakers would not consider it as such.
Nice. Thanks for clearing that up.
Hi fellow Lingqers. Toward(s) means something that happens before an event - going to, but not necessarily arriving at something. e.g. she went toward the door.
However, to my mind with a sentence such as “what are your feelings towards her/him”, then towards would take the meaning as being ‘about’.
Not easy is it?! 
Sue
This is such an interesting question. I never considered how complex my own language might be. In my humble opinion, the short answer to your question is “YES” toward(s) can me around. However, it is somewhat archaic. In the examples you provided, 1. and 3. make the most sense. In my 39years in America I have never heard someone say #2. It stopped raining toward noon. It would be more common to hear, “It stopped raining around noon.” (either would technically be correct as both are being used as prepositions.) If you want more specific details, see: Toward Definition & Meaning | Dictionary.com All of your examples utilize “toward” as a preposition, which is how you would use it 99% of the time. There is also the use of “toward” as an adjective, which might have been more common in old English (starting around the 12th C.) In reference to “toward” versus “towards”, it looks like there is slight variation between the US and Canadian use of “toward” and the British and Australian use of “towards”, though technically either one would be correct. http://www.write.com/writing-guides/general-writing/miscellaneous/the-difference-between-toward-and-towards/