I have a WD MyBook Essential 1TB external hard drive installed with my Mac OSX 10.5.8. The drive is only being used for Time Machine and my iTunes backup. The drive will randomly unmount itself and I get an error message saying the device was improperly removed. Hours or minutes later, it will randomly remount itself and it will work fine until it randomly ejects itself again. Ive searched other forums but cant seem to get a clear answer as to how to remedy this issue. Any help would be appreciated.

Windows 8 and Mac do not use the same data structure format.

How was the drive formated? If it was formated as NTFS, OSX can only read - it won't write.

If you're going to be using it on your Mac, then you should repartition/reformat it in your disk utility. That way you will get better performance out of it.

dude try flipping it over and replacing the power cable

Set your itunes drive to the external WD drive, easy. Itunes -> Preferences -> Advanced -> Store Location -> Set to your external drive

The 1TB drive is USB 2.0, make sure you're not connecting to a USB 1.0 port on your computer.

Mybook does not require any additional driver to work on systems from Win XP onward, same for recents Linux and MAC OS.
If the drive is not detected on more of one computer, then it is usually because of a fault.
Try a replacement cable (mybook uses Mini USB to USB, available at computer and at camera shops). If still no luck contact WD, mybooks have one year warranty. If you want to recover data, the disk must be mounted on a different enclosure, that service can be asked when discussing repair.
Regards

load the driver for mac use, the external hard drive comes with cd, the mac driver should be inside, load it to your mac computer. if you donot have the cd go online to western digital and download it. just load the driver and u will be fine, make sure u connect the cable in right places.

I’m happy to help further over the phone at https://www.6ya.com/expert/mustafa_06f84c65ab5cc745

it must be initialised /mounted 1st for osx

Make sure the power supply (power brick) for the mybook is working. (unplug both ends or the power cable and plug back end)

do the same for the USB cable. Still no luck? Plug the USB connector into a different port on the PC and see if that changes your luck.

Window and OSX - fun and joy.
Since you formatted a 1TB drive and it works fine in Windows, I have to concluded the the drive was formatted NTFS.
Here is the issue in a nutshell, OSX supports reading NTFS but have very limited write cababilities.
If you want both Windows and OSX to have full access to an external drive you should format it FAT32. The only issue then is that under normal conditions a FAT32 drive has a maximum size of 32GB.
I would partition the drive to have 1 or more FAT32 partitions and then have the rest of the drive NTFS.

Is the OSX version correct or should it be 10.3. If it is actually 1.3 it would mean you have the OSX Server edition that originally came out in 1999 and it may not have very good USB support - version 1.2 would only support 1 USB device.