  In June 1888, Oliver Heaviside received by mail an officially unpublished
pamphlet, which was written and printed by the American author Willard J. Gibbs
around 1881-1884. This original document is preserved in the Dibner Library of
the History of Science and Technology at the Smithsonian Institute in
Washington DC. Heaviside studied Gibbs's work very carefully and wrote some
annotations in the margins of the booklet. He was a strong defender of Gibbs's
work on vector analysis against quaternionists, even if he criticized Gibbs's
notation system. The aim of our paper is to analyse Heaviside's annotations and
to investigate the role played by the American physicist in the development of
Heaviside's work.
