Hi Leo and others,
How about this, no LLs :

To get : 6.2 ^ 3.9 = soln.

equals 3.9 log 6.2 = log soln.

3.9 times .792 = log soln.

3.09 = log soln.

Set up .09 on L find 1.23 on scale C.

So soln. is 1230.

You're right, the high end of LL3 is just an approx, but working as above,
gets you more confident :-) . And can be used for any power prob
on a rule w/o LLs.

Gary Flom

----- Original Message -----
From: amin_aur
To: slideruleforum@yahoogroups.com
Sent: Tuesday, May 01, 2007 1:24 AM
Subject: [Slide Rule Forum] Re: Beauty and the Forum


Leo,

Very interesting technique. I've never seen this before. Thanks.

Cheers,
Amin

--- In slideruleforum@yahoogroups.com, Leo Ackley <la@...> wrote:
>
> >>
> >> In addition to discussing different slide rules, how about
discussing
> >> how to USE these slide rules in solving problems. After all,
this is
> >> a forum for the utilitarian beauty of the slide rule. Just my
humble
> >> thoughts.
> >>
> >> Cheers,
> >> Amin
>
>
> Yes indeed!
>
> I too am very visually oriented (being an artist-a painter). I have
> used a trick for years that in my opinion uses the "utilitarian
beauty"
> of the slide rule. It would also have great pedigogical value.
> Explaining to yourself (or to others) exactly what is going on here
> would sharpen one's understanding of the number system.
>
> The choreography here is for a vintage Hemmi 260, made in 1960. She
has
> a full set of LL and LL/0 scales. On a rule with LL scales a big
pain
> in the glutius maximus in that the LL3 scale gets so compressed in
the
> last quarter or so to the right. This thing is sort of magifies
that
> end of the scale.
>
> You set the number you want to raise to a certain power on the LL3
> (say, 6.2). If you now set an exponent (say 3.9) on the C after
lining
> the left index up with the LL3(6.2), all you can read on LL3 is
1200
> something.
>
> Instead, set the 3.9 on the CI scale above 6.2(LL3). And rather
than
> reading at the right index, reset the hairline at CI(2.3025) and
read
> the answer (3.09)on the D. What I am doing is dividing log base e
of
> the number I am looking for by this number and get log base 10. The
> setting is delicate: The hairline just kisses the 2.3 slightly to
the
> left.
>
> This 3.09 is the entire log, charactoristic and mantissa. Extract
the
> mantissa and set it on the L scale on the other side of the rule.
Above
> 0.09 on L is 123, so the charactoristic 3 gives 1230. A calculator
says
> that 6.2**3.9 is 1231.19...
>
> If the exponent is negative and you are looking for a number on the
far
> right end of the LL/3, read the value off the DI (instead of the D)
> from the L. If the above exponent is negative (6.2** -3.9), the
method
> gives 0.000812, agreeing with a calculator value in all three
digits.
>
> It doesn't always work this smooth, but I would say the thing gets
you
> 2.5+ significant digits. And it's just fun to do. Do the settings
with
> a magnifying glass and see how close you can really get. I have
never
> seen this in a manual, and if it is, than I have invented it
> independently.
>
> It is possible to multiply on a set of LL-LL/0 scales and in some
> ranges get four signicant digits.
>
> It is also possible to raise numbers to a wide range of powers
without
> using the LL scales, using on K,A,B,C and D. (Like for instance,
> something to the 0.444...th power.)
>
> One way I amuse myself is to set something on the Hemmi 260 at
random
> and try to figure out what ALL the inplications of that setting are.
>
> Take an analogue in music: it is said that the key of C major has
not
> been exhausted yet....
>
> Take care,
> Leo
>





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