Time Machine, changed interface wants to start again

How can I persuade Time Machine to continue incremental back-ups when it wants to start from scratch?
I have been running Time Machine, backing-up to a Seagate GoFlex Desk (2TB) via a Firewire 800 connection successfully for a while. I want to use the Firewire connector elsewhere and so swapped the base to usb, reasoning that the usb2 connection would be fast enough for incremental back-ups. Problem was the disk was not recognised as the Time Machine disc and when selected to be the back-up disc Time Machine wanted to start from scratch - which would take too long over usb2. I can see and open the previous back-ups, can anyone tell me how to persuade Time Machine to continue incrementally backing-up and not start again?
iMac C2D 3.06 4GB running 10.9.2.
Thanks, psammey

Thanks Brian33, that looks very promising, I'll give it a go!
psammey

Success - mostly!

Back-ups have been inherited ok, seamlessly open those before and after changed connection. The first back-up after was larger than usual, ~6.5GB, but that's a lot better than ~300GB! and now back to usual size. During that first back-up the disc was not being displayed as a Time Machine disc on screen (brown compared to turquoise) and the Time Machine symbol in the menu bar didn't rotate to indicate backing-up in progress, now, having restarted the iMac, the disc symbol is ok (turquoise) but the Time Machine symbol in the menu bar still does nothing during backing-up; I can live happily with that.

Thanks again Brian33!

psammey

Status messages are being displayed ok during back-up.
It took me a few attempts to get the instructions right in Terminal (rushing, never a good idea!) so maybe one of my false attempts messed things up.
Next I will restart without symbol being displayed in menu bar and then re-select it.
psammey

I partitioned the disk to use for Time Machine back-ups for my MBP as well as my iMac.
Now doing first TM back-up from MBP (also running 10.9.2) via usb2 interface (slow, ~25 GB/hr) menu bar TM icon is not rotating, progress info is being displayed.
Wondering if menu bar icon doesn't rotate during TM backing-up via USB under Mavericks?, I've always used firewire connections in the past.

psammey

Thanks matrix07 for solving that issue.

psammey