Added second My Book for Mac to use with my iMac - after plugging in both drives are not recognized

I have an existing My Book for Mac that was working fine. I bought a second one to use as a second backup for my backups.

I plugged the second one in and ran the existing WD utility. BOth drives appeared. Then suddenly both drives disappeared and their status lights went out.

I unplugged the USB on the new drive. Then I unplugged the USB on the old drive and then plugged it back in.

THe old drive is briefly recognized and then it disappears and the status light goes out.

How do I get both drives to be recognized? Why are they disappearing?

I am running Mac OSX Yosemite on a late year 2009 27 inch iMac.

Thanks!

Hello and welcome to the WD community.

Does this also happens when you only have one of the drives connected to the computer?