Mathematical Treasure: James Clerk Maxwell’s Treatise on Electricity and Magnetism

James Clerk Maxwell (1831–1879) was raised and educated in Edinburgh and then studied at the University of Cambridge. Although he struggled to secure a long-term university position, he was the greatest mind working on electricity and magnetism in the 19th century. He is best known for collating and formulating the set of partial differential equations that are now known as Maxwell’s equations. He first mentioned them in an 1861 paper, “On the Lines of Force,” but his work on them was most mature and fully-developed in his two-volume Treatise on Electricity and Magnetism, which was published in 1873. The title page of volume 1 and some of his notation appears below.

In volume 2, part IV, chapters 8–9, Maxwell used letters to denote 11 equations as the fundamental equations of classical electromagnetism. After his death, Oliver Heaviside (1850–1925) reduced the equations to the set of four that are taught today. The first two groups of equations are shown as “(A)” and “(B)” below.

Reference

Achard, F. 2005. James Clerk Maxwell, A Treatise on Electricity and Magnetism, First Edition (1873). In Landmark Writings in Western Mathematics, 1640–1940, edited by Ivor Grattan-Guinness, 564–587. Amsterdam: Elsevier.

Full digitizations of the copies of volume 1 and volume 2 owned by the University of California are available from the Internet Archive.

Index to Mathematical Treasures