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Commemorative Biographical Record of the County of Kent, Ontario
Alexander Macfarlane

ALEXANDER MACFARLANE, one of the most distinguished citizens of Ontario, a leader in scientific thought and author of the highest merit, and a savant in whom both his native land and his adopted country take pride, was born at Blairgowrie, Scotland, April 21, 1851.  His education was obtained in the public school and his selection as a pupil-teacher as early as the age of thirteen years gives testimony to the quick ripening of his powers.  His ambition was to reach the University of Edinburgh, and in 1869 he entered that great educational institution.  Mr. Macfarlane first entered the Junior classes in Latin and Greek, and at the end of the session stood fourth in the former and fifth in the latter, in classes of 200, largely composed of high school graduates.  At the beginning of his second year he won the Miller scholarship, worth $400, in open competition, and at the beginning of the third year he won, in open competition, the Spence scholarship, worth $1,000.  His third year of study was given to Senior Mathematics, Natural Philosophy and Logic.  It was the custom of Prof. Kelland to introduce Quaternions to his Senior students.  The addition of vectors was intelligible, but the product of vectors seemed to be a universal difficulty, and to assist in his understanding young Macfarlane purchased a copy of Tait’s “Treatise on Quaternions”.  This was the beginning of his special work as a mathematician.  Prior to entering the class of Logic Mr. Macfarlane had already become familiar with the works of Hamilton and Mill, and while a member of the class he read, at the invitation of the professor, a paper which criticized the statement of the law of Excluded Middle, given by Jevons in his “Lessons on Logic”, a paper which displayed unusual merit for so young a mind.,  It was his first intention to study for honours in Logic and Philosophy, but perceiving how much they depended upon the principles of science, he took up the advanced classes in Mathematics and Physics, and in Mathematical Physics he not only gained the highest honours but also the appreciation and the personal friendship of Prof. Tait, the head of the Physical Department of the University.  In 1874 he was appointed Neil Arnott instructor in Physics, and in 1875 finished an unusually extensive course of undergraduate study by taking the degree of M.A. with honours in Mathematics and Physics.

Having after graduation, won in competitive examination the Maclaren fellowship, worth $1,500., he proceeded to study for the recently instituted degree of Doctor of Science, and, after one year spent on Chemistry, Botany and Natural History, and two years on Mathematics and Physics, he obtained the doctorate in 1878.  His remarkable thesis was an experimental research on the conditions governing the electric spark, and it was subsequently published in the “Transactions of the Royal Society of Edinburgh”.  It also brought him under the notice of the celebrated electrician and philosopher, Clerk Maxwell.,  In 1878 Dr. Macfarlane was elected a Fellow of the Royal Society of Edinburgh, and the first contribution which he read personally was a memoir on the Algebra of Logic.  In 1879 he enlarged its scope and published it under the title of “Principles of the Algebra of Logic”.  This volume was received with favour and brought the author into correspondence with many of the leading scientists and savants of the world.  In 1879 he was able to meet many of them at the meeting of the British Association at Sheffield.  During 1880 Dr. Macfarlane was interim Professor of Physics at the University of St Andrews, and in 1881 he was appointed, for the usual period of three years, Examiner in Mathematics in the University of Edinburgh.  During these years he contributed to the Royal Society a series of valuable papers on “Analysis of the Relationships of Consanguinity and Affinity”..  A paper on this subject, read before the Anthropological Institute of London, contains as perfect a notation for relationship as is the Arabic notation for numbers.  His notable paper on “Plane Algebra” and his “Physical Arithmetic” were prepared during his tenure of office as Examiner.

In 1885 Dr. Macfarlane was called to the Chair of Physics at the University of Texas, where he became a colleague of his fellow logician, Dr. Halsted, and during that same year he met many American men of letters and science at the Ann Arbor meeting of the association.  In 1887 he received the honourary degree of LL.D. from the university of Michigan.  His first year at the University of Texas was wholly taken up with the organization of the department, but in 1889 appeared a sequel to “Physical Arithmetic”, namely, a volume of “Elementary Mathematical Tables”.  During this year he visited Paris, and at the meeting of the French Association became acquatined with many continental savants.  On his return from Europe he began to publish the results of his study of the algebra of space, and a few of the notable papers read and prepared were the following, showing a mass of learning and an exactness of reasoning quite beyond the ordinary intelligence:  “Principles of the Algebra of Physics”; “On the Imaginary of Algebra”; “The Fundamental Theorems of Analysis Generalized for Space”; “On the Definitions of the Trigonometric Functions”; “The Principles of Elliptic and Hyperbolic Analysis”; “The Analytical Treatment of Alternating Currents”; “On the Fundamental Principles of Exact Analysis”; and “The Principles of Differentiation in Space Analysis”.  In 1891 Dr. Macfarlane took an active part in organizing the Texas Academy of Science, and for two years acted as its Honourary Secretary.  He contributed many papers, among which may be mentioned:  “An Account of the Rainmaking Experiments in San Antonio” and “Exact Analysis as the Basis of Language”.  For nine years Prof. Macfarlane remained at the University of Texas, resigning in 1894.  The benefits accruing to the institution through his connection with it placed it far ahead of competitors.  The course in mathematical physics which he arranged called forth a special approving article from a mathematical journal published at Turin, Italy.  Since 1885 he has been a member of the Canadian Institute, Toronto, and in addition to belonging to a number of American and British societies he also holds membership with several of the leading ones of the European continent.  He is prominently mentioned in the issue of “Who’s Who”, in America.

Since coming to reside in Ontario Prof. Macfarlane has continued to write many papers on the algebra of space and has carried on the work of secretary of an International Society organized for promoting that branch of mathematics, and which includes in its membership many of the most active mathematicians of the several countries of the world.

Dr. Macfarlane is a grandson of Alexander and Jeanette (Steele) Macfarlane, honoured old residents of Perthshire, Scotland.  Their sons were:  James, Peter, Alexander and Daniel, the last of whom was the Doctor’s father.  The only member of this family who came to Canada was the late James Macfarlane.

Dr. Macfarlane married Miss Helen Swearingen, daughter of Patrick and Mary E. (Toland) Swearingen, of Texas.  The former, descended from one of the Dutch founders of New York, was an attorney of prominence and held the rank of lieutenant-colonel in the Confederate army during the Civil war in the States.  To Dr. and Mrs. Macfarlane have been born three sons, Alexander S., Robert H.K., and Henry S.  In politics Dr. Macfarlane favours the Liberal party; in religion he is a Presbyterian.  He occupies his beautiful farm of 400 acres, on Lots 16 and 17, 6th Concession, during the  summer season, his residence occupying its center.  It is probably the most valuable, as it certainly is the most highly cultivated and improved, estate of the county, and everything is arranged in geometrical order.

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