# James B. Scarborough Papers, 1908-1966: Finding Aid

Published in June 2017

### Summary Information

**Publisher:**United States Naval Academy. Special Collections & Archives.**Publisher Address:**

589 McNair Road

Annapolis, Maryland 21402-5029, USA

Phone: 410-293-6917

https://www.usna.edu/Library/sca/index.php**Call number:**MS 447**Location:**Special Collections & Archives Department - Manuscripts**Title:**James B. Scarborough Papers**Dates:**1908-1966**Size:**1.88 linear feet**Container Summary:**4 manuscript boxes, 1 half-manuscript box**Creator:**Scarborough, James B. (James Blaine), 1885-**Language(s) of material:**English**Abstract:**James B. Scarborough was a professor of mathematics at the United States Naval Academy. The James B. Scarborough Papers span from 1908 to 1966, although a high percentage of the materials are undated. The papers focus on Scarborough's research, writings, and teaching in the fields of numerical analysis, differential equations, calculus, geometry, and trigonometry.

## Biography of James B. Scarborough

James Blaine Scarborough was born in Mount Gilead, North Carolina on June 22, 1885. After working for the Mount Gilead post office from 1905 to 1909, Scarborough enrolled at the University of North Carolina at Chapel Hill where he studied mathematics. Following graduation in 1913, Scarborough pursued master's level studies at the University of North Carolina for one year, and would ultimately earn a Ph.D. from Johns Hopkins in 1923. From 1914 to 1918, he served as an Instructor in Mathematics at N.C. State College. In January 1918, Scarborough was appointed to the faculty at the United States Naval Academy, where he taught until retiring with the rank of Professor on June 30, 1950. Upon his retirement, Scarborough received the title of Professor Emeritus.

While at the Naval Academy, Scarborough published numerous articles and papers, as well as *On the Computation of the Probable Error of a Weighted Mean* and *Numerical Mathematical Analysis*, the latter of which was used extensively during the development of early computers. Scarborough also settled numerous mathematical questions and devised new methods and formulas in the fields of the comparison of the inherent accuracy of quadrature formulas, the Theory of Errors, and the true elliptic path of projectiles in a vacuum, which was ultimately used to calculate the paths of V-2 rockets. In 1948, Scarborough was also appointed a consultant at the Naval Ordnance Laboratory in numerical analysis and the use of computers for solving differential and integral equations in fluid mechanics research. During his retirement, Scarborough continued his mathematical research and writing, publishing *The Gyroscope: Theory and Applications* and *Differential Equations and Applications for Students of Mathematics, Physics, and Engineering*. James B. Scarborough died of a stroke on December 29, 1974 in Annapolis, Maryland.

## Description of Contents

The James B. Scarborough Papers, comprising 1.88 linear feet of documentation, span from 1908 to 1966, although a high percentage of the materials are undated. The papers focus on Scarborough's research, writings, and teaching in the fields of numerical analysis, differential equations, calculus, geometry, and trigonometry.

The collection is composed of mathematical notes, articles, reports, and correspondence.

The Scarborough Papers are organized into two series by document type. Series 1: Writings and Publications consists of articles, reports, and manuscripts on various mathematical topics by both Scarborough and a selection of other notable mathematicians. Series 2: Research Notes consists of Scarborough's handwritten formulas, mathematical problems, and solutions on various topics related to both his writings and his teaching at the United States Naval Academy.

## Arrangement

The James B. Scarborough Papers are organized into the following two series:

- Series 1: Writings and Publications, 1925-1966
- Subseries 1a: Scarborough, 1925-1965
- Subseries 1b: Others, 1926-1966
- Series 2: Research Notes, 1908-1962

## Access and Use

### Access

Access is unrestricted.

### Copyright and Permission

The James B. Scarborough Papers are the physical property of Nimitz Library. Copyright belongs to the authors or creators of the works, or their legal representatives. For further information, consult the Head, Special Collections & Archives.

It is the responsibility of the researcher to secure written permission to publish, reprint, or reproduce material from Special Collections & Archives. The researcher assumes responsibility for infringement of copyright or literary or publication rights. Please contact the Head, Special Collections & Archives for permission to publish and for further information.

## Acquisition and Appraisal

### Provenance and Acquisition

Gift of William K. Scarborough in May 1984. Accession No. 84-15.

## Related Materials

### Related Archival Material

Additional material pertaining to the life and career of James B. Scarborough may be found in his Civilian Personnel Jacket and in the Special Collections Vertical File, Special Collections & Archives, Nimitz Library.

### Materials Cataloged Separately

No materials have been removed from this collection and cataloged separately.

## Processing and Other Information

Collection arrangement imposed during processing. Folder titles supplied by James B. Scarborough prior to accessioning.

### Preferred Citation

James B. Scarborough Papers, MS 447

Special Collections & Archives Department

Nimitz Library

United States Naval Academy

### Processing Information

This collection was processed by David D'Onofrio in June 2017. Finding aid written by David D'Onofrio in June 2017.

## Subject Headings

### Name and Subject Terms

- Coriolis force
- Differential equations
- Mathematical physics
- Mathematics
- Mathematics -- Formulae
- Numerical calculations
- Scarborough, James B. (James Blaine), 1885-

### Genre Terms

- Articles
- Faculty papers
- Manuscripts
- Reports
- Research notes

## Contents List

### Series 1: Writings and Publications, 1925-1966 Boxes 1-2

**Series Description**

Published articles, lectures, and reports, as well as manuscript material written by Scarborough and other mathematicians. The writings focus heavily on numerical analysis and numerical integration, as well as analytic geometry and trigonometry.

**Series Arrangement**

Organized into two subseries by author.

#### Subseries 1a: Scarborough, 1925-1965 Boxes 1-2

**Subseries Description**

Articles, reports, and manuscripts written by Scarborough on mathematical subjects such as numerical analysis, Simpson's Rule, Weddle's Rule, linear interpolation, and parabolic curves, as well as applied mathematical topics such as aerodynamic lift and the weight of sea water. In addition to published articles, the subseries includes research notes and correspondence, as well as manuscript notes detailing the problems and solutions presented in Scarborough's textbook *Numerical Mathematical Analysis*.

**Subseries Arrangement**

Arranged chronologically.

#### Subseries 1b: Others, 1926-1966 Box 2

**Subseries Description**

Articles, reports, and lectures produced by mathematicians other than Scarborough, including Milton Abramowitz, Ernest William Brown, Richard Courant, Prescott Durand Crout, R. T. A. Innes, Charles-Jean de la Vallee Poussin, and Edward Willis. The writings focus on such topics as integrals, numerical analysis, and analytic geometry. Included among the writings are occasional pieces of correspondence.

**Subseries Arrangement**

Arranged alphabetically by Scarborough's original folder titles and article/publication title.

### Series 2: Research Notes, 1908-1962 Boxes 2-5

**Series Description**

Handwritten notes consisting primarily of mathematical formulas, problems, and their solutions. The notes focus on such subjects as Coriolis acceleration, the mathematics of curved surfaces, transformation of coordinates, differential equations, and the curvature of the Earth. Included among the notes are occasional lesson plans and hand-outs for use in Scarborough's classes.

**Series Arrangement**

Arranged alphabetically according to Scarborough's original folder titles.

#### Mathematical Notes, 1929-1943, undated

"1. The Delta-Epsilon Proof; 2. Wind Pressure; 3. Finding Center of a Central [Cone?]; 4. Brodetsky and Smeal's Treatment of Graeffe Method; 5. Bipolar Coordinates; 6. Weber's Treatment of Regula Falsi Method; 7. Huygens' approximation to Circular Arcs; 8. Parabolas as Limiting Form of Ellipse on Hyperbola; 9. Deming's papers on Least Square." Also includes materials on ballistics and Lobatto's Modification of Gauss's Quadrature Formula.