The actual URL of the image is what you get if you concatenate:

http://web.archive.org/web/20010331084854/
http://www.lileks.com/institute/interiors/bhg/chpt8/6.jpg

What you are seeing starts with the second http://. Perhaps you have some setting that the wayback machine recognizes, or perhaps something about your browser settings causes it to misbehave.

Try going directly to [link|http://web.archive.org/web/20010331084854/http://www.lileks.com/institute/interiors/bhg/chpt8/6.jpg|that] and see what happens.

And if you can't see that, be assured that the images do exist, and some day you may join the elite who can see them. Trust me, this isn't all a plot to make you doubt your sanity. (Why waste energy on what already happens?)

Cheers,
Ben