When you use the Mac OS, drive mapping is not required. Mac's do not use the A, B, C D drive identifying method like Windows.
Drives in a Mac appear on the desktop (are mounted) when they are connected.
As you are using such old operating systems, 8 & 9, it may be that your Mac's are also very old and do not have USB or FIrewire ports. That would have been an easy way to transfer files from the Windows machine to the Mac, and vice versa.
Are the Mac's connected to your Local Area Network (LAN)?
While it is possible to connect these machines together, the software required, DAVE, may not be in production. OS 8 and 9 did not have the built in ability to connect to a Windows environment. OS X does but you will need new machines for that OS, probably.
BTW, what sort of files are these that want to transfer? As you may know, applications written for the Mac will not run on a Windows machine.
Have you thought of emailing these files to the windows machine?
P
I have Mac OS8 and OS9 at work. I try to copy files from Mac to Windows. I think about mapping a drive to Windows or use FTP. I've never used Mac before, and I don't know how to accomplish this task. Could someone help. Thank you.

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