How to connect a URL to a class file

My question is: How to get the URL
http://localhost/Alpha
(no :8080) to run the Java servlet
/MyPath/Whatever/Beta.class
What is the chain of linkages required?

I don't use CVS, I don't use Ant, I don't use JSP,
I am not using the Tomcat Manager.
But I can be root and edit any file on the hard disk.
Yes I've read the Tomcat documentation.
it is tool-oriented and confused and sometimes wrong.

I have Ubuntu Linux 10.04
and Apache 2.2.14
and Tomcat6 6.0.24.

FYI I can configure apache2 to alias /Alpha to /MyPath
and so it run /MyPath/index.php which consists of
<?php
system( "java Beta" )
?>
but in that case Beta is not a sevlet,
just an ordinary Java program.

FYL I've been writing PHP for several years.

Chnage Tomcat to listen on port 80 and map the servlet properly in the deployment descriptor.

Bear Bibeault wrote:Chnage Tomcat to listen on port 80

I can try this. But won't it interfere with Apache serving up my other web sites? On the web is a blog from 2001 saying that to get Apache to talk to Tomcat I have to recompile Apache, but of course that is rediculous.

Bear Bibeault wrote: map the servlet properly in the deployment descriptor.

By "deployment descriptor" do you mean
$CATALINA_BASE/conf/server.xml
or $CATALINA_BASE/conf/web.xml
or $CATALINA_HOME/webapps/default_root/META-INF/context.xml
or /MyPath/WEB-INF/web.xml
or /MyPath/META-INF/context.xml

The sample web.xml file has sample <servlet-mapping> entries but they do not seem to have any concept of a disk directory. So how does Apache (or Tomcat) know that when it sees "Alpha" it must look to "/MyPath"?

No, you don't need to recompile Apache to have it use a Tomcat instance handle servlet requests; see http://tomcat.apache.org/connectors-doc/webserver_howto/apache.html for all you need to know about the integration.

The DD for your web app would be /MyPath/WEB-INF/web.xml. In it you need appropriate <servlet> and <servlet-mapping> elements; if you're not sure how those work, see the servlets-examples web app that comes with Tomcat, or consult a servlet tutorial.