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Re: recommendation for slide rule ?
From: Paul Hirose
Date: 2009 May 17, 15:25 -0700

```Other than a few beginner or specialized models, just about all slide
rules have a full set of trig scales: S, T, and ST (also called SRT).
Some basic models combine S and ST into one scale, cutting accuracy in half.

Don't expect results as accurate as sight reduction tables, at least
from an ordinary 10 inch rule. Take a look at the trig scales in some
good close up photos (I'll supply some links later) and see if the
graduations are fine enough to meet your needs. Of course if you're just
doing this for fun, who cares?

Sines, arc sines, cosines, and arc cosines are found with scale S. One
scale suffices for all due to symmetry, e.g., sin 30° = cos 60°. All
that's required is double numbering for the graduations.

Scale T takes care of tangent, arc tangent, cotangent, and arc
cotangent. This scale goes up to 45°. Tangents of larger angles are
obtained by symmetry. E.g., tan 60° = 1 / tan 30°. So, to multiply by
tan 60°, you manipulate the slide rule as if dividing by tan 30°. As on
the S scale, T scale graduations are double numbered to make this easier.

It's still a little confusing, at least at first. A few slide rules
provide the luxury of a double T scale so you don't have to invert your
thinking for angles over 45°. The computational power is no greater, but

Scale ST or SRT handles small angles, less than about 5.7°. In this
range sine and tangent are practically identical, so a single scale
suffices for both.

With these scales you can find any trig function to about 1 part in 1000
accuracy with a 10 inch rule. That's true for any angle, though a little
knowledge of trig identities may be required. For example, how do you
get the tangent of 89°, when the T scale goes no higher than 84.3°? The
solution is to realize that tan 89° = cot 1° = 1 / tan 1°. So use ST to
find tan 1°, then take the reciprocal.

Another dodge will find the sine or tangent of arbitrarily small angles.
For example, to find the sine of .5° (off scale on ST), get the sine of
5° and mentally divide by 10. It works because the sine or tangent of a
small angle is practically proportional to the angle.

That kind of knowledge is far more important than owning a fancy slide
rule. For sight reduction you don't need features like double length
root scales, log log scales, and the like.

K+E's 4080 family are classic science and engineering rules, though
overkill for navigation. On the other hand, they are plentiful and
affordable on eBay. The company published a nice hardbound manual, and
these also come up for auction frequently.

There are several variants, denoted by model number. The second digit is
0 if plastic covered mahogany, 1 if solid plastic ("Ivorite"). The
fourth digit is 0 if trig scales are sexagesimal, 1 if decimal
("Decitrig"). That last is something to keep in mind for celestial use.
A dash number gives the length: -1 = 5", -3 = 10", -5 = 20".

Over the years K+E made several changes to the scale set. I think the
last was the addition of the DI scale in the 1950s.

One notorious problem with K+E rules of a certain age is deterioration
of the plastic in the top and bottom cursor bars. It's known as KERCS
(K+E rotting cursor syndrome). A material change around 1940 eliminated
that problem. I have a 50 year old 4181-3 which has much signs of use
but no trace of plastic breakdown.

Wood can have problems too. In some pictures I've seen online, the
uneven gap between the slide and body indicates something has warped
slightly. Most of these were really old rules from the early 1900s, though.

This site has information on K+E slide rules:
http://www.mccoys-kecatalogs.com/index.htm

Incidentally, the top two contestants in the 2009 World Champion Slide
Rule Competition used rules from the K+E 4080 family.

Back in the day, Pickett marketed a "Texas Speed Rule" designed for this
competition. Nowadays these fetch high prices on eBay, but ordinary
Picketts are inexpensive. The cheap models are plastic, but most are
aluminum. According to the company, the slide is supposed to be
lubricated with petroleum jelly. I think that's messy. A few years ago I
sprayed mine with gun cleaning solvent (after removing the plastic
cursors), lubed with Break-Free, then wiped everything dry, including
the sliding surfaces. This treatment didn't affect the markings at all,
and the rules still work fine.

Others use silicone lube. Or you could just run the rule unlubricated.
I've handled some beat-up student Picketts which clearly had never been
given any care at all. Their action was surprisingly good, enough to
make me wonder if lubrication was worth the bother.

Sterling is another make you see a lot on eBay. These are inexpensive
plastic rules. I still use the 9-scale Sterling Precision rule given to
me as a kid.

Those are the brands I have owned and used much. There are many more.
Dietzgen and Post are both well known. From Japan there are Ricoh and
Hemmi , both with extensive lines of bamboo rules. I've never handled
one, but bamboo is said to be dimensionally stable and self lubricating,
excellent for slide rules. From Germany you have the Aristo brand,
common on eBay. Note that European slide rules often (but not always)
put the trig scales on the body, not the slide. I can't help thinking
this would make something like cos b cos c cos A awkward. Then there are
the British Thornton rules with their unique "differential trig" scales.

Some informative sites:
http://www.oughtred.org/
http://tech.groups.yahoo.com/group/sliderule/
http://www.sliderulemuseum.com/
http://www.geocities.com/usra482b/index.html
http://home.att.net/~ross3/HemmiCat.htm
http://www.sliderule.ca/index.shtml
http://www.sliderules.info/

The cheapest, widest selection of slide rules is on eBay, but if you'd
rather pay a higher price to avoid the "item is sold as-is", try these
vendors:
http://home.att.net/~ross1/SRTC/SRTC.htm
http://www.sphere.bc.ca/test/sruniverse.html

Online slide rule simulator:
http://www.antiquark.com/sliderule/sim/index.html

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