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Issue No.03 - July-September (1998 vol.20)
pp: 33-50
ABSTRACT
<p>The Mathematical Tables Project, one of the last large human computing groups, began operation in 1938 as a WPA project in New York City. Unlike preceding computing organizations, the Math Tables Project mass-produced calculations using unskilled labor. Prior to 1938, most hand computing organizations used well-educated computing assistants who could operate independently. Over its 10-year history, the Math Tables Project completed 28 published volumes of tables and calculations for dozens of scientific and war projects. During World War II, it acted as a general computing contractor for the Office for Scientific Research and Development and prepared LORAN Navigation Tables for the Navy. After the war, it was absorbed by the National Bureau of Standards. It proved to be a transitional institution in the history of computing, promoting mass scientific computation and developing the numeric methods that would eventually be used on electronic computers.</p>
CITATION
David Alan Grier, "The Math Tables Project of the Work Projects Administration: The Reluctant Start of the Computing Era", IEEE Annals of the History of Computing, vol.20, no. 3, pp. 33-50, July-September 1998, doi:10.1109/85.707573
REFERENCES
1. In this paper, the word "computer," when unmodified by the adjective "electronic" or "mechanical," will refer to a human being who was employed in the task of calculation.
2. When used without modifiers, the word "project" will refer to the Math Tables Project.
3. WPA regulations forbade selling the products of its projects. (A.N. Lowan to L. Briggs, 19 October 1939, Briggs Records.) The Math Tables Project circumvented this regulation by giving its manuscripts to the National Bureau of Standards, who in turn published them through Columbia University Press. Columbia University Press priced the volumes to cover its own costs. (L. Briggs to A.N. Lowan, 4 October 1939, Briggs Records.)
4. A. Lowan quoting F. Benford of General Electric Laboratory in The Whys and Wherefores of Mathematical Tables.New York: WPA, 1942.
5. R.C. Archibald, "Mathematical Table Makers, Portraits, Paintings, Busts, Monuments, Bio-Bibliographical Notes," Scripta Mathematica Studies, vol. 3, 1948.
6. Employment application, A. Lowan, January 1937, WPA Records.
7. A. Lowan, Applying Laplace Transform to Problem of Cooling of Earth, unpublished PhD thesis, Columbia Univ., 1934
8. D.A. Grier, "Gertrude Blanch of the Mathematical Tables Project," Annals of the History of Computing, vol. 19, no. 4, pp. 18-27, 1997.
9. At Cornell, Blanch was a member of Sigma Delta Epsilon, a sorority for women graduate students studying science. Many of the members were research assistants for male professors and did computation and data reduction. See Membership list, 1933-1934 and Annual Report, 1933-1934, Box 2, Sigma Delta Epsilon files, (37/4/835), Rare Book and Manuscript Collection, Carl A. Kroch Library, Cornell University.
10. D.A. Grier, op. cit.
11. G. Blanch, A.N. Lowan, R.E. Marshak, and H.A. Bethe, "The Internal Temperature Density Distribution of the Sun," J. Astrophysics, pp. 37-45, 1942. Bethe deeply valued the contribution of the Math Tables Project, stressing to his biographer the group's contributions. See J. Bernstein, "Profiles (Hans Bethe—Part 1)," New Yorker, 3 December 1979, pp. 50-107.
12. The division was originally called the "The National Applied Mathematics Laboratory," but this paper will use the modern name throughout. J. Curtiss, "The National Applied Mathematics Laboratory—a Prospectus," Internal Report of the National Bureau of Standards, Washington, D.C., 1947. Republished in Annals of the History of Computing, vol. 11, no. 1, pp. 12-30, 1989.
13. H. Salzer, "New York Mathematical Tables Project," Annals of the History of Computing, vol. 11, no. 1, pp. 52-53, 1989.
14. G. Blanch and I. Rhodes, "Table Making at N.B.S.," B.R. Scaife, ed. Studies in Numerical Analysis: Papers in Honor of Cornelius Lanczos.London: Academic Press, 1974.
15. R. Slutz, "Memories of the Bureau of Standards SEAC," N. Metropolis et al. eds. A History of Computing in the Twentieth Century.London: Academic Press, 1980, pp. 471-477.
16. D. Gurer, "Women's Contributions to Early Computing at the National Bureau of Standards," IEEE Annals of the History of Computing, vol. 18, no. 3, pp. 29-35, 1996.
17. A. Lowan, "The Computational Laboratory at the National Bureau of Standards," Scripta Mathematica, vol. 15, pp. 33-63, 1949.
18. A. Chandler, The Visible Hand.Cambridge, Mass.: Belknap Press, 1977, pp. 240-243.
19. See N. Oreskes, "Objectivity or Heroism? On the Invisibility of Women in Science," Osiris, 2nd Series, vol. 11, pp. 87-113, 1996.
20. Rossiter argues that computation was a job early classified as appropriate for women. See M. Rossiter, Women Scientists in America: Struggles and Strategies to 1940.Baltimore, Md.: Johns Hopkins Univ. Press, 1982, pp. 51-72. In academic and military settings, male students often filled this role. For example, at the Univ. of Chicago during the 1920s, the Dept. of Physics employed both the wife of a professor and a stream of graduate students. See Box XVI, Records of the Physics Dept., Special Collections, Univ. of Chicago.
21. P. Mack, "Women in Astronomy in the United States, 1875-1920," BA Honors Thesis, Harvard Univ., 1977.
22. M. Croarken, Early Scientific Computing in Britain, Oxford Univ. Press, Oxford, 1990.
23. T.A. Bancroft, "Roots of the Iowa State University Statistical Center: 1914-1950," Iowa State J. Research, vol. 57, no. 1, pp. 3-10, Aug. 1982.
24. H.T. Davis, Tables of the Higher Mathematical Functions, vol. 1. Bloomington, Ind.: Principia Press, 1933. H.T. Davis, Adventures of an Ultra-Crepidarian.San Antonio, Texas: Principia Press of Trinity College, 1962, pp. 270.
25. J.F. Brennan, The IBM Watson Laboratory at Columbia University.New York: IBM Corporation, 1971.
26. C. Christ, History of the Cowles Commission: Economic Theory and Measurement, a Twenty Year Research Report, 1932-1952.Chicago: Cowles Commission, 1952.
27. G.W. Baehne, ed., Practical Applications of the Punched Card Method in College and Universities.New York: Columbia Univ. Press, 1935, pp. 166-170.
28. P. Schwartz, "History of the Proving Ground," undated typescript, Aberdeen File, Oswald Veblen Papers, Library of Congress. P. Schwartz to O. Veblen, March4 1924, Correspondence, Oswald Veblen Papers, Library of Congress.
29. D.S. Howard, The WPA and Federal Relief Policy.New York: Da Capo Press, 1973 (c 1943). See also J.D. Millett, The Work Projects Administration in New York City, Public Administration Service, 1938.
30. The different accounts are somewhat contradictory on this point. The range is between 100 and 150.
31. Blanch and Rhodes, op. cit. Interview with Gertrude Blanch by H. Tropp, Smithsonian Archives Center, Record Group 196.
32. R. Kanigel, The One Best Way: Frederick Winslow Taylor and the Enigma of Efficiency.New York: Viking-Penguin, 1997.
33. Grier, op. cit.
34. Fig. 4high res imageis drawn from a diagram in Report of the New York Project for the Computation of Mathematical Tables, Feb.28 1942, WPA (765) Records.
35. Report of the New York Project for the Computation of Mathematical Tables, Feb.28 1942, WPA (765) Records. See also Lowan, op. cit.
36. See note 35 plus Interview with Gertrude Blanch by H. Tropp and A.N. Lowan to L.J. Comrie, April7 1939, Lyman Briggs Correspondence, 1939, N.B.S.-EC Records.
37. A. Lowan to L. Briggs Dec.22 1939, War Department Correspondence, Math Tables Project files, N.B.S.-EC Records..
38. F. Culled of the Army Corps of Engineers (Intelligence Branch) to General I. Huie, Administrator of the WPA, July1 1942, WPA (765) Records.
39. Culled of Army Engineers to General Huie, July1 1942, cited above.
40. See W. Weaver of the Applied Mathematics Panel to M.A. Chanderly of Consolidated Edison, 10 Feb. 1943 and W. Weaver to A. Lowan, Sept.1 1943, Correspondence of the Applied Mathematics Panel, 1942-1943, Box 15, AMP Records.
41. A. Lowan to R.W. Smith at N.B.S., Dec.21 1945, Briggs Records.
42. Lowan, op. cit., gives a detailed description of the methods of the project. The preface to each of the volumes of tables gives the specific computing method used for each mathematical function.
43. Blanch and Rhodes, op.cit.
44. Lowan, op. cit.
45. Lowan often had to prod the managers at the WPA to approve his computing plans so that the human computers would not run out of work. See Night Letter (special discount rate overnight telegram) from A. Lowan to L. Briggs, Aug. 1940, Briggs Records.
46. G.S. Bryan Rear Admiral of U.S. Navy (Ret.) hydrographer of Hydrographic Office to Major I.V.A. Huie, administrator of NYC Work Projects Administration, Jan.6 1943, WPA (765) Records.
47. Admiral G.S. Bryan to A. Lowan, 6 Jan. 1943, 28 Feb. 1942, WPA (765) Records. W. Weaver to D. Moreland, National Defense Research Council, Feb.15 1943, Applied Mathematics Panel Correspondence, 1942-1943, Box 16, AMP Records.
48. J.A. Pierce et al., Loran, Long Range Navigation.New York: McGraw-Hill, 1948, pp. 19.
49. Ibid., p. 404. M. Eastman to Admiral J. Furer, July2 1942, ONR General Records.
50. R. Schlatcher Officer in Charge of New York Hydrographic Institute to Hydrographer, Oct.9 1944, Hydrographic Records.
51. Officer in Charge of New York Hydrographic Institute to Hydrographer of the Navy, Oct.9 1944, Hydrographic Records.
52. See Monthly Reports of the Math Tables Project, 1943-1945, A.M.P. Records.
53. C. Reid, Neyman: From Life.New York: Springer Verlag, 1982, pp. 190. On 23 Nov. 1943, the Navy assigned Neyman to a special project for the Destruction of Obstacles to Landing Operations Committee.
54. Reid, op. cit., pp. 190.
55. Blanch interview with Thatcher.
56. W. Weaver to A. Lowan, Dec.10 1943, correspondence of the Applied Mathematics Panel, 1942-1943, Box 15, AMP Records.
57. A. Lowan, "Report on the War Work of the Math Tables Project," Box 26, A.M.P. Records.
58. Letter from M. Rees to A. Lowan, June21 1945, "On the Evaluation of a Certain Integral," General Correspondence of the Applied Mathematics Panel, Box 4, AMP Records.
59. W. Weaver to V. Bush, Aug.17 1945, General Correspondence of the Applied Mathematics Panel, AMP Records.
60. See A. Lowan to W. Weaver, 30 Sept. 1943; W. Weaver to G. Stibbitz, 20 June 1944; and M. Rees to O. Veblen, member of the Applied Mathematics Panel, June9 1945, Correspondence of the Applied Mathematics Panel concerning the Math Tables Project, File 3, Box 4, AMP Records.
61. Blanch and Rhodes, op. cit.
62. G. Blanch, Notes for a Class on Numerical Analysis, Taught 1943-1945 at the New York Mathematical Tables Project, Blanch Papers, Stern Family Collection.
63. Memo from A. Lowan to Math Tables Project Staff, Oct.16 1946, Monte Carlo Computations File (back used as scratch paper), AMP Records.
64. Gurer, op. cit.
65. Abramowitz and Stegun, eds., The Handbook of Mathematical Functions.Washington, D.C., Government Printing Office, 1965.
66. G. Dantzig, "Reminiscences About the Origins of Linear Programming," Operations Research Letters, vol. 1, no. 2, pp. 43-48, Apr. 1982; G. Dantzig, "Origins of the Simplex Method," S.G. Nash, ed. A History of Scientific Computing.New York: ACM Press, 1990. Linear programming is an optimization technique. In this test, it attempted to determine the cheapest diet, selected from 77 different foods, that would meet the nutritional requirements of the Air Force. It probably remains the largest linear programming problem ever done by hand.
67. G. Dantzig to J. von Neumann, Apr.28 1948, Correspondence "D," J. von Neumann Papers, Library of Congress. von Neumann's scribblings are incomplete.
68. See A. Lowan to W. Weaver, 22 Sept. 1945, General Correspondence of the Math Tables Project, AMP Records. A. Lowan to E. Condo, Jan.14 1946, N.B.S. Director's Records.
69. The move began in July and ended on 30 Sept. 1948. Reports of the National Bureau of Standards, March 1948 and September 1948.
70. Lowan, op. cit.
71. T. Fry to F.K. Richtmyer, Apr.3 1933, M.T.A.C. Records.
72. R. Cochrane, Measures for Progress.Washington, D.C.: Government Printing Office, 1966, p. 331. See also "Blue Folder Files," Civil Works Administration Projects folder #680, Boxes 46-47, Briggs Records.
73. J.M. Burns, The Lion and the Fox.New York: Harcourt Brace, 1954, p. 316.
74. Letter from P. Brockett to F. Lillie, Oct.21 1937, SAB Records.
75. H. Ickes, Secret Diary of Harold Ickes, vol. 2. New York: Simon and Schuster, 1954, p. 243.
76. T. Kessner, Fiorello La Guardia and the Making of Modern New York.New York: McGraw-Hill, 1989, p. 339.
77. P. Brockett to F. Lillie, Oct.18 1937, SAB Records.
78. Testimony of S. Katz before the House Committee on Un-American Activities, Feb. 1956, p. 3,400.
79. Washington, D.C., Street Directory for 1946,Washington, D.C.
80. Office memorandum no. 433, Oct.21 1937, SAB Records.
81. A. Barrows to F. Lillie, Oct.18 1937, SAB Records.
82. P. Brockett to F. Lillie, Nov.1 1937, SAB Records.
83. Proposal for a Project to Recompute Mathematical Tables, WPA (395) Records.
84. Herb Salzar and Ida Rhodes give two slightly contradictory stories about how Lowanwas recruited. Both claim that Dr. van Ostrand of the U.S. Geologic Survey brought Lowan to Briggs's attention. Salzar claims that the connection happened either through mathematicians at Columbia University or Brooklyn College (interview, Feb. 1996). Rhodes claims that von Ostrand read an article about Lowan in the "Sunday paper" (letter to Merzbach, files stored with Smithsonian Collections). Neither has first-hand knowledge of this event. Rhodes joined the project in 1940, while Salzar joined in 1941.
85. Letter from A. Barrows to F. Lillie, Jan.27 1938, SAB Records.
86. Minutes of National Research Council Executive Committee, Division of Physical Sciences Meeting, Apr.1 1938, National Research Council Records, National Academy of Sciences Archives.
87. Ida Rhodes, a mathematician who joined the Planning Committee in 1940, claims in an interview that the WPA provided no supplies and that the Planning Committee had to purchase pencils and paper for the computers. (Letter to Merzbach, files stored with Smithsonian Collections.) This is almost surely not true, as the records indicate.
88. See Rhodes, Letter to Merzbach, op. cit. G. Blanch, interview with H. Thatcher. In this interview, Blanch gives an especially telling account of her search for an office job in 1936. She recollects that out of 50 applicants, she was the only one who submitted a letter without grammatical errors.
89. A. Chandler, op. cit., pp. 240-244.
90. H.T. Davis, ibid.
91. Detailed descriptions of the computing plans are given in each of the major published volumes of the Math Tables Project.
92. M. Coarken, op. cit., pp. 23-46.
93. G. Blanch interview with H. Thatcher, Mar.17 1989, Stern Family Collection.
94. Blanch and Rhodes, op. cit. R. Merzbach letter. G. Blanch interview with H. Thatcher. Blanch Smithsonian interview.
95. Office Memorandum no. 433, Oct.21 1937, SAB Records.
96. Lowan to Briggs, Apr.13 1938, Briggs Records.
97. Mathematical Tables Project, Tables of the Exponential Function, Report of Official Project 765-97-3-10, New York, Federal Works Agency for the City of New York, 1939.
98. Mathematical Tables Project, Tables of the First 10 Powers of the Integers From 1 to 1,000, Report of Official Project 765-97-3-10, New York, Federal Works Agency for the City of New York, 1938.
99. J.H. Curtiss, "Review of Powers of Integers and the Exponential Function," Amer. Mathematical Monthly, vol. 48, no. 1, Jan. 1941.
100. See Lowan correspondence, N.B.S.-EC Records.
101. J. von Neumann to Lowan, Sept.19 1940, Box 15, AMP Records.
102. L. Briggs to A. Lowan, 22 Nov. 1939, and reply from Lowan, Nov.24 1939, Briggs Records.
103. A. Lowan to L. Briggs, June28 1939, Briggs Records.
104. L. Briggs to A. Lowan, July27 1939, Briggs Records.
105. Major H. Loper, Army Corps of Engineers, Intelligence Division, to A. Lowan, July1 1941, WPA (765) Records.
106. A.M. Schlesinger, Jr., The Politics of Upheaval.Boston: Houghton Mifflin, 1960, p. 348.
107. J.R. Beniger, The Control Revolution: The Technological and Economic Origins of the Information Society, Harvard University Press, Cambridge, Mass., 1986.
108. Bernstein, op. cit.
109. A. Lowan to H. Bethe, Nov.28 1938, Bethe File, AMP Records.
110. P. Morse, In at the Beginning.Cambridge, Mass.: MIT Press, 1977, p. 139.
111. K. Compton to Lowan, 20 Nov. 1940 and Weekly Reports, Oct.20 1941, WPA (795) Records.
112. A. Lowan to W. Weaver, 23 Dec.23, 1943, General Correspondence, AMP Records.
113. The original letter (dated 16 May 1941 and addressed To Whom It May Concern) read as follows: "The WPA project of computing mathematical tables, executed under the sponsorship of the National Bureau of Standards and the direction of Dr. Arnold N. Lowan, fills an important need which exists in mathematics, both for research work and for applied mathematics and physics. Dr. Lowan possesses the background and the qualifications to direct such work, and the result has fully justified the undertaking. I do not hesitate to express a feeling which is undoubtedly shared by most mathematicians, that work of real lasting value has been done." It was signed by J. von Neumann. Miscellaneous Correspondence "L," John von Neumann Papers, Library of Congress.
114. See A. Lowan to J. von Neumann, 7 May 1941; J. von Neumann to A. Lowan, 16 May 1941; A. Lowan to J. von Neumann, 17 May 1941; J. von Neumann to Lowan, May22 1941, Miscellaneous Correspondence "L," John von Neumann Papers, Library of Congress.
115. Chief of Medicine and Surgery to Office of Naval Research, Feb.17 1942, ONR Records.
116. Lowan could not even get a unanimous vote of support from his advisory board, the Committee on Mathematical Tables and Other Aids to Computation. See W.J. Eckert to R.C. Archibald, 7 Jan. 1942. Archibald, a supporter of Lowan and the Math Tables Project, chose to ignore Eckert's protest. See Archibald to "Gentlemen of the Committee on Mathematical Tables and Aids to Computation," Apr.20 1942, correspondence relating to the journal Mathematical Tables and Other Aids to Computation, Wallace Eckert papers, CBI 9, Charles Babbage Institute, University of Minnesota.
117. Officer of David Taylor Model Basin to Admiral Julius Furer, 10 Jan. 1942, ONR Records. It should be noted that this same officer quickly changed his opinions on such matters and soon became a strong advocate of large-scale computing. See Officer in charge of David Taylor Naval Basin, Nov.9 1943, ONR Records.
118. Diary of W. Weaver, Dec.10 1942, Box 15, AMP Records.
119. W. Weaver to D.L. Moreland, Feb.15 1943, Correspondence 1942-1943, AMP Records.
120. W. Weaver to J. Conant, Feb.3 1943, General Correspondence, 1943, A.M.P. Records.
121. W. Weaver to E.L. Moreland of the National Defense Research Council, Feb.15 1943, Correspondence of the Applied Mathematics Panel, 1942-1943, Box 15, AMP Records.
122. W. Weaver to J. Conant, May17 1943, Correspondence 1943, AMP Records.
123. See Eckert to Butler, 1 Feb. 1940, Box 1 and L. Goldberg to Eckert, Apr.18 1947, Wallace Eckert Papers, CBI 9, Charles Babbage Institute, Univ. of Minnesota.
124. W. Eckert to Archibald, Sept.16 1943, Correspondence relating to the journal Mathematical Tables and Other Aids to Computation, Wallace Eckert papers, CBI 9, Charles Babbage Institute, Univ. of Minnesota.
125. Letter from W.J. Eckert to D.W. Rubidge, Commercial Research Department of IBM, Jan.11 1941, Box 1, File Wallace J. Eckert papers, CBI 9, Charles Babbage Institute.
126. L.J. Comrie, "The Math Tables Project," mimeograph note attached to Lowan to Weaver, Mar.9 1944, AMP Records. Quoted by I. Rhodes in interview with H. Tropp, Record Group 196, Smithsonian Archives Center.
127. L.J. Comrie to J.L. Ginniff, May6 1942, WPA (765) Records.
128. Certain volumes of Math Tables Project tables can often be found in nearly pristine condition (albeit dusty) on the shelves of research libraries. However, the early electronic computing groups are also open to this charge. One of the first tasks undertaken by Aiken on the Mark I was to produce a large multivolume table of Bessel Functions. Rarely can one find a copy that shows any signs of use. The Math Tables Project also produced smaller tables, called "Lilliputian."
129. See note 127. Lowan often had to write WPA urging them to approve projects in order to keep the computers busy. See A. Lowan to L. Briggs, Aug.29 1940, Briggs Records.
130. See note 63.
131. W. Weaver to A. Lowan, Mar.9 1943, Correspondence, 1942-1943, AMP Records.
132. See note 119 and W. Weaver to LeMer, Feb.15 1943, Correspondence 1942-1943, AMP Records.
133. W. Weaver to L. Briggs, Feb.23 1943, Correspondence, 1942-1943, AMP Records.
134. W. Weaver to L. Briggs, Mar.8 1943, Correspondence, 1942-1943, AMP Records.
135. Report on War Service of the Math Tables Project, Dec.4 1945, Box 26, AMP Records.
136. See thread of correspondence on mechanical computation of tables that begins with W. Weaver to A. Lowan, Aug.25 1943, Correspondence, 1942-1943, AMP Records.
137. Letter from W. Weaver to L. Briggs, Apr.19 1943, Correspondence of the Applied Mathematics Panel, 1942-1943, Box 16, AMP Records. "From the work which is now before us, it seems clear that this project will be of very real usefulness in the war effort, and the amount of work promises to increase enough so that we felt it was only prudent to ask for $100,000 rather than the annual level of $75,000 which was proposed somewhat earlier."
138. W. Weaver to Dean H.V. Gaskill, Iowa State College, Nov.4 1943, Iowa State File, Box 20, AMP Records.
139. With most mathematicians, Weaver was relaxed and informal. He would occasionally call von Neumann "Johnny" or Oswald Veblen "Veb." However, he always called Arnold Lowan "Dr. Lowan" or "Mr. Lowan." Given that Lowan worked with these two mathematicians when he was at the Institute for Advanced Study, this seems ample evidence that Lowan never entered the social circle of U.S. mathematics. See General Correspondence, A.M.P. Records.
140. M. Rees to O. Veblen, June9 1945, Correspondence, 1945, AMP Records. This letter may be the first to use the retrologism "hand computing."
141. No footnote.
142. P. Morse to W. Weaver, Oct.20 1944, General Correspondence, AMP Records.
143. See note 140.
144. J. Curtiss to A. Lowan, Apr.12 1945, N.B.S. Director's Records.
145. A. Lowan to W. Weaver, 22 Sept. 1945, General Correspondence, AMP Records. E. Condon to A. Lowan, Jan.16 1946, N.B.S. Director's Records.
146. R.C. Archibald to R.C. Gibbs, Apr.27 1948, M.T.A.C. Records.
147. L. Issacson Representative of the 24th Congressional District of New York to E. Condon, June23 1948, N.B.S. Director's Records. See also J. Todd, Oral Interview, Archives, California Institute of Tech nology.
148. S. Finkelstein president, United Public Workers of America, Apr.9 1948, M.T.A.C. Records.
149. Todd Interview. Remarks by Curtiss, mimeographed document, M.T.A.C. Records.
150. Todd interview.
151. See J.D. Millett, op cit., pp. 52-56.
152. During World War II, a Harvard mathematician had attacked the Applied Mathematics Panel with the charge that it was incompetent. Careful study of his claims indicates that he was less concerned with the competency of the panel and more interested in the fact that it was dominated by mathematicians from New York City who did not seem to give many projects to Harvard's Mathematics Department. Marshall Stone File, AMP Records. For Curtiss's opinion on the relevancy to the Math Tables Project move, see J. Curtiss to J. Condo, Mar.6 1946, Director's Correspondence, N.B.S. Director Records.
153. Report from the Committee on Mathematical Tables and Other Aids to Computation, Apr. 1946, Records of the Division of Physical Sciences, National Research Council Archives, National Academy of Sciences.
154. Report 7 of the Eastern Assoc. for Computing Machinery, May30 1949, Folder 9, Box 1, Papers of E.C. Berkeley, CBI 50, Charles Babbage Institute. It should be noted that the EACM produced two newsletters labeled "Report 7." The first one is dated 25 Feb. 1949.
155. J. Gleick, Chaos: Making a New Science, Penguin Putnam, New York, 1987.
156. Salzer, op. cit.
157. The exact figure is impossible to determine without a detailed study of the records of Dover Publishing and the Government Printing Office, the two organizations that publish the handbook. No one connected with the publication of the handbook disputes that it has sold extremely well, and uninformed estimates of its sales range between 50,000 and 500,000. The estimate of 200,000 was achieved by compiling publication records from various editions of the book itself.
158. National Bureau of Standards, Applied Mathematics Laboratory, Projects and Publications, Washington, D.C., July 1965.
159. Monte Carlo File, Math Tables Project files, N.B.S.-EC Records. The back of the Mathieu Function sheet was used as scratch paper for Monte Carlo computations.
160. Math Tables Project files, N.B.S.-EC Records.
161. Lowan, op. cit.
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