THE FOLLOWING INSTRUCTIONS ARE TAKEN FROM QUALCOMM EUDORA USER MANUAL:

SMTP authentication operates automatically in Eudora.

Eudora can log in to an SMTP server when sending mail, just like it does for receiving mail. Not all SMTP servers require or allow such authentication. Eudora will attempt authentication to servers that allow it. The preferred SMTP authentication method is CRAM-MD5. If CRAM-MD5 is not available, LOGIN or PLAIN will automatically be used.
Once Eudora discovers that your SMTP server allows authentication and when you send messages, a dialog appears that prompts you to enter a password. For more details on Eudora please go to:

http://www.eudora.com/email/docs/index.html