Upvote:3
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:
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 chrΓ©tiens de l'Orient.
Le Pape Pie IX aux Orientaux
Google translated:
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.