October 17, 2010

The Faber-Castell 111/38 Stadia 360° desktop surveyor’s rule seems to be extremely rare. My searches of the Internet have brought up a few examples of the 111/38 Stadia 400g, but almost none of the 360° version. My father found this one in an antique shop, in nearly mint condtion, complete with its case. Thanks Dad!

Front of the Faber-Castell 111/38 Stadia 360° slide rule.

The 111/38 is a full-sized rule, with scales on only one side of the stator, but both sides of the slide. The front contains L, A, B, CI, C, D, P, S, and T scales (the P scale computes 1-x2, which is also the cosine of the angle on S) These scales are all self-documenting, with the scale name at the left end of the scale, and its mathematical formula at the right end. A noticeable ommission is the K scale. Perhaps surveyors don’t have much need to compute cubes or cube roots.

Along the upper edge of the rule is a 10-inch measuring scale, subdivided to 1/32 of an inch. The combination of an inch scale and angles measured in degrees leads me to believe that this rule was manufactured for the North American market.

Being the 360° model of the rule, the angles on the S and T scales are expressed in degrees. The subdivisions are in decimal degrees, as opposed to the minutes and seconds found on some slide rules.

Back of the Faber-Castell 111/38 Stadia 360° slide rule.

The back of the slide appears to have five scales, but there are actually only three:

• The 1−cos2 scale is double length, covering 1.85° to 5.75° in one range and 5.7° to 20° in the second.
• Similarly, the 1¾-length sin·cos scale has two ranges, covering 0.5° to 6° and 5° to 40°. For an angle α, this is used to compute sin α  times cos α.
• Finally, there is a ¼-length cos2 scale, covering the range of 5° to 40°.

These special scales, used in surveying calculations, can be used in two ways:

1. With the slide installed so the front (B, CI, and C) is showing, the desired angle on the scale of interest can be slid under the hairlines found on the back of the rule in the stator cut-outs. The result can then be read on the C scale above the index of the D scale.
2. With the slide reversed (surveying scales showing) and the slide’s index marks aligned with the index of D, the cursor can be moved to the desired angle on the scale of interest and the result read on the D scale.

The back of the rule shows four diagrams illustrating various surveying situations and the formulae involved. There is also a table of values to be used in conjunction with these formulae.

Specifications
Make and Model: Faber-Castell 111/38 Stadia 360°
Manufactured: Germany
Overall Dimensions:   30cm × 5cm × 0.65cm (12″ × 2″ × 0.25″)
Scale Length: 25cm (9.8″)
Construction: All Plastic
Scales: L A | B CI C | D P S ST
| 1−cos2 sin·cos cos2 |
Cursor: Plastic with One Hairline
Date Acquired: October 2010

The plastic display and carrying case is in very good condition. I suspect it spent a lot of time in a drawer, but had never been in the field. The felt pads that keep the rule away from the case are still clean and white.

This rule came complete with carrying case, in very good condition.

Unfortunately, there was no instruction manual for this rule, and I haven’t found one online anywhere either. It was fairly straightforward to figure out how to use it, but I’m curious about the sorts of surveying computations that it was designed for.

Update 2011-Jan-01: My father wrote to Faber-Castell in Germany, where Ms. Stefanie Bauer took the time to photocopy the manual in their archives and mail it to us. I haven’t yet had the time to read through all of it (reading German requires a bit of concentration on my part), but here’s an excerpt about the sin·cos scale:

An excerpt from the 111/38 manual. Click to see the entire page.

The manual covers both the 360° and 400g versions of the 111/38 rule, as well as the 4/38 and 67/38b rules. Thanks again Dad, and danke schön Ms. Bauer!

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1. October 18, 2011

I’m old enough to have used slide rules at my grammar school in the UK in the late ’50’s/early 60’s before electronic calculators were invented. The Faber-Castell model was always envied as it was top of the class! It was owned by a couple of our wealthier classmates but didn’t give any different answers than our less costly models (I think I’ve still got mine somewhere which went on to be used at College/University at Plymouth till 1970.

2. December 08, 2012

I have a display case in my office that contains my grand-father’s slide rules (unknown manufacture), my father’s slide (Keuffel & Esser 4081-3) and my slide ruler (Faber-Castell Novo Duplex 2/83N).

Even though I work with sophisticated mathematical software packages, I still keep my inexpensive Sterling slide rules on my desk.

3. March 15, 2013

Survey use includes reducing stadia observations to horizontal and vertical components. Theodolites used to have two additional cross hairs, as well as the normal centre hair. If you read three values on a levelling staff (or tape measure), on e at each hair, the difference between TOP and BOTTOM multiplied by 100 is the distance to the tape. Middle value is a check, being average of TOP and BOTTOM. For horizontal line, this is straightforward, but if the theodolite telescope is not horizontal, the desired horizontal distance and vertical height difference is calculated by Sin of the slope multiplied by the slope distance, and Tan slope multiplied by slope distance. Diagrams on slide rule may make sense of this. Nice instrument.

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