5 tube balancing argument

Mark Solomon Mark.Solomon at Yale.edu
Wed Oct 9 13:35:18 EST 1996


In article <jpcd0-0910961641090001 at macr1-5.welc.cam.ac.uk>,
jpcd0 at mole.bio.cam.ac.uk (John Dixon) wrote:

: I reckoned that if you put three tubes in, in a triangle ie in holes 1,5,9
: these are balanced. Then you can balance the two others opposite each
: other in holes 2 and 8.

Good.

: Then another guy said that he balances five by putting them in as near a
: pentagonal position as he can ie 1, 3, 5, 8, 10. I dont think this is OK
: because you cannot remove a balanced pair to leave a balanced three,
: although I doubt it does much harm.

Not so good.

Basically, your way of thinking about it guarantees that you will always
be in balance (a worthy goal for all of us!).  For 12-place rotors, the
only configurations that are impossible to balance (with identical tubes
and contents...) are 1 and 11.  Note the symmetry:  if you can do 5 tubes
and 7 holes you can also do 7 tubes and 5 holes.  For 18-place rotors,
don't try 1 or 17 tubes; all others work.  Sometimes I wonder, though,
whether it might just be quicker to grab a balance tube than to stare at
13 tubes and an 18-place rotor!

Mark Solomon
Yale University



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