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AuthorBiographies M. A. (Ken) Clements’s masters and doctoral degrees were from the University of Melbourne, and at various times in his career he has taught, full-time, in primary and secondary schools, for a total of 15 years. He has taught in six universities, located in three nations, and is currently professor in the Department of Mathematics at Illinois State University. He has served as a consultant and as a researcher in Australia, Brunei Darussalam, India, Malaysia, Papua New Guinea, South Africa, Thailand, the United Kingdom, the United States of America, and Vietnam. He served as co-editor of the three International Handbooks of Mathematics Education—published by Springer in 1996, 2003 and 2013—and, with Nerida Ellerton, co-authored a UNESCO book on mathematics education research. He has authored or edited 31 books and over 200 articles on mathematics education, and is honorary life member of both the Mathematical Association of Victoria and the Mathematics Education Research Group of Australasia. Nerida F. Ellerton has been professor in the Department of Mathematics at Illinois State University since 2002. She holds two doctoral degrees—one in Physical Chemistry and the other in Mathematics Education. Between 1997 and 2002 she was Dean of Education at the University of Southern Queensland, Australia. She has taught in schools and at four universities, and has also served as consultant in numerous countries, including Australia, Bangladesh, Brunei Darussalam, China, Malaysia, the Philippines, Thailand, the United States of America, and Vietnam. She has written or edited 16 books and has had more than 150 articles published in refereed journals or edited collections. Between 1993 and 1997 she was editor of the Mathematics Education Research Journal, and since 2011 she has been Associate Educator of the Journal for Research in Mathematics Education. In 2012, and in 2013, Springer published the 223-page Rewriting the History of School Mathematics in North America 1607–1861 and the 367-page Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books, respectively. She jointly authored both of those books with M. A. (Ken) Clements. M. A. (Ken) Clements, & N. F. Ellerton, Thomas Jefferson and his decimals 1775–1810: Neglected years 177 in the history of U.S. school mathematics, DOI 10.1007/978-3-319-02505-6, © Springer International Publishing Switzerland 2015 Appendix A Notes on Thomas Jefferson’s (1784) “Some Thoughts on a Coinage” The two-page document, “Some Thoughts on a Coinage,” is printed in Volume 7 of Julian P. Boyd’s (1953), The Papers of Thomas Jefferson (Vol. 7 March 1784 to February 1785), published by Princeton University Press. Jefferson’s original handwritten pages were undated, but Boyd indicated that they were prepared around March 1784—that is to say, before Jefferson left for Paris, in July 1784, to serve as Minister Plenipotentiary to France. According to Boyd (1953), “Some Thoughts on a Coinage” was written entirely in Jefferson’s hand, and was “erroneously placed with the rough draft and notes of Jefferson’s report to the House of Representatives of a plan for establishing uniformity in currency, weights and measures” dated July 4, 1790 (p. 175). The document is in the Library of Congress, Washington, DC, Thomas Jefferson Papers, 233, 41972. “Some Thoughts on a Coinage” needs to be distinguished from the better-known and much longer “Notes on Coinage,” which was written between March and May 1784 (and is printed in Boyd, 1953, pages 175–185). With respect to “Some Thoughts on a Coinage,” Boyd (1953) wrote: It is now known that Jefferson considered at this time a comprehensive plan for the decimalization of weights and measures as well as money. Document III [“Some Thoughts on a Coinage”], never before published, shows that Jefferson’s “Some Thoughts on a Coinage” was in reality an outline of “Notes on Coinage.” It was probably drawn up as early as March, or even February, 1784. At that time Jefferson must have intended to advocate the dollar as the money unit as well as a decimalized coinage, and once these points were established, to make a transition to a decimal reckoning in weights, measures, and perhaps time. But he must have concluded that the country was not ready for such a thoroughgoing innovation and that the latter parts of his program could be more readily accomplished after the coinage had been settled. In this sense, then, Jefferson’s “Notes on Coinage” must be regarded merely as the preliminary expression of a plan to which he returned six years later, immediately on assuming office as Secretary of State. (pp. 155–156). Here is how Boyd’s (1953) reprinting of “Some Thoughts on a Coinage” appeared. Jefferson’s misspellings and idiosyncratic use of upper-case first letters have been retained. III. Some Thoughts on a Coinage [ca. Mch 1784] Some Thoughts on a Coinage and the Money Unit for the U.S. 1. The size of the Unit. 2. It’s division. 3. It’s accommodation to known coins. The value of a fine silver in the Unit. M. A. (Ken) Clements, & N. F. Ellerton, Thomas Jefferson and his decimals 1775–1810: Neglected years 179 in the history of U.S. school mathematics, DOI 10.1007/978-3-319-02505-6, © Springer International Publishing Switzerland 2015 180 Jefferson’s (1784) “Some Thoughts on a Coinage” The proportion between the value of gold and silver. The alloy of both 1. oz in the pound. This is Brit. standard of gold, and Fr[ench] Ecu of silver. The Financier’s plan. A table of the value of every coin in Units. Transition from money to weights. 10 Units to the American pound. 3650 grs = 152 dwt. 2 grs. = 7 oz. 12 dwt. 2 grs Transition from weights to measures. Rain water weighing a pound, i.e. 10 Units, to be put in a cubic vessel and one side of that taken for the standard or Unit of measure. Note. By introducing pure water and pure silver, we check errors of calculation proceeding from heterogeneous mixtures with either. Transition for measures to time. I find new dollars of 1774, 80, 81 (qu. Mexico Pillar) weigh 18 dwt. 9 grs. = 441 grs. If of this there be but 365 grs. Pure silver, the alloy would be 2.1 oz. in the lb. instead of 19 dwt. The common Spanish alloy, which is 1 dwt. Worse than the Eng. Standard. Whereas if it is of 19 dwt. In the lb. troy, it will contain 406 grs. Pure silver. The Seville piece of eight weighing 17½ dwt. By Sir I. Newt’s assay contained 387. grs. Pure silver. The Mexico peice of 8 [weighing] 17 dwt. 10 5 grs. (alloy 18 dwt. as the former) 385½. The Pillar peice of 8 9 [weighing] 17–9 (alloy 18 dwt.) 385¾. The old ecu of France or peice of 6, gold Tournois is exactly of the weight and fineness of the Seville peice of 8. The new ecu is by law 1. oz. alloy, but in fact only 19½ dwt. 19 dwt. 14½ grs. pure metal is 432¼ grs. Dollars Weight In water Loss a1773 17—8½ 15—15 1—17½ a1774 17—8 15—14 1—18 a1775 17—8½ 15—15½ 1—17 1776 1777 a1778 17—9½ 15—16 1—17½ a1779 17—9½ 15—16 1—17½ a1780 17—10 15—17½ 1—16½ a1781 17—8½ 15—15½ 1—17 1782 aThese average 417. grs. weight in air 41.3 grs. loss in water. i.e. 1/10 or nearly 1/1000 [Jefferson meant 100/1000] or ten times the weight of water. Cassini makes a degree in a great mile contain Jefferson’s (1784) “Some Thoughts on a Coinage” 181 Miles D 69 864 = 365,184 feet Then a geographical mile will be 6086.4 feet. a Statute mile is 5280 f. A pendulum vibrating seconds is by Sr. I. Newton 39.2 inches = 3.2666 &c. feet Then a geographical mile of 6086.1 f. = 1863 second pendulums. Divide the geometrical mile into 10. furlongs each furlong 10 chains each chain 10. paces Then the American mile = 6086.4 f. English = 5280 f. furlong = 608.64 f. = 660 chain = 60.864 = 66 pace = 6.0864 fathom = 6. Russian mile .750 of a geographical mile English mile .8675 Italian mile 1. Scotch and Irish do. 1.5 old league of France 1.5 small league of do. 2. great league of do. 3. Polish mile 3. German mile 4. Swedish mile 5. Danish mile 5. Hungarian mile 6 A rod vibrating seconds is nearly 58½ inches. Comments by Clements and Ellerton (2014) “Some Thoughts on a Coinage” is a historically remarkable document that reveals Jefferson’s struggles to achieve a scientific and mathematical overview of the situation with respect to coinage and weights and measures. Reading the document makes it obvious that before he went to Paris Jefferson was extremely well read with respect to the key issues, and that he thought a totally integrated system of weights and measures and money was what the newly-created United States of America should strive to achieve. It is also obvious that in “Some Thoughts on a Coinage” he is not merely reiterating what someone else has advised him. He had taken on the challenge of devising a coordinated system that fitted the demands of science and mathematics, yet at the same time would be convenient in day-to-day practices. “Some Thoughts on a Coinage” should be read in conjunction with the slightly later, and better known “Notes on Coinage” (see Boyd, 1953. pp.
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