I've read that providing pid in the newsyslog.conf is to ensure that the process writes in the new log file. However, I've tried log rotation without providing a pid because I couldn't find one for the process, and it worked (the process wrote new log entries in the new file).
Now I'm not sure when I need to provide a pid file. The process that I tested here is a launchd process, and is it maybe because of that?
