REVISED: How do I send e-mail to lots of users at a remote unix site?

[thermal%solgel.hepnet at CSA2.LBL.GOV]

I apologize for my first posting, which did not quite exactly
say what I wanted it to say.  Below is the revised posting,
which I believe now says what I wanted it to say.  Read carefully.
Thanks for your reply.

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I would like to be able to send a mail message to all the users on
ANOTHER unix machine via Internet.  Of course, I could do it the long
and tedious way, that is, by sending a mail message to each user, one
at a time.  Is there a quicker way? (it seems to me there could be two
or three different ways, such as setting up a mailing list file on my
machine which will automatically mail the message to all on the list,
or sending one message to the remote machine and somehow instruct it
to distribute the message to all the users).  Obviously, I'm not a
unix guru or wizard, so make your explanation understandable, please.

Thanks, Dana