proportional dividers
Datecirca 1925
Inventory Number1997-1-1917
ClassificationProportional compass
Subject
Maker
Keuffel & Esser Company
1867 - 1987
User
William R. Osgood
Cultural Region
Place of Origin
Dimensions17.4 x 1.3 x 1 cm (6 7/8 x 1/2 x 3/8 in.)
Material
Accessoriescase
DescriptionThis proportional compass comes in a black, rectangular box with embossed, gold leaf lettering. The box opens with hinges on the long edge of one side of the box.
The body of the compass consists of two arms, attached with a blue colored screw in the center. Each arm also has a very skinny, pointed, rounded attachment at each end. At one end, the extensions are very short, appearing like small points emerging from the arm. At the other end, the attachments are longer and held in place by a screw.
Each of the main arms has two rectangular tracks (holes) in it. A round, raised, screw mounted on a rectangular frame slides in one of the tracks. On the opposite side of the arms from the track (i.e. on the 'back' of the compass) the 'bottom' track (i.e. the one furthest from the sliding screw) is marked in engraved black numerals from 10 at the top (closer to the shorter pointy extensions) to 2 at the bottom (closer to the longer extensions). The higher the numeral, the smaller the space between it and the next lowest number: e.g. 5 and 4 are further from each other than 10 and 9. The screw on the 'front' of the compass can be loosened and moved along the track with the marked increments. The position of the screw in the track determines how far apart the pointed extensions of the compass can be. The higher the number, the further apart they can be.
Both of the long extensions are skinny and pointed. One is round -- like a long cylinder. The other is flat -- like a long triangle.
The body of the compass consists of two arms, attached with a blue colored screw in the center. Each arm also has a very skinny, pointed, rounded attachment at each end. At one end, the extensions are very short, appearing like small points emerging from the arm. At the other end, the attachments are longer and held in place by a screw.
Each of the main arms has two rectangular tracks (holes) in it. A round, raised, screw mounted on a rectangular frame slides in one of the tracks. On the opposite side of the arms from the track (i.e. on the 'back' of the compass) the 'bottom' track (i.e. the one furthest from the sliding screw) is marked in engraved black numerals from 10 at the top (closer to the shorter pointy extensions) to 2 at the bottom (closer to the longer extensions). The higher the numeral, the smaller the space between it and the next lowest number: e.g. 5 and 4 are further from each other than 10 and 9. The screw on the 'front' of the compass can be loosened and moved along the track with the marked increments. The position of the screw in the track determines how far apart the pointed extensions of the compass can be. The higher the number, the further apart they can be.
Both of the long extensions are skinny and pointed. One is round -- like a long cylinder. The other is flat -- like a long triangle.
Signedembossed in gold leaf on the top of the box: KEUFFEL & ESSER Co N.Y.
engaved on an arm: KEUFFEL & ESSER CO NY GERMANY
stamped on the bottom of the case: W.R.O. [for William R. Osgood]
Inscribedembossed in gold leaf on the front of storage box: 728
FunctionThe proportional compass is used to divide the circumference of a circle or a straight line into equal parts and to alter the size of an image. For the equal division of lines and circumferences, the long extensions of the compass arms can be fixed a particular distance from one another. That distance can then be marked repeatedly onto a line or circumference to incrementally divide it. For enlargements and reductions of an image, the long extensions are set with a distance between them from two components of the image (a vertex to the opposite side of a triangle, for example) with the adjustment screw at some particular point in the track (measured with the increments on the back of the instrument). The measured relation is increased or decreased some fixed amount (again using the marked increments on the back). So long as the original measurements are made with the adjustment screw in the same place, and the reproductions (with larger or smaller relations) are made with the adjustment screw in the same other place, the reproduced image will be identical to the original with the desired augmentation or reduction. This is to say that the compass preserves internal relations while altering the scale of an image.
Crosby Steam Gage & Valve Company
Date: circa 1910
Accessories: original and photocopy of letter from Dr. Joachim Fischer in Berlin requesting information and photographs of mechanical integrating devices from William J.H. Andrewes, dated 13 October 1993
photocopy of letter from William J.H. Andrewes to Dr. Joachim Fischer, providing information on the planimeter and requesting details for his desired photographs; original and photocopy of letter from William J.H. Andrewes to Dr. Joachim Fischer, responding to a request regarding mechanical integrators acquired from the Aiken computer laboratory, dated 11 April 1997; letter from William J. H. Andrewes to Dr. Joachim Fischer that accompanied the photographs, dated 26 April 1995; film and eleven color photographs of the instrument, probably copies of those sent to Dr. Joachim Fischer
Object number: 1995-1-0003
Adrien Gavard
Date: circa 1860
Accessories: hinged mahogany case with original trade label; extra arm; writing implements; instrument weights; small ivory wheels with brass frames
Object number: 1997-1-1856
Charles Thurber
Date: circa 1860
Accessories: wooden framed, glass paned case; original and photocopied letter from the Massachusetts Historical Society Director, Stephen T. Riley to David P. Wheatland dated June 28, 1961regarding permanent loan of the pantograph (in instrument file); original and photocopied hand-written letter from David P. Wheatland to Stephen T. Riley regarding permanent loan of the pantorgraph dated March 16, 1962 (in instrument file); original and photocopied hand written letter from David P. Wheatland to Stephen T. Riley regarding the pantograph dated June 23 1961 (in instrument file)
Object number: 1998-1-1617
Walter Balcke
Date: 1952-1964
Accessories: mahogany case; two circular protractors; clear plexiglass rule with serated edge
Object number: 1990-5-0028
English
Date: circa 1880
Accessories: original case
Object number: DW0465
Walter Balcke
Date: circa 1958
Accessories: in library folder (Lib 4927):
-twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)
-three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department
-photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)
-photocopy of instructional card for object 1997-1-1671
- seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Brianchon's Concurrent Lines, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread
- photograph of the display case containing Balcke's models in the Harvard Mathematics department
Object number: 1997-1-1597