Benjamin Alvord (August 18, 1813 – October 16, 1884) was an American soldier, mathematician, and botanist.

Early life and career

Alvord was born in Rutland, Vermont, where he developed an interest in nature. He attended the

United States Military Academy The United States Military Academy (USMA), also known Metonymy, metonymically as West Point or simply as Army, is a United States service academies, United States service academy in West Point, New York. It was originally established as a f ...

and displayed a talent in mathematics. He graduated in 1833.Marquis Who's Who, Inc. ''Who Was Who in American History, the Military''. Chicago: Marquis Who's Who, 1975. P. 9 He was assigned to the 4th U.S. Infantry and participated in the

Seminole Wars The Seminole Wars (also known as the Florida Wars) were three related military conflicts in Florida between the United States and the Seminole, citizens of a Native American nation which formed in the region during the early 1700s. Hostilities ...

. He returned to West Point as an assistant professor of mathematics until 1839, when he was again assigned to the 4th Infantry. He spent 21 years of his military career with that regiment. He was on frontier, garrison, and engineer duty until 1846, when he participated in the military occupation of the new state of Texas. Subsequently, he served during the

Mexican–American War The Mexican–American War, also known in the United States as the Mexican War and in Mexico as the (''United States intervention in Mexico''), was an armed conflict between the United States and Second Federal Republic of Mexico, Mexico f ...

, being

brevetted In many of the world's military establishments, a brevet ( or ) was a warrant giving a commissioned officer a higher rank title as a reward for gallantry or meritorious conduct but may not confer the authority, precedence, or pay of real rank. ...

successively to

captain Captain is a title, an appellative for the commanding officer of a military unit; the supreme leader of a navy ship, merchant ship, aeroplane, spacecraft, or other vessel; or the commander of a port, fire or police department, election precinct, e ...

and major for gallantry in a number of important battles, including the

Battle of Palo Alto The Battle of Palo Alto ( es, Batalla de Palo Alto) was the first major battle of the Mexican–American War and was fought on May 8, 1846, on disputed ground five miles (8 km) from the modern-day city of Brownsville, Texas. A force of so ...

and the

Battle of Resaca de la Palma The Battle of Resaca de la Palma was one of the early engagements of the Mexican–American War, where the United States Army under General Zachary Taylor engaged the retreating forces of the Mexican ''Ejército del Norte'' ("Army of the No ...

. He served as General Riley's chief of staff to Major Folliott T. Lally's column on the march from

Vera Cruz Veracruz is a state in Mexico. Veracruz or Vera Cruz (literally "True Cross") may also refer to: People * María González Veracruz (born 1979), Spanish politician * Philip Vera Cruz (1904–1994), Filipino American labor leader * Tomé Vera Cruz ...

to Mexico City in 1847. He joined the

Aztec Club of 1847 The Aztec Club of 1847 is a military society founded in 1847 by United States Army officers of the Mexican–American War. It exists as a hereditary organization including members who can trace a direct lineal connection to those originally elig ...

in 1871. After the Mexican–American War, he went from line to staff when he was named paymaster and promoted to major. He was assigned to various posts and was sent with the 4th Infantry to the West Coast. He was the engineer in charge of building the military road in southern Oregon. He was then chief paymaster in

Oregon Oregon () is a state in the Pacific Northwest region of the Western United States. The Columbia River delineates much of Oregon's northern boundary with Washington, while the Snake River delineates much of its eastern boundary with Idah ...

from 1854 until 1862.

Civil War service

From 1862 to 1865, during the

American Civil War The American Civil War (April 12, 1861 – May 26, 1865; also known by other names) was a civil war in the United States. It was fought between the Union ("the North") and the Confederacy ("the South"), the latter formed by state ...

, Alvord was at

Fort Vancouver Fort Vancouver was a 19th century fur trading post that was the headquarters of the Hudson's Bay Company's Columbia Department, located in the Pacific Northwest. Named for Captain George Vancouver, the fort was located on the northern bank of the ...

as the commander of the District of Oregon with the rank of

brigadier general Brigadier general or Brigade general is a military rank used in many countries. It is the lowest ranking general officer in some countries. The rank is usually above a colonel, and below a major general or divisional general. When appointed t ...

of volunteers. He was named to that post by George Wright, the commanding officer of the

Department of the Pacific The Department of the Pacific or Pacific Department was a major command (Department) of the United States Army from 1853 to 1858. It replaced the Pacific Division, and was itself replaced by the Department of California and the Department of Ore ...

. Wright wanted an experienced

Regular Army A regular army is the official army of a state or country (the official armed forces), contrasting with irregular forces, such as volunteer irregular militias, private armies, mercenaries, etc. A regular army usually has the following: * a standi ...

officer in that post, rather than a volunteer, since the District was large (encompassing the present-day states of Oregon, Washington, and Idaho), underdeveloped, and had a history of friction between the native peoples and settlers. As commander of the District, Alvord built up the defenses around the mouth of the Columbia River, but was unable to do the same for Puget Sound. Because of low enlistments from Oregon and Washington, he supported the military draft, and failing that, supported the payment of bounties. He was removed from command in March 1865. He was ordered to the East Coast, where he resigned his volunteer commission and became paymaster in New York City.

Circles and spheres

Alvord was interested in the classical

problem of Apollonius In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 190 BC) posed and solved this famous problem in his work (', "Tangencie ...

, to find a circle

tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. Mo ...

to three given circles, and the

special cases of Apollonius' problem In Euclidean geometry, Apollonius' problem is to construct all the circles that are tangent to three given circles. Special cases of Apollonius' problem are those in which at least one of the given circles is a point or line, i.e., is a circle of ...

, as well as the generalization to spheres. In 1855, he published in ''Smithsonian Contributions to Knowledge''. Posted to the remote Fort Vancouver, he continued his investigations and submitted his findings in 1860, but was frustrated by a fire. In 1882, when he found that there are 96 circles which cut four given circles at a fixed angle and there are 640 spheres which cut five given spheres at a fixed angle, he assembled all his results for an article in ''

American Journal of Mathematics The ''American Journal of Mathematics'' is a bimonthly mathematics journal published by the Johns Hopkins University Press. History The ''American Journal of Mathematics'' is the oldest continuously published mathematical journal in the United ...

'', where he explained the delay: :All of this memoir, except the last two problems, were completed and sent to the

Smithsonian Institute The Smithsonian Institution ( ), or simply the Smithsonian, is a group of museums and education and research centers, the largest such complex in the world, created by the U.S. government "for the increase and diffusion of knowledge". Founded ...

in January 1860, from Fort Vancouver, Washington Territory, but the manuscript was burned in January 1865 when the upper story of the Smithsonian building was on fire. The article is graced with annotations by

Arthur Cayley Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, Cayley enjoyed solving complex maths problems ...

and the concession that

Darboux Darboux is a surname. Notable people with the surname include: *Jean Gaston Darboux (1842–1917), French mathematician *Lauriane Doumbouya (née Darboux), the current First Lady of Guinea since 5 September 2021 *Paul Darboux Paul Darboux (May 10, ...

had preceded Alvord in print.

Postbellum

After the war, he subsequently became paymaster of the District of Omaha and paymaster of the

Department of the Platte The Department of the Platte was a military administrative district established by the U.S. Army on March 5, 1866, with boundaries encompassing Iowa, Nebraska, Dakota Territory, Utah Territory and a small portion of Idaho. With headquarters in Oma ...

. He became

Paymaster General His Majesty's Paymaster General or HM Paymaster General is a ministerial position in the Cabinet Office of the United Kingdom. The incumbent Paymaster General is Jeremy Quin MP. History The post was created in 1836 by the merger of the posit ...

of the Army in 1872 and served in that capacity until his retirement from active service in 1880. He was promoted to brigadier general in 1876. He also wrote on natural history, writing the first scientific description of the ability of the compass plant (''

Silphium laciniatum ''Silphium laciniatum'' is a species of flowering plant in the family Asteraceae known commonly as compassplant or compass plant. It is native to North America, where it occurs in Ontario in Canada and the eastern and central United States as fa ...

'') to orient itself in a north-south direction, as well as writing about winter grazing in the Rocky Mountains. Alvord was a contributor to ''

Harper's Magazine ''Harper's Magazine'' is a monthly magazine of literature, politics, culture, finance, and the arts. Launched in New York City in June 1850, it is the oldest continuously published monthly magazine in the U.S. (''Scientific American'' is older, b ...

'', and a member of the

Literary Society of Washington The Literary Society of Washington was formed in 1874 by a group of friends and associates who wished to meet regularly for "literary and artistic improvement and entertainment". - page 3 For more than 140 years, this literary society has convene ...

.Alvord is listed in the directory of members of the Society in Helen Nicolay's
Sixty Years of the Literary Society
', Washington, D.C., 1934. Library of Congress call number PN22.L53 N5. Google Book

Personal life and family

He married Emily Louise Mussey in 1846, and they had six children. His son, Benjamin Alvord, Jr., became a soldier and was a general in

World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...

. His daughter Louise married Thomas Craig, one of the main professors of mathematics at

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consiste ...

during its first two decades.

Death and legacy

He died on October 16, 1884 in Washington, D.C. He and his wife Emily Louise Mussey (1826–1885) are buried at Evergreen Cemetery, Rutland, Vermont, Section 4, Lot 4. Alvord Valley and the

Alvord Desert The Alvord Desert is a desert located in Harney County, in southeastern Oregon in the Western United States. It is roughly southeast of Steens Mountain. The Alvord Desert is a dry lake bed and averages of rain a year. Two mountain ranges ...

in Oregon were named in his honor.Corning, Howard M. ''Dictionary of Oregon History''. Binfords & Mort Publishing, 1956.

Notes

References

*Hubbell, John T., and James W. Geary (editors). ''Biographical Dictionary of the Union: Northern Leaders of the Civil War''. Westport, CT: Greenwood Press, 1995. . *Johnson, Allen (editor). ''Dictionary of American Biography''. New York: Charles Scribner's Sons, 1946. *Johnson, Rossiter (editor). ''The Twentieth Century Biographical Dictionary of Notable Americans''. Boston: The Biographical Society, 1904. *Warner, Ezra J., ''Generals in Blue: Lives of the Union Commanders''. Louisiana State University Press, 1964. Reissued in 2006 by Easton Press. Attribution *

External links

* * George Washington Cullum (1891
Cullum's Register #728
from Bill Thayer at

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...

. * {{DEFAULTSORT:Alvord, Benjamin 1813 births 1884 deaths People from Rutland (town), Vermont United States Military Academy alumni 19th-century American mathematicians American botanists American military personnel of the Mexican–American War Members of the Aztec Club of 1847 Union Army generals People of Vermont in the American Civil War United States Army paymasters People of Oregon in the American Civil War Snake War Scientists from Vermont Mathematicians from Vermont Paymaster-General of the United States Army Burials at Evergreen Cemetery (Rutland, Vermont)