How to continuously scroll content within a DIV using jQuery?

You'll need to duplicate your content element and align them so that they're vertically next to each other, and scroll them in tandem. Your current scrolling should work, the jump will be invisible because it should jump from the top of the bottom element to the top of the top element, that is, to a same-looking part. I'd put both copies of the content (you can just .clone it to get the other copy) in a container and scroll that, that way you don't have to worry about moving two elements.

If you want to really optimize it, you could only display the top part (enough to hide the jump) of the content in the bottom element, but unless your content is really complex and heavy, it's not worth the effort.