The document that @depperm located at archive.org IS the one you're looking for, pdf here. As Andrew Leach said, the Vatican website doesn't list this document.
The 44 page PDF document contains:
- One page of context, from the Orthocath Nov 3, 2010 blog article Pope & Patriacts: The 1848 Letters of Pope Pius IX and the Orthodox Patriachs about the origin of the English translation of the Pope's letter (i.e. from the French journal Irenikon in 1929).
- Pope Pius IX letter, dated 6 January 1848 (pages 2-13)
- Orthodox Bishops's reply, dated May 1848 (pages 14-44)
In the English translation, the title says
On the Supreme Throne of Peter the Apostle
Apostolic Letter of Pope Pius IX, dated 6 January 1848
But in the French language Irenikon version (pdf here), the title says
Lettre de N. S. P. le Pape Pie IX aux chrétiens de l'Orient.
Le Pape Pie IX aux Orientaux
Letter from N. S. P. Pope Pius IX to the Christians of the East.
Pope Pius IX to the Orientals
which is close enough to either the Wikipedia title Epistle to the Easterners or the title of the English translation of the reply A Reply to the Epistle of Pope Pius IX, "to the Easterns".
When I compare the French text and the English text using Google translate of the first and last paragraphs, they are the same.