1864 — Smallpox, Fort Alton IL/54, Chicago/283, Philly/260, Northern VA/112, SC, DC-712

 — 712  Blanchard tally of Alton and Chicago, IL and Northern VA fatalities noted below.[1]

District of Columbia ( >3)

–>3  Jan 13. NY Times. “From Washington…The Reports About Small-Pox.” 1-13-1864, p. 1.[2]

—  ?  Jan 14. NYT. “House of Representatives…Small-Pox in the District…” 1-14-1864, p.8.[3]

—  ?  Feb 1. Sixty smallpox cases were reported amongst 27 physicians at a business meeting.[4]

 

Illinois                        (337)   Chicago (283) and Fort Alton Prison (54)

–283  Chicago. Historical Society of Chicago, Encyclopedia of Chicago, “Epidemics”

–283  Chicago (presumably). Illinois State Board of Health. 1883, p. 332.

–283  Chicago. U.S. National Board of Health. Annual Report of the Board 1883, p. 134.[5]

—  54  Fort Alton, IL. Kempland. “Confederate POW Burials…Smallpox Island, Alton, IL.” 2004.[6]

 

Pennsylvania             (260)   Philadelphia

–260  Philadelphia. City of Philadelphia Annual Report (Volume III), 1907, p. 99.[7]

 

South Carolina          (<20)   Hilton Head Island

–>20.  Hilton Head. Downs. “Freed Slaves Battle Small Pox…Other Diseases,” Historynet.com[8]

 

Tennessee                   (     )

–?  Nashville. Cumberland Hospital. NYT. “From Tennessee…Small-Pox Hospital….” 5-21-1864, p8.[9]

 

Virginia                      (112)   Especially Claremont Smallpox Hospital, Fairfax County.

–112  Smallpox Hospitals, Feb-Nov 1864.[10]

—    1  Camp Casey, Arlington, May 22. Pvt. James R. Phillips, 20, Co. E, 29 USCI.[11]

–108  Claremont Smallpox Hospital, Fairfax County.[12]

–1  Jan 30, 1864. John Botts or Bolt, 3. (Dennee, p. 23.)

— 35  Claremont Smallpox Hospital, Feb 1864 (32 Small Pox; 3 Varioloid).[13]

–1  Feb 5, 1864. Unknown child, 9 months. (Dennee, p. 38.)

–1  Feb 6, 1864. Lucinda Wormley, 35. (Dennee, p. 41.)

–1  Feb 9, 1864. Thompson Blanon or Blanham, 28. (Dennee, p. 23.)

–1  Feb 9, 1864. Jessie Payne, 26. (Dennee, p. 34.)

–1  Feb 10, 1864. Larking Diggs, 28. (Dennee, p. 27.)

–1  Feb 10, 1864. Andrew Savage, 19. (Dennee, p. 35.)

–1  Feb 10, 1864. Elizabeth Thompson, 4. (Dennee, p. 37.)

–1  Feb 11, 1864. Mary Banks, 36. (Dennee, p. 22.)

–1  Feb 14, 1864. Henry Handley, 16. (Dennee, p. 29.)

–1  Feb 20, 1864. Ann Banks, 23. (Dennee, p. 22.)

–1  Feb 21, 1864. Lucy Marshall, 25. (Dennee, p. 32.)

–1  Feb 22, 1864. William Craig, 7. (Dennee, p. 26.)

–1  Feb 23, 1864. Philip Elkins, 21. (Dennee, p. 27.)

–1  Feb 23, 1864. William Hutchinson, 1. (Dennee, p. 29.)

–1  Feb 24, 1864. Lewis Franklin or Walker, 30. (Dennee, p. 28.)

–1  Feb 24, 1864. Frank Wilson, 25. (Dennee, p. 41.)

–1  Feb 26, 1864. Philo or Philip Payne, 27. (Dennee, p. 34.)

–1  Feb 27, 1864. Jackson Fisher, 40. (Dennee, p. 27.)

–1  Feb 27, 1864. Edward Randolph, 22. (Dennee, p. 34.)

–1  March 2, 1864. Hugh Brown, 19 (varioloid and measles). (Dennee, p. 24.)

–1  March 6, 1864. William Cox, 25. (Dennee, p. 26.)

–1  March 6, 1864. Samuel Dixon, 21. (Dennee, p. 27.)

–1  March 7, 1864. John McIntosh, 13. (Dennee, p. 32.)

–1  March 8, 1864. Edmund Davis, 40. (Dennee, p. 26.)

–1  March 10, 1864. Henry Johnson, 70. (Dennee, p. 30.)

–1  March 11, 1864. Lucretia Craig, 30. (Dennee, p. 26.)

–1  March 11, 1864. Eliza E. Young, 7. (Dennee, p. 42.)

–1  March 12, 1864. Jane Greene, 10. (Dennee, p. 28.)

–1  March 13, 1864. William Cook, age not noted. (Dennee, p. 26.)

–1  March 13, 1864. Richard B. Willis, 26. (Dennee, p. 41.)

–1  March 15, 1864. James H. Banks, 25. (Dennee, p. 22.)

–1  March 15, 1864. Elijah Dickinson, 21. (Dennee, p. 27.)

–1  March 16, 1864. Mark Ferguson, 8. (Dennee, p. 27.)

–1  March 17, 1864. William F. D. Canley, 4. (Dennee, p. 25.)

–1  March 17, 1864. John Simms, 40. (Dennee, p. 35.)

–1  March 25, 1864. Amy Jones, 40. (Dennee, p. 31.)

–1  March 26, 1864. Taylor Blackwell, 15. (Dennee, p. 23.)

–1  March 26, 1864. William Ferguson, 30. (Dennee, p. 27.)

–1  March 27, 1864. Eliza Brown, 3 months. (Dennee, p. 24.)

–1  March 27, 1864. Silas Nickson, 23. (Dennee, p. 34.)

–1  March 28, 1864. Henry Jones, 6. (Dennee, p. 31.)

–1  March 30, 1864. Littleton Canley, 40. (Dennee, p. 25.)

–1  March 30, 1864. Frank Whiting, 35. (Dennee, p. 40.)

–1  March 31, 1864. Flora Johnson, 31. (Dennee, p. 30.)

–1  March 31, 1864. Forrester Mason, 35. (Dennee, p. 32.)

–1  March 31, 1864. William Washington, 30. (Dennee, p. 40.)

–1  April 1, 1864. Fanny Taylor, 31. (Dennee, p. 36.)

–1  April 2, 1864. Samuel Neffer, 70. (Dennee, p. 33.)

–1  April 6, 1864. Arthur Freeman, 27. (Dennee, p. 28.)

–1  April 8, 1864. Laura Beverly, 4. (Dennee, p. 23.)

–1  April 8, 1864. William Thornton, 40. (Dennee, p. 38.)

–1  April 11, 1864. Milly Gibson, 16. (Dennee, p. 28.)

–1  April 11, 1864. Dolly Ann Nickson, 24. (Dennee, p. 34.)

–1  April 12, 1864. Richard Payton, 3. (Dennee, p. 34.)

–1  April 13, 1864. George Rolls or Ralls, 19. (Dennee, p. 35.)

–1  April 14, 1864. Elias A. Brown, 10. (Dennee, p. 24.)

–1  April 15, 1864. Maria Thornton, 2. (Dennee, p. 37.)

–1  April 16, 1864. Harriet Beverly, 6. (Dennee, p. 23.)

–1  April 17, 1864. Bernard Blackwell, 2. (Dennee, p. 23.)

–1  April 17, 1864. Milly Green or Greene, 50. (Dennee, p. 28.)

–1  April 20, 1864. Benjamin Harris, 20. (Dennee, p. 29.)

–1  April 22, 1864. Davenport Thornton, age not noted. (Dennee, p. 37.)

–1  April 23, 1864. Lewis Edwards or Edward Lewis, 22. (Dennee, p. 27.)

–1  April 23, 1864. Jane Thornton, 6. (Dennee, p. 37.)

–1  April 26, 1864. Berty Washington, 16. (Dennee, p. 38.)

–1  April 28, 1864. Oscolia Fields, 13. (Dennee, p. 27.)

–1  May 2, 1864. Griffin Ricks, 37. (Dennee, p. 34.)

–1  May 5, 1864. Martin Carter, 20. (Dennee, p. 25.)

–1  May 5, 1854. Lewis Dent, 35. (Dennee, p. 27.)

–1  May 6, 1864. Caroline Brown, 12. (Dennee, p. 24.)

–1  May 6, 1864. Jerry Newby, 10. (Dennee, p. 33.)

–1  May 12, 1864. Charles Thompson, 1. (Dennee, p. 37.)

–1  May 15, 1864. George W. Brink. (Dennee, p. 24.)

–1  May 17, 1864. Mary J. Miles, 6 months. (Dennee, p. 33.)

–1  May 18, 1864. Thomas Alexander, 50 (gov. employee). (Dennee, p. 22.)

–1  May 19, 1864. Martha A. Miles, 6 months. (Dennee, p. 33.)

–1  May 20, 1864. Leanna Davis, 40. (Dennee, p. 26.)

–1  May 22, 1864. Sarah Dorsey or Darcy, 30. (Dennee, p. 27.)

–1  May 22, 1864. Charles H. Harris, 31. (Dennee, p. 29.)

–1  May 28, 1864. Ada Coleman, age not noted. (Dennee, p. 26.)

–1  June 12, 1864. Pvt. Cato Flowers, Co. C/H, 29 USCI. (Dennee, p. 43.)

–1  June 14, 1864. Pvt. Wesley Jacobs, 20, Co. F, 5 MA Cav. (Dennee, p. 44.)

–1  June 15, 1864. Caroline Neil, 18. (Dennee, p. 33.)

–1  June 16, 1864. Hennie Neil, 30. (Dennee, p. 33.)

–1  June 21, 1864. Josiah Mackey, 20. (Dennee, p. 32.)

–1  July 1, 1864. Eveline Carter, 30. (Dennee, p. 25.)

–1  July 8, 1864. Angeline Bole, 16. (Dennee, p. 23.)

–1  Aug 1, 1864. Unknown man. (Dennee, p. 38.)

–1  Aug 21, 1864. Henry Williams, 6 or 30. (Dennee, p. 40.)

–1  Aug 22, 1864. Virginia Carter, 3. (Dennee, p. 25.)

–1  Dec 17, 1864. Jane Coleman, 22. (Dennee, p. 26.)

— 1  “Field” noted as location, May 18. Virginia Collins, 18. (Dennee, p. 26.)

— 1  L’Ouverture Hosp., Alexandria, March 8. Robert/Richard Johnson, 15 or 16.[14]

— 1  Regimental Hosp, May 12. Pvt. Cyrus Gasper, 19, Co. K, 39 USCI. Dennee, 44.

 

—  1  Unknown location (presumably VA), unknown soldier, age not noted, March 19.[15]

 

Narrative Information

 

Dennee: “The disease prevailed to a greater extent among troops in the vicinity of cities than among those in the field. Thus, during the year of greatest prevalence there were as many cases among the 30,000 men in the Department of Washington as among the 104,000 in the Army of the Potomac… The cases reported from the Army of the Potomac were mostly due to exposure in the cities of Washington and Alexandria. The sufferers were usually men recently returned from furlough or general hospital….

 

“Small-pox prevailed to a greater extent among the colored troops than among the white commands. During the three years of their service 6,716 cases, with 2,341 deaths, were reported. The cases equaled an average annual rate of 36.6 per thousand strength, the deaths a rate of 12.2… The maximum in 1864 occurred in March, when 8.04 cases per thousand was attained; in 1865 a maximum of 3.57 was recorded in February; in 1866 the highest rate, 9.73, was reached in March. During the first winter the prevalence of the disease was due to the operation of causes similar in character to those affecting the white troops; but the contagion had a wider diffusion and found a greater susceptibility to its action among the negroes than among the whites. The smaller rate of the second winter is the result of efforts to suppress the disease, while its prevalence in the year following the war gives expression to the carelessness which arose from anticipations of disbandment.”  (p. 5)

 

“By the end of January 1864, the numerous outbreaks of the disease among a growing population rendered insufficient the capacity of the army smallpox hospitals in Washington, and the Claremont staff began to treat soldiers as well as civilians of all colors. In mid March there were 113 patients, 50 of whom were soldiers.[16] African-American civilians in the Claremont Eruptive Fever General Hospital—now a branch of Alexandria’s Third Division General Hospital—continued to comprise more than half of all patients as they were joined in their misery by many black troops, especially members of the 23rd U.S. Colored Infantry.[17] Initially intended to accommodate 80 beds, the facility’s civilian patients were said to have numbered as many as 140 in early 1863. The capacity later grew to 164 or 174—perhaps only because 164 was the maximum number of patients at one time (April 29-30, 1864) while a military hospital. But although it had had as many as 170 sick civilians during an outbreak in mid 1863, the hospital seems to have possessed few more than 150 actual beds ever.[18]” (pp. 9-10)

 

““Inoculating all those who could be exposed to the smallpox virus was a huge challenge, made all the more desperate by the fact that there was little doctors could do for patients who developed a severe case. The afflicted had to struggle through or die. Smallpox hospitals were primarily quarantine facilities, established for the welfare of the community more than that of the patients. Treatments were mostly palliative; perhaps the most common “medicine” was alcohol, in the form of whiskey, brandy, wine, ale and porter, often administered alone or to wash down other substances.[19] It was not that doctors failed to try. The records of Washington’s Kalorama Eruptive Fever Hospital indicate that its staff administered a range of materia medica including, but not limited to, calomel (mercurous chloride), tincture of sulphur, tincture of ferric chloride, potassium chloride, zinc sulphate, glycerine, slippery elm, mustard, morphine, quinine, tincture of cinchona, ‘milk punch,’ seltzer with lemon, and remarkably, ‘lead water to [the] throat.’[20] One of many unsuccessful cures was attempted at Claremont in the spring of 1864, when John Thomas Lane was permitted to test on patients an old American Indian remedy, the northern pitcher plant (Sarracenia pupurea). After several weeks’ observation by the doctors of the Third Division General Hospital, this herb ‘proved to be without any curative powers in this disease, and Mr. Lane a humbug. He lost more than fifty per cent. of the cases of variola committed to him, more than were lost by any other treatment.’[21] (p. 11) ….

 

“Nearly 28 percent of patients died at Claremont, consistent with historical fatality rates. Assuming accurate records, 79 percent of the Claremont dead had not been vaccinated (90 percent in the above sample), seventeen percent had, and the vaccination status for four percent is unknown. None of these numbers, including the ages of those who were infected or died, can be claimed as a representative sample of Alexandria’s civilian African-American population. The very young and very old were presumably the most vulnerable, and death rates had been historically much higher for infants and children. The median age at death at Claremont was a little over twenty years, suggesting that a great number of these deaths were indeed among minors—as young as three, six and nine months—but many of the youngest afflicted may have simply perished in their homes. Indeed, many people succumbed before making it to a hospital, including 30-year-old William Craig, who perished near the Quartermaster’s office (northeast corner of Princess and Fairfax Streets).[22] Some were at death’s door when admitted, including some not lucid enough to provide their names.” (p.21) (Dennee, Tim and Friends of Freeedmen’s Cemetery. African-American Civilians and Soldiers Treated at Claremont Smallpox Hospital, Fairfax County, Virginia 1862-1865. 11-24-2011 modification.)

 

Downs: “….By 1864 the virus was cropping up throughout the South. Describing his experience in Hilton Head, S.C., in 1864, a freedman recounted the initial symptoms of a smallpox infection: ‘We tuck down wid feber…’case we hasn’t got nuttin’ for keep warm.’ In one colony in Hilton Head where former slaves took refuge, smallpox killed freed people by ‘tens and twenties.’

 

“As one Freedmen’s Bureau official noted in 1864, “In country parishes where vaccination is not the custom, with no physician near, where the colored children are poorly fed and clad, and much exposed, they sicken, die, and are buried, without a record of their numbers.” The Christian Recorder added, ‘You may see a child well and hearty this morning, and in the evening you will hear of its death.’”

 

District of Columbia

 

Jan 7: “Mr. Brandegee (Conn.) offered a resolution that the Committee for the District of Columbia be instructed to call the attention of the municipal or other authorities to the extension and prevalence of the small-pox in the District of Columbia, and urge the necessity or suitable sanitary regulations, and some compulsory system of vaccination to prevent the further spread of this terrible scourge of mankind. Mr. Cox (Ohio) thought that the appeal to the municipal authorities there would be ineffectual. The resolution was adopted.” (Philadelphia Inquirer. “House of Representatives. Small-pox in the District.” 1-7-1864, p. 4.)

 

Source

 

Chicago Historical Society. “Epidemics.” The Electronic Encyclopedia of Chicago. 2005. Accessed 12-26-2008 at: http://www.encyclopedia.chicagohistory.org/pages/432.html

 

City of Philadelphia. First Annual Message of John E. Reyburn, Mayor of the City of Philadelphia with the Annual Reports of the Departments of Public Health and Charities, Supplies, Public Education, Law, City Controller, City Treasurer, Commissioners of the Sinking Funds, Receiver of Taxes, and Board of Revision of Taxes for the Year Ending December 31, 1907 (Vol. III). Philadelphia: Dunlap Printing Co., 1908. Google digitized. Assessed 12-5-2012: http://books.google.com/books?id=0ihNAAAAMAAJ&printsec=frontcover#v=onepage&q&f=false

 

Dennee, Tim, and the Friends of Freeedmen’s Cemetery. African-American Civilians and Soldiers Treated at Claremont Smallpox Hospital, Fairfax County, Virginia 1862-1865. 11-24-2011 modification. Accessed 1-21-2015 at: http://www.freedmenscemetery.org/resources/documents/claremont.pdf

 

Downs, Jim. “Freed Slaves Battle Small Pox and Other Diseases,” Historynet.com, originally published in Civil War Times, June 2013, adapted from his book: Sick From Freedom: African-American Illness and Suffering During the Civil War and Reconstruction. Oxford University Press, 2012. Accessed 11-18-2019 at: https://www.historynet.com/dying-to-be-free.htm

 

The Friends of Freedmen’s Cemetery. “African-American Civilians and Soldiers Treated at Claremont Smallpox Hospital…” Accessed 12-26-2008 at: http://www.freedmenscemetery.org/resources/resources.shtml

 

Illinois State Board of Health. Fifth Annual Report of the State Board of Health of Illinois.  Springfield, IL: H. W. Rokker State Printer and Binder, 1883. Digitized by Google at:  http://books.google.com/books?id=rR-086nb37cC&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q&f=true

 

Kempland. Phil. “Confederate POW Burials on Smallpox Island, West Alton, IL.” Usgwarchives.net. Accessed 11-17-2019 at: http://www.usgwarchives.net/mo/civilwar/smallpox.htm

 

New York Times. “From Tennessee…Small-Pox Hospital…” 5-21-1864, p. 8. Accessed 11-18-2019 at: https://timesmachine.nytimes.com/timesmachine/1864/05/21/90119674.html?pageNumber=8

 

New York Times. “From Washington…The Reports About Small-Pox.” 1-13-1864, p. 1. Accessed 11-18-2019 at: https://www.nytimes.com/1864/01/13/archives/from-washington-indemnity-for-losses-during-the-war-the-enrollment.html

 

New York Times. “House of Representatives…Small-Pox in the District…” 1-14-1864, p. 8. Accessed 11-18-2019 at: https://www.nytimes.com/1864/01/14/archives/house-of-representatives-the-delegate-from-dakotah-the-confiscation.html

 

New York Times. “News From Washington…Number of Small Pox Cases.” 2-2-1864, p. 4. Accessed 11-18-2019 at: https://timesmachine.nytimes.com/timesmachine/1864/02/02/78716757.html?pageNumber=4

 

Philadelphia Inquirer. “House of Representatives. Small-pox in the District.” 1-7-1864, p. 4. Accessed 11-19-2019 at: https://newspaperarchive.com/philadelphia-inquirer-jan-07-1864-p-4/

 

United States National Board of Health. Annual Report of the National Board of Health, 1883.  Washington, DC: GPO, 1884.  Digitized by Google at:  http://books.google.com/books?id=MtuxEGC1Vp4C&printsec=frontcover&source=gbs_v2_summary_r&cad=0#v=onepage&q&f=true

 

 

 

 

 

 

 

[1] Compiled by B. Wayne Blanchard, Dec 2008, modified Nov 2019 for: http://www.usdeadlyevents.com

[2] “The reports of the prevalence of the small-pox in Washington are much exaggerated. Though it prevails to a greater extent than heretofore, it is generally in a mild form, and there are comparatively few deaths.” (For the purpose of contributing to a tally we translate “relatively few” deaths to “at least three.”

[3] Notes discussion on “resolution…adopted several days ago, instructing the Committee for the District of Columbia to inquire and report relative to the prevalence of small-pox.” Mr. Steele (D, NY) indicated there “was no occasion for unusual alarm, and that the accommodations in the hospitals are ample.”

[4] New York Times. “News From Washington…Number of Small Pox Cases.” 2-2-1864, p. 4.

[5] “Table of mortality from small-pox in the city of Chicago from 1851 to 1882, inclusive.”

[6] Our number based on counting the names of those who are listed as having died of smallpox at the prison in 1864.

[7] Table entitled “Deaths from Smallpox from 1807 to 1907, inclusive, and Rate per 1,000 of Population.” Notes smallpox death rate of 0.45 per 1,000 population. Previous year death rate had been 0.30.

[8] “In one colony [of freedman] where former slaves took refuge, smallpox killed freed people by ‘tens and twenties.’” For the purpose of contributing to a tally we translate “tens and twenties” into “at least twenty.”

[9] The report is from a NYT Correspondent in Nashville, dated 5-12-1864. References a Cumberland smallpox hospital. Article notes: “The small-pox hospital–in tents and in the field– also lies a few hundred rods from the Cumberland [Hospital]. This has been populous during all the Winter, the number of patients in it at one time rising as high as a thousand. The present number is 464. This is a large per centage of the population. But the place has been sadly scourged with this frightful disease during several months past, though its force is now diminishing. A military order last Winter required the whole city to be vaccinated…The dangerous prevalence of the disease is exhibited in the light of such an order. With this exception, Nashville has remained a healthy place during the war…”

[10] Dennee. African-American Civilians and Soldiers Treated at Claremont Smallpox Hospital… p. 20, citing: “Special Report for Small-Pox Hospitals [for 1864]” in Entry 620, Papers Relating to Cholera, Smallpox and Yellow Fever Epidemics, 1849-1893, Reports on Diseases and Individual Cases, Medical Records, 1814-1919 in Record Group 94, Records of the Office of the Adjutant General, National Archives and Records Administration.

[11] (Dennee, p. 45.)

[12] Located on south bank of Cameron Run overlooking Alexandria, VA, 2½  miles to the east-northeast. (Dennee)

[13] Freedmenscemetery.org. African-American Civilians and Soldiers Treated at Claremont Smallpox Hospital… p.13. The named fatalities total 19.

[14] Dennee, p. 31.

[15] Dennee, p. 45.

[16] Julia A. Wilbur Diaries, 1844-1894 (March 18, 1864), Haverford College. Miss Wilbur was an example of a person vaccinated at least twice to defend against repeated exposure to those infected.

[17] Record Group 94, Entry 544, Virginia Vols. 276, 353, 524, 525 and 527. The index of Alexandria hospital records states that the military branch of the hospital was established January 20, 1864 and that the civilian staff had previously treated “Contrabands” there. The book of morning reports commences with February 3, 1864, indicating that the soldiers‟ wards were in operation from at least the previous day.

[18] Record Group 94, Entry 561; Sprouse, p. 113; Francis Trevelyan Miller, ed., The Photographic History of the Civil War In Ten Volumes: Volume Seven, Prisons and Hospitals, (New York: The Review of Reviews Company, 1912), p. 235; Record Group 94, Entry 544, Virginia Vol. 527. According to an inspection report found by Sprouse, the top capacity reached in 1864 was said to be 194. Sprouse (October 1989), p. 114.

[19] Whisky may have been as common and ineffectual a “medicine” as any administered to smallpox patients at the time, as it was used for the purpose at the Alexandria Alms House in early 1862. Ruth M. Ward, “The Alexandria Alms House and Work House,” in The Arlington Historical Magazine, Vol. 6, No. 4, October 1980, p. 64.

[20] Record Group 94, Entry 544, District of Columbia Vol. 559.

[21] Charles Frederick Millspaugh, American Medicinal Plants: An Illustrated and Descriptive Guide to the American Plants Used as Homeopathic Remedies: Their History, Preparation, Chemistry, and Physiological Effect, New York and Philadelphia, 1887, p. 72. Another nineteenth-century “remedy” was repeated ingestion of a combination of zinc oxide, digitalis, sugar and water. John Gruber, Hagerstown Town & Country Almanack, (Hagerstown, MD: Gruber Almanack Co., 1881), p. 15.

[22] Pippenger, p. 29.