UNIVERSITY OF ROCHESTER 
SCHOOL OF ENGINEERING AND APPLIED SCIENCE
DEPARTMENT OF ELECTRICAL ENGINEERING
[phone, fax, email]

                                                      April 16, 1998
To whom it may concern:

I have read the recent signed statements by William Hones, Edward Hones,
Peter Campbell, and others concerning the case that Hones and Hones have
attempted to construct in justification of their position regarding the
relationship of the Harrigan invention [1] to their own [2].  In connection
with this matter, I make the following observations:

1)  Hones and Hones continue to discount as insignificant the importance of
rotation in achieving levitation of the Levitron TM.  I am surprised by this
stance, because it is clearly the rotation of the top – not mere design
details of the base magnet’s configuration – that makes the Levitron TM
work.  Earnshaw’s theorem is circumvented, and levitation made possible, by
rotating the top.  Recent statements issued by the Honeses and others must
not distract us from what is crucial about what makes the Levitron TM work.  
 
2)  Hones and Hones tell (or have allowed to circulate) a strange story of
long and fruitless years spent searching for the right magnet configuration
to achieve levitation.  What is strange is that this quest was destined to
fail from the start.  Without some means to counter the inevitable
orientational instability, levitation of a permanent magnet in the field of
another permanent magnet is impossible.  I must admit to puzzlement that
Edward Hones, a trained physicist, would have pursued this unattainable goal
because it would appear from their own reports that he was trying to find an
exception to Earnshaw’s theorem, when in fact there are no exceptions to
Earnshaw’s theorem.  There are situations where this famous theorem does not
apply, and Harrigan’s invention is one of these.  
 
3)  Given the blind alley where Hones and Hones found themselves, it is
difficult to believe that they ever could have published their patent and
developed the Levitron TM without employing Harrigan’s elegant solution of
using rotation to control the levitated magnet’s orientation.  In his
patent, Harrigan clearly recognized the value of rotation in suppressing
orientational instability to achieve levitation.  In fact, his patent
describes a second method of overcoming the natural orientational
instability using a pendulum-like attachment to the levitated magnet.  The
fact that this approach is less practical than rotation does not weaken
Harrigan’s position; rather, it shows that Harrigan understood the real
problem – viz… suppression of the orientational instability – and worked
hard enough to come up with more than one solution to it.

4)  The Hones patent does contain one interesting statement to the effect
that the magnetic base plate must have corners in order to achieve the
necessary lifting and centering forces.  All published theoretical and/or
computational models for the Levitron TM that I know of, including those of
Berry [3], Simon et al. [4], Jones et al. [5], and Gans et al. [6] show
unequivocally that an axisymmetric base magnet, e.g., a ring or torus with a
circular periphery, will work fine.  The claim of Hones and Hones – that the
base magnet must have corners – is wrong.
 
5)  In the Honeses patent, the claim that the base plate can be flat instead
of dish-shaped figures less prominently in the text than does their
(erroneous) claim that the base plate must have corners.
 
6)  Far more important to a robust design for the Levitron TM than either
the magnetization orientation or the shape of the outer periphery is a
central hole (or a reversed-magnetized region) in the base magnet.  This
feature is neither mentioned nor claimed in the Honeses patent, despite the
fact that it is employed in the commercial version of the Levitron TM sold
by Fascinations Inc.  Interestingly enough, one of Harrigan’s magnet designs
– the one using an array of small cylindrical magnets mounted in a circle –
takes advantage of this idea.  The central hole promotes creation of the
magnetic field reversal on the axis near the base that facilitates spinning
the top by hand before it is raised up by the lifter plate.  A central hole
in the base also helps to shape the field for a good locus of stability.
Harrigan would probably refer to this field shaping in terms of his "cone".

These points, while hardly complete, do provide some representation of my
views on the true origin of the magnetic levitation device commonly called
the Levitron TM.  The recent testimony of William Hones, Edward Hones, Peter
Campbell, and others has not changed the opinion I formed when I first read
the two patents [1,2] several years ago.

Sincerely,

[signature]

T.  B. Jones
Professor of Electrical Engineering


Numbered References:

1.  R.M. Harrigan, U.S. Patent # 4,382,245, "Levitation Device". May 3, 1983.

2.  E.W. Hones and W. G. Hones, U.S. Patent #5,404,062, "Magnetic levitation
device and method", April 4, 1995.

3.  M.V. Berry, Proc. Royal Soc. (London) 452, 1207 (1996).

4.  M. D. Simon, L. O. Heflinger, S. L. Ridgway, Amer. J. Phys 65, 286 (1997).

5.  T. B. Jones, M. Washizu, and R. Gans, Journal of Applied Physics 82,883
(1997).

6.  R. Gans, T. B. Jones, and M. Washizu, Journal of Physics: D. Applied
Physics 31, 671 (1998).