MySQL localhost database from another host

Hi,

I am trying to connect to MySQL database at on one host (Host1) from another host(Host2).

While I try to connect to the database at Host1 from Host1 itself the next is working fine for me:
mysql_connect("localhost","username","password")

Now I am trying to find out what to use instead of localhost? I tried to replace localhost with host's url:port (I tried number of ports)

but this is not working (even when I am connecting from Host1 itself).

May be you need to add a user to the mysql users table that connects from the remote IP to tell MySQL it is OK to accept connections from that host as that user to the specified database.