  In 1893, the "physicist-engineer" Andr\'e Blondel invents the oscilloscope
for displaying voltage and current variables. With this powerful means of
investigation, he first studies the phenomena of the arc then used for the
coastal and urban lighting and then, the singing arc used as a transmitter of
radio waves in wireless telegraphy. In 1905, he highlights a new type of
non-sinusoidal oscillations in the singing arc. Twenty years later, Balthasar
van der Pol will recognize that such oscillations were in fact "relaxation
oscillations". To explain this phenomenon, he uses a representation in the
phase plane and shows that its evolution takes the form of small cycles. During
World War I the triode gradually replaces the singing arc in transmission
systems. At the end of the war, using analogy, Blondel transposes to the triode
most of the results he had obtained for the singing arc. In April 1919, he
publishes a long memoir in which he introduces the terminology "self-sustained
oscillations" and proposes to illustrate this concept starting from the example
of the Tantalus cup which is then picked up by Van der Pol and Philippe Le
Corbeiller. He then provides the definition of a self sustained system which is
quite similar to that given later by Aleksandr Andronov and Van der Pol. To
study the stability of oscillations sustained by the triode and by the singing
arc he uses, this time, a representation in the complex plane and he expresses
the amplitude in polar coordinates. He then justifies the maintaining of
oscillations by the existence cycles which nearly present all the features of
Poincar\'e's limit cycles. Finally, in November 1919, Blondel performs, a year
before Van der Pol, the setting in equation of the triode oscillations. In
March 1926, Blondel establishes the differential equation characterizing the
oscillations of the singing arc, completely similar to that obtained
concomitantly by Van der Pol for the triode. Thus, throughout his career,
Blondel, has made fundamental and relatively unknown contributions to the
development of the theory of nonlinear oscillations. The purpose of this
article is to analyze his main work in this area and to measure their
importance or influence by placing them in the perspective of the development
of this theory.
