Ron Brown wrote:
Thanks for your help. Unfortunately, I'm not getting it to work. I have enabled enabled 'show-all-files' in finder.
You don't need to enable hidden files. I suggest you disable that - it simply encourages you to poke at things that you do not need to see.
To make the user Library visible in Finder follow this guide (but it really isn't required)…
http://www.macobserver.com/tmo/article/mavericks-easily-make-user-library-folder -visible
Ron Brown wrote:
Attached are views of (1) the backup 'Application Support' directory, which is truncated at the letter 'S',
You are looking in the wrong place! There are MANY library folders on OS X. Each has it's own content…
Ron Brown wrote:
(3) the 'Application Support' directory on a new Macbook than covers the entire alphabet...

Look at the bottom of that window…
Macintosh HD / Users / ronbrown / Library / Application Support
Your other windows appear to show you are looking inside a folder called 'archworks' (which is probably the system disk name). You are looking in the wrong place - this is why you need to stop digging into the backups in Finder.
To view those files in the backup open the path ~/Library/Application Support via the go menu & use 'Enter Time Machine' as described.