The Discovery of Magnetic Effects of Electrical Current
Hans Christian Ørsted (1777-1851) [Wikipedia]
AKA. Hans Christian Œrsted, Hans Christian Oersted, Johannis Christianus Öersted
1820 Johannis Christianus Öersted
Experimenta circa effectum conflictus electrici in acum magneticam
(Typis Schultzianis, København, Danmark, 1820).
[The Royal Library, Copenhagen] [Smithsonian]
*Four-page private publication.

[Latin as it is]
Johannis Christianus Oersted
Experimenta circa effectum conflictuse electrici in acum magneticam
Journal für Chemie und Physik, Volume 29, 275-281 (1820).
(AKA. Schweigger's Journal)
[Google] [Google]

[French translation]
J. Chr. OErsted
Experimenta circa effectum, etc. Expériences sur l'effet du conflict électrique surl'aniguille aimantée,
Annales de Chimie et de Physique, Volume 14, 417-425 (1820).
[Google] [Gallica]

[Another French translation]
J. C. Œrsted
Expériences sur un effet que le courant de la pile excite dans l'Aiguille aimantée,
Journal de Physique, Volume 91, pp. 72-76 (1820).

[English translation]
John Christian Oersted
Experiments on the effects of a current of electricity on the magnetic needle
Annals of Philosophy, Volume 16, pp. 273-276 (1820).
Translated from a printed account drawn up in Latin by the author, and transmitted by him to the Editor of the Annals of Philosophy.

[English translation]
John Christian Oersted
Experiments on the effect of the electric conflict on the magnetic needle
in Selected Scientific Works of Hans Christian Ørsted
(ed.) K. Jelved, A. D. Jackson, O. Knudsen, and A. D. Wilson
(Princeton University Press, Princeton, NJ, 1998) pp. 413-416.
1820 J.-C. Œrsted
Nouvelles expériences électro-magnétique
Journal de Physique 91, 78-80 (1820).
*The second paper of Oersted.
1813 Ørsted had expected relationships between electricity and magnetism before his finding in 1820.

Hans Christian Œrsted
Recherches sur l'indentité des forces chimiques et électriques [*]
(J. G. Dentu, Paris, 1813).
Chapter VIII. Du Magnétisme., p. 234-238.
[Gallica] [Google] [Google]
[*] Originally published in German (Berlin, 1812, at the High School Book Shop) is not available.

[English translation]
View of the chemical laws of nature obtained through recent discoveries
Selected Scientific Works of Hans Christian Ørsted
translated and edited by Karen Jelved, Andrew D. Jackson and Ole Knudsen
with an introduction by Andrew D. Wilson
(Princeton University Press, Princeton, NJ, 1998), Chapter 30, pp. 310-392.

At the same time, an attempt should be made to discover if it is possible to produce some effect on the magnet as a magnet in one of the states in which electricity is found to be extremely bound.
This would not be without difficulty because the electricity would react on both magnetic and non-magnetic bodies, but perhaps it would be possible to obtain some information on this by comparing magnetic and non-magnetic needles.
1857 Oersted's discovery was not accidental.

A Letter from Professor Hansteen to Faraday
... But as Lagrange has said of Newton in a similar occasion, "such accidents only meet persons who deserve them."

Bence Jones: The Life and Letters of Faraday Vol. II (Longmann, Green and Co., London, 1870) pp. 389-392.
Bence Jones: The Life and Letters of Faraday Volume 2 (Cambridge University Press, Cambridge, UK, 2010) pp. 389-392.