I have a Filemaker Server machine in San Francisco. I want to use my web server in New York. Is this possible? Do both machines have to be on the same network?

Yes. However the difficulty will be making sure the "pipe" between the two servers isn't blocked by routers, vpns or firewalls.

I have a Filemaker Server machine in San Francisco. I want to use my web server in New York. Is this possible? Do both machines have to be on the same network?

They don't have to be on the "same" network, but they do have to be able freely to communicate with one another across the Internet or some other WAN. And ports must be properly configured as Vaughan points out in his post.

Then there is the question of where the Web Publishing Engine, the third part of this configuration, will live. Will it be on the database server or on the web server or on its own machine? I'd probably put it on the same machine as the database server, but I don't know what your total configuration is, so I'd reserve final judgment on this.

There is one other option if you have an existing web site hosted in New York. You could put all 3 parts of FileMaker Web Publishing on the server in San Francisco and then put links to that into your exisiting New York hosted site.

Steven