In his 'Vorlesungen über Dynamik', 1842-1843, Jacobi also discusses the papers by William Rowan Hamilton.
Jacobi asserted that Hamilton had inadvertendly introduced a superfluous equation, which of course introduced unnecessary complexity. Is there indication that at any point Hamilton became aware of this?
David R Wilkins has created transcripts of many of the papers by William Rowan Hamilton.
There is a page specifically for links to Hamilton's papers on Dynamics that were published in the Proceedings of the Royal Sociedty
Availble at John Hopkins University:
A machine searcheable .pdf file with scanned pages of Jacobi's Vorlesungen über Dynamik
First Lecture, page 3
Hamilton hat den schönen Zusammenhang, den er gefunden hat, etwas unzugänglich gemacht und verdunkelt, und zwar dadurch, dass er seine charakteristische Function noch zugleich von einer zweiten partiellen Differentialgleichung abhängen lässt. Die Hinzufügung dieser Bestimmung macht die ganze Entdeckung unnöthig complicirt, da eine genauere Untersuchung zeigt, dass die zweite partielle Differentialgleichung vollkommen überflüssig ist.
[My translation]
Hamilton has made the beautiful interconnection he found somewhat inaccessible and obscure because he has made his characteristic function dependent on a second partial differential equation. This addition makes the whole discovery unnecessarily complicated because a closer examination shows that the second partial differential equation is completely superfluous
19th lecture, page 153
Hamilton [...] steht zugleich noch eine zweite partielle Differentialgleichung auf, welcher V ebenfalls genügen soll. Diese kann man aber fortlassen, weil sie sich aus der schon aufgestellten herleiten lässt [...]"
[My translation]
Hamilton sets up a second partial differential equation that V must satisfy. This can however be omitted because it can be derived from the already stated equation.
[Jacobi proceeds to present that derivation]
