I have a php script that shows a log of its actions as the script proceeds. The log is getting quite long, up to the point where it will echo its information past the bottom
I think what you're looking for is this: http://www.w3schools.com/jsref/met_win_scrollto.asp
And then, used with conjunction with this: http://www.w3schools.com/jsref/prop_element_scrollheight.asp
You can make something like:
function scrollToBottom{
window.scrollTo(0, document.body.scrollHeight);
}