Skip to main content Skip to footer site map
Nimitz Library
Nimitz Library

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
  • Call number: MS 447
  • Location: Special Collections & Archives Department - Manuscripts
  • Title: James B. Scarborough Papers
  • Dates: 1908-1966
  • Size: 1.9 linear feet (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, comprising 1.9 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.

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.

Back to Top

Description of Contents

The James B. Scarborough Papers, comprising 1.9 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.

Back to Top


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
Back to Top

Access and Use


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.

Back to Top

Acquisition and Appraisal

Provenance and Acquisition

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

Back to Top

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.

Back to Top

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.

Back to Top

Subject Headings

These materials have been indexed in the Naval Academy Library online catalog using the following terms. Those seeking related materials should search under these terms.

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
Back to Top

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.

Box 1 Folder 1
"Some Problems on the Lift and Rolling Moment of Airplane Wings", 1925

National Advisory Committee for Aeronautics Report No. 200.

Box 1 Folder 2
"Formulas for the Error in Simpson's Rule", 1926

Published in The American Mathematical Monthly.

Box 1 Folder 3
"On the Relative Accuracy of Simpson's Rules and Weddle's Rule", 1927

Published in The American Mathematical Monthly.

Box 1 Folder 4
"On the Relative Accuracy of Simpson's Rules and Weddle's Rule. A Reply", 1927

Published in The American Mathematical Monthly.

Box 1 Folder 5
"The Invalidity of a Commonly Used Method for Computing a Certain Probable Error", 1929

Published in The Proceedings of the National Academy of Sciences.

Box 1 Folder 6
"The Weight of Sea Water and Its Variation with Salinity and Temperature", 1930

Published in United States Naval Institute Proceedings.

Box 1 Folder 7
"Numerical Mathematical Analysis", 1930

Overview of Scarborough's book of the same title.

Box 1 Folder 8-12
Solutions to Exercises in Numerical Mathematical Analysis, 1930 (approximate)
Box 2 Folder 1
Solutions to Exercises in Numerical Mathematical Analysis, 1930 (approximate)
Box 2 Folder 2
"Kryloff on Mathematical Physics", 1932

Published in Bulletin of the American Mathematical Society.

Box 2 Folder 3
"On the Computation of the Probable Error of a Weighted Mean", 1935

Published in The American Mathematical Monthly.

Box 2 Folder 4
Paper Presented at Swampscott, Mass., 1940 June 27
Box 2 Folder 5
"Linear Interpolation with Several Variables", 1944

Includes drafts and research notes.

Box 2 Folder 6
"The Caustic Curve of an Off-Axis Parabola", 1963-1965

Published in Applied Optics. Includes correspondence and research notes.

Box 2 Folder 7
"Differential Equations and Applications", undated

Promotional leaflet for Scarborough's Differential Equations and Applications for Students of Mathematics, Physics, and Engineering.

Box 2 Folder 8
Manuscript and Other Material for "Numerical Integration" for Handbook of Engineering Mechanics, undated

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.

Box 2 Folder 9
"Aeronautical Services, Inc.", undated

Pamphlet of products and services.

Box 2 Folder 10
"Application of Siacci's Method to Flat Trajectories" by H. P. Hitchcock and R. H. Kent, 1938

Aberdeen Proving Ground Ballistic Research Laboratory Report No. 114.

Box 2 Folder 11
Courant's "Advanced Methods in Applied Mathematics", 1941

Notes of New York University lecture course by Richard Courant.

Box 2 Folder 12
Cowell's Method of Numerical Integration, Rice Institute Pamphlets by E. W. Brown and Vallee-Poussin. Also Crout's Paper on Integral Equations, 1925-1940
Box 2 Folder 13
"On the Practical Evaluation of Integrals" by Milton Abramowitz, 1954
Box 2 Folder 14
Paper on Numerical Analysis by L. E. Jones, University of Toronto, 1966, undated
Box 2 Folder 15
"Spherical Analytic Geometry" by Edward J. Willis, 1926
Box 2 Folder 16
Miscellaneous Correspondence, 1952

Cover letters for publications submitted to Scarborough.

Back to Top

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.

Box 2 Folder 17

Acceleration in Polar and Spherical Coordinates, undated

Box 2 Folder 18

Angular Velocity of the Earth's radius drawn to a vehicle at any place and time, undated

Box 2 Folder 19

Approximation Methods in Applied Mathematics, also Differentiation under the Integral Sign, undated

Box 2 Folder 20

Asymptotes and Infinite Roots, undated

Box 3 Folder 1

Bernoulli's Theorem, undated

Box 3 Folder 2

Binary Scale of Notation, undated

Box 3 Folder 3

Calculus of Variations from Byerly and Wilson, undated

Box 3 Folder 4

Certain Tough Types of Differential Equations, undated

Box 3 Folder 5

Change of Variables in Derivatives, undated

Box 3 Folder 6

Concerning Gravity and Other Matters Pertaining to the Shape of the Earth, including Parvin's Lecture Notes, 1960-1962, undated

Includes lecture notes for Richard H. Parvin's "The Earth and Inertial Space."

Box 3 Folder 7

Coriolis Acceleration, undated

Box 3 Folder 8

Coriolis Acceleration: Extracts from Moulton, Appell, and Craig, undated

Box 3 Folder 9

Coriolis Problem: Range of Projectile at Equator, undated

Includes printed material for classroom use.

Box 3 Folder 10

Derivation of Short Rule on Wallis's Formulas, undated

Box 3 Folder 11

Differences in Terms of Derivatives, undated

Box 3 Folder 12

Distance from a Point to a Curve on a Surface, undated

Box 3 Folder 13

Double Pendulum, undated

Also referred to as the bell and clapper problem.

Box 3 Folder 14

Examples in Complex Numbers, undated

Box 3 Folder 15

Examples in Fine's Calculus, undated

Box 3 Folder 16

Examples in Trigonometric Analysis (Wilczysnki's Trig Series), undated

Box 3 Folder 17

Formulas Giving the Difference between the Arc and Chord of a Circle, based on the Huygens Formula, undated

Box 3 Folder 18

Fourier Series Problem, undated

Box 3 Folder 19

German Words, undated

Notebook of German words and phrases.

Box 3 Folder 20

Heat Conduction and Insulation, undated

Box 3 Folder 21

Improper Integrals and Principal Values, undated

Box 3 Folder 22

Interesting Problems on Various Topics, undated

Box 3 Folder 23

Interpolation Formulas, undated

Box 3 Folder 24

Investigation on Willis Method, 1955-1956, undated

Box 4 Folder 1

Lesson Assignments, 1946-1959

Syllabi for Scarborough's math classes.

Box 4 Folder 2

Math Notes, undated

"This envelope contains: 1. Original drawings of Projectile Problem; 2. Lagrange's and Laplace's Theorems; 3. Formulas for computing the differences of two nearly equal quantities; 4. Scrap material relating to 2 and 3 above; 5. Data on the dimensions of the Earth.

Box 4 Folder 3

Mathematical Geography: Geographical Applications of the Law of Cosines, 1948, undated

Includes printed material for classroom use.

Box 4 Folder 4

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.

Box 4 Folder 5

Mathematical Problems,

"Vertical curves; Prismoidal Formula; Steering (automatic) Problem; Shaft Alignment, Mathematics of; Strong Man Pulling Fire Engine; General Compound Pendulum Swinging Gate."

Box 4 Folder 6

Mathematics of Barrels, undated

Box 4 Folder 7

Middlemiss Calculus Problems, undated

Box 4 Folder 8

Miscellaneous Math, undated

Box 4 Folder 9

Miscellaneous Mathematical Problems, undated

"Curvilinear Motion, Falling Parachutes, Stresses in Fly Wheels, Dynamics of Agility, Growth of a dollar at compound Interest, and several others."

Box 4 Folder 10

Non-Homogeneous Partial Differential Equations of the Second Degree, undated

Box 4 Folder 11

Non-Linear Vibrations, 1942 (approximate)

Notes by J. J. Stoker and A. S. Peters.

Box 4 Folder 12

Notes on Luroth, undated

Box 4 Folder 13

On Reading Verniers, Also other matters pertaining to Surveying, undated

Box 4 Folder 14

Partial Differentiation, undated

Box 4 Folder 15

Planimeter Data, Operation, and Theory, 1908-1949, undated

Includes copies of several planimeter manuals by Keuffel & Esser Co.

Box 4 Folder 16

Population Problem, undated

Box 5 Folder 1

Reduction of the General Equation of the Second Degree and Reduction of a Quadratic Form to a Sum of Squares, undated

Box 5 Folder 2

Ritz Method, undated

Box 5 Folder 3

Roots of Numerical Equations, undated

Includes printed material for classroom use.

Box 5 Folder 4

Solution of Spherical Triangles, 1948, undated

Includes printed material for classroom use.

Box 5 Folder 5

Surveying Problems, undated

Box 5 Folder 6

Thermodynamics Problems from Allen and Bursley's "Heat Engines", undated

Box 5 Folder 7

Tidal Forces, undated

Box 5 Folder 8

Tilt of Trunnions, undated

Box 5 Folder 9

Transformation of Coordinates, undated

Box 5 Folder 10

Transformation of Coordinates by Means of Euler's Angles, undated

Box 5 Folder 11

Uniform Convergence, undated

notes, problems, and solutions

Box 5 Folder 12

Variation of Curvature of the Earth with Horizontal Distance, undated

Box 5 Folder 13

Wallis's Formulas, undated

Includes printed material for classroom use.

Back to Top