How do I restart Time Machine backup (to provide more space on my backup USB disk)?

I use Time Machine daily (I use a third party application, which name I do not recall, to change the frequency from the default Time Machine setting of one hour) backups (from 26 Jun 2013 to date) to my 1 TB USB external disk on my MacBook Pro OS 10.7.5, 500 GB internal HD - also with Parallels - Windows 7 Desktop.  However, the remaining space is only 300 GB on the USB drive.  The remaining storage on the Mac Main HD  is only 88 GB.  How do I terminate the current incremental backup, and restart the process with a fresh backup to my cleaned (deleted all previous backups) USB external HD?
Appreciatively, Arbyem
R_Bruce_MorrisColonel (Retired)Asked:
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Martin LissOlder than dirtCommented:
For no points the third party application is probably "TimeMachineEditor".
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R_Bruce_MorrisColonel (Retired)Author Commented:
Thanks MartinLiss, I now recall the name, although the application does not appear in my Applications folder!
I will await any other responses, although I have been assuming that I ought to be able to delete all backups from my external USB HD, and Time Machine ought to detect that there are no longer any previous backups, and hence restart with a complete backup.  
Bruce
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Martin LissOlder than dirtCommented:
I've never done it but can't you just select Time Machine in Finder and delete some of the old backups?
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Tom GrellCOMMUNICATIONS SPECIALISTCommented:
You can stop Time Machine, delete the entire backups folder, and restart Time Machine to make it start a new set of backups, but you don't need to do this. Time Machine will automatically delete the oldest backups to make room for new once the drive becomes full. Manually deleting older individual backups may cause problems, as Time Machine uses dynamic links to a single copy of each file, so that it only has to copy the files that have changed between backups.
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R_Bruce_MorrisColonel (Retired)Author Commented:
Hi tgrell: Thanks for the useful information/advice.  I prefer to delete the entire backups folder and restart, because I need some storage space on my USB HD for offloading some large amounts of folders/files from my near-capacity Main HD and my Windows 7 VM partition.
I will close this post and award points, unless I hear any other input.
Appreciatively, Arbyem
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R_Bruce_MorrisColonel (Retired)Author Commented:
Hi all: I now have a 1 TB internal HD, and use daily backups to my 1 TB external USB HD, scheduled via TimeMachineEditor.  My daily backups appear to operate successfully, except that, too often, some are delayed, for reasons unknown to me.
I also suffered significant crashes with both Mac OS 10.7.5 and Parallels Desktop Windows 7, while in Largo, FL in December 2014.  The Best buy Geek Squad in Clearwater, FL worked for five weeks before having to remove my newly purchased Parallels Desktop 9 (Windows 7 Home Premium) upgrade, upgrading to Mac OS 10.9.5 (Maverick), and forcing me to use my Windows 7 separately under Boot Camp.  Since I had a few original installation CD/DVDs for some key products (FrontPage 2003, Microsoft Office 2007, and Quicken XG 2007, I was able to operate some key Windows applications. However, I am still attempting to reload all of my remaining numerous Windows applications, most of which had been downloaded from websites. Needless to say, the challenges of locating the sources for all of my associated activation codes have been daunting!
Thanks again for all of the assistance, with apologies for having taken so long to finally close this question.
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