Mader-Ott Harmonic Analyzer
Object Details
- Description
- A harmonic analyzer is a mechanical instrument for reducing a curve to its expression as a Fourier expansion. It calculates the coefficients to be used when the curve is expressed as the sum of a series of sines and cosines. In 1909, the German engineer Otto Mader introduced this form of harmonic analyzer, which used a set of wheels to find successive coefficients for the expansion of a plotted curve. This version of Mader’s invention was made the firm of A. Ott in Kempten, Germany.
- The wooden box, 34 ¾” wide x 27” deep x 3 ¼” high contains the following components:
- 1. A triangular carriage, measuring 18” x 12” with three wheels. This contains a smaller triangular carriage with a rack as well as a plate with holes for inserting gear wheels. A mark on the gear wheel plate reads: A. Ott, Kempten, no. 2253. A mark on the bottom reads: 5650A. A mark on the bottom of the smaller carriage reads “2”. Another mark there reads: A. Ott Kempten.
- 2. Some 108 brass gear wheels (two sets of 54), the smallest 5/8” in diameter and the largest 3 1/8” in diameter.
- 3. A tracer arm, 26 ½” long, graduated in tenths from 2 to 73. A pivot is at one end and a guide knob controlling the height at the other. Attached are a moveable tracer pin as well as a rotating lever. The lever is 7 ¾” long with a pivot at the other end.
- 4. A guide rail, 28 3/8” x 1 ¾”, graduated from 0 to 36. It has one groove, two notches, and two holes for fastening pins.
- 5. A lever 15” x 8 ¼” x 16 ½”. The first side is a tracer arm graduated from 2 to 37 in tenths that contains a moveable tracer pin, ball pivot, and guide knob like (3).
- 6. A triangle, 11 ½” x 11 ½” x 5 ¾”. It has one wheel, two ball pivots, and one hole; and is stamped “2” on the bottom.
- 7. A guide rule, 17 ¼” long, with a grooved piece 5 ½” long attached at the left end. It is stamped on the bottom: 29. The grooved piece is graduated in tenths with the zero-point at the center, and runs from 0 to 37 in both directions. A second set of readings runs from 0 to 36 using the same scale reading from +36 to -36 of first set.
- 8.Two brass and steel compensating polar planimeters, both marked: A. Ott Kempten. One is also marked with a serial number “No. 49475”, the other “No. 49476”. Each consists of a tracer arm, 7” long, attached to a plate containing a measuring roller and counter, and a pole arm, 8 ¾” long with pole.] Each planimeter has a pole plate and a control rule 4” long. Each planimeter also has a screwdriver (a metal piece ¾” x ¾”) for replacing the pivot point. Both planimeters are in black wooden cases that measure 10 ½” x 3 5/8” x 1 ¾”. A listing of constants in German is pasted inside the case.
- 9. A wooden base, 19 ¾” x 10 ¼” x 1 ¾”.
- Unless indicated otherwise, the components are made of steel with chrome and aluminum finish.
- References:
- NMAH Accession file 254098.
- Detlef Zerfowski, “Calculating Waves Not only on the Beach, Mechanical Calculation of Harmonic Waves by Harmonic Analyzers,” Proceedings of the 25th International Meeting of Collectors of Historical Calculating Instruments, September 20th to 22nd, 2019, The Hague & Scheveningen, The Netherlands, pp. 191-210. See https://www.zerfowski.com/Papers/Zer2019-1_Calculating_Waves.pdf , accessed September 1, 2020.
- Compare the example at the Science Museum, London – see https://collection.sciencemuseumgroup.org.uk/objects/co60186/harmonic-analyser-maders-form-in-fitted-case-harmonic-analyser-planimeter, accessed September 2, 2020.
- Location
- Currently not on view
- Credit Line
- Transfer from U.S. Naval Weapons Laboratory
- Data Source
- National Museum of American History
- date made
- 1931
- ID Number
- MA.324276
- catalog number
- 324276
- accession number
- 254098
- maker
- Ott, Albert
- Object Name
- harmonic analyzer
- Measurements
- overall: 8.2 cm x 88.3 cm x 68.6 cm; 3 7/32 in x 34 3/4 in x 27 in
- place made
- Germany: Bavaria, Kempten
- See more items in
- Medicine and Science: Mathematics
- Mechanical Integrators and Analyzers
- Science & Mathematics
- Subject
- Mathematics
- Record ID
- nmah_1215086
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