TO: Readers other than Pat:
If you have not read the article referred to in Pat's message, this
may not be clear what I'm talking about. Maybe you'll just want to
skip this or maybe you'll want to read the article)
.
On 2007 Jul 19 , at 5:40 AM, Pat Naughtin wrote:
Here is another reference that refers to John Wilkins and the
invention of the metre.
http://blog.plover.com/physics/meter.html
Pat,
I've replied to the author of that reference regarding his
mystification over a factor of 0.4 (or 2/5) in an equation Wilkins
used.* I believe I can relate that 2/5 factor to the 2/5 in the
equation for the moment of inertia of a sphere of mas M and radius R
when it is rotating about its diameter. That moment of inertia is I=
(2/5)MR^2.
Wilkins has apparently accounted for an effect of which the author,
Mark Dominus, is unaware. It's some interesting physics.
I have not yet carried through the calculations but I think it will
be relatively straight forward, although perhaps tedious..
Regards,
Bill Hooper
Fernandina Beach, Florida, USA
* The equation uses, for the effective length of a pendulum, the
length from the support to the center of the spherical weight and
Wilkins gives it as:
length = d + 0.4r
where d is distance from support to center of the spherical bob and r
is the radius of the (spherical) bob. (and the factor of 0.4 is just
2/5.) Actually, Wilkins uses x in place of r in the above. I think
this is an error, possibly just typographical. I think x is supposed
to be the extra length that needs to be added to the length of the
pendulum (measured to the center of the bob) to obtain the effective
length of the entire pendulum. If I am correct then his d+0.4x should
be d+0.4r instead.
