What do I use for the Path to the Craft folder? I want to place my Craft folder above the root.   But, this is for an add-on site that sits within the public_html folder of the main site. 

So, the index.php file sits here...

../public_html/add-onsite-folder/public/index.php


The Craft folder sits just above the /public_html folder of the main site.

So, how - specifically - do I set the $craftPath?   It's not the default '../craft'; and I have tried numerous variations.

I am not installing locally. 

Thanks
You will definitely want to put it above the root even if it's an add-on site, in which case the proper setup would be '../../../../craft' but this would generate a conflict with the main site craft install since there would be two folders with the same name above /public_html, so you could rename the add-on site craft folder to craftaddon and than the path would be '../../../../craftaddon'. 

In case there's a really good reason for leaving it below the root, you would just use '../../../craft' but that does come with security risks that are pretty much not worth taking.