I took the suggestion from your first reply and did that (mv the syslog file from cron.hourly to /etc/logrotate.d and move the logrotate file from cron.daily to cron.hourly). But that has produced another problem that I need to solve (a problem you mentioned in your second post); after it rolls this audit file, compressing it and renaming it with the date as part of the name, it doesn't "re-initialize" the file it just rolled. It leaves that file there, which is not what I want. I want that file deleted so that a new one can be started from a new file (a file that starts out as empty).

Now, I noticed that in that "syslog" file that I have now moved into the /etc/logrotate.d directory, there is a line that instructs that /etc/init.d/syslog reload should be run. I'm thinking that what I need to do is to create a shell script, maybe also putting it into the /etc/init.d directory and in that shell script have the following command:

service syslog stop
rm /var/log/audit/taudit.log
service syslog start

and then in that syslog file located in /etc/logrotate.d directory, change that line that says /etc/init.d/syslog reload to
/etc/init.d/syslogt reload and name my shell script located in /etc/init.d syslogt. Would that work?

See it isn't just a metter of rolling the log file. I also need to delete the old one while initializing a new one. The whole point being to reduce disk space consumption. Otherwise, I'll run out of disk space in just 2 days.