Time machine and my external hard drive

Please help.... if you can....
I am seriously nearly suicidal. I had a lot of PhD data on my external hard drive - its compatible with PC and Mac its a LaCIE biometric access TB drive.
I thought time machine would back up my current Macbook Air - I recently had it stolen and lost quite a bit of software and other stuff.
I asked time machine to backup to my hard drive.
The backup started, because it was going to take so long I cancelled after a short while. I now seem to have lost all the data on my hard drive. Is there any way of recovering this? I didn't complete the time machine backup. I am desperate....
Thank you anyone who can suggest anything....

In summary ....

1. You had an external drive with a lot of data.
2. You bought a new Mac and connected your external drive
3. Time Machine detected the external drive and asked you if TM could use it as a backup disk
4. You answered yes.
5 The backup from your new Mac to your external drive started and you cancelled it.

Is that what happened ?

If I am not mistaken Time machine will erase and format the drive that you assign to it prior to your first backup. I also believe that the user is informed about this on the screen before you authorise it to continue.
( Another member of the forum may correct me if I am wrong )

In that is what happened that the data that was on the external hard disk is .... gone.

Cheers ... McBie

Yes - this is what happened.
I expected the Macbook Air backup to go to the external hard drive IN ADDITION to the stuff already on there rather than the data on the hard drive being deleted and replaced with my Macbook Air content.

It sounds like there is no way back....?

Just do one more check .....
Attach your external drive and in Finder see if there is anything on your external drive.
You should see a sparsebundle , which is your TM backup.
If you see 2 of them, you might still have a chance.

Also, on the dock, right click the TM icon and select " Browse other Time Machine Disks " and see what shows there .....


Cheers ... McBie