I have not taken the snapshot of the header, but it displayed 50M of free memory ...

Why not use the same tool (i.e. top instead of ps aux) after 24 hours? That would make it easier to assess what's going on (for example, the ps output does not show system buffer/cache usage).

That said, I don't really see a significant change in either the resident or virtual memory usage of the apache processes after 24 hours (in the ps output), so I suspect there's some misinterpretation of the data going on... It's pretty normal for a Linux system to show only around 50M "free" after it has been running for a while — independently of how much RAM it has. That doesn't necessarily mean there's something wrong.  How does your memory "problem" actually manifest, i.e. how does Apache behavior change, and/or what doesn't work any longer?

In other words, I don't think there are any leaks in your case. Linux is just using the memory for buffering purposes etc. to improve performance, instead of leaving it sit there unused...  It's maybe worth pointing out that those buffers will be discarded and the memory made available as soon as there's a "better" use for it, such as when an application needs memory.  So, don't worry, be happy! :)  And google for Linux memory management for some more background.