Certificates contain a name (host and domain name, typically) and this name is compared to the URL requested. If they don't match, the certificate will not be honored by the client.
You're requesting a URL using an IP address, not a name. This will not work from a client that requires the name to be valid.
Dave Watts, CTO, Fig Leaf Software
Actually, as one can see from the certificate shown by the browser in my second post, the common name IN the certificate IS the IP address.
And now, through no concious effort in my part, it is working properly. The only thing I can think of, is that the self signed certificate on the IIS server had expired as it has been some time since we last played with it. While stumbling around in the dark, I may have regenerated the certificate for some three years.
But I would really like to know more about managing these things so that I am not stumbling around in the dark!