The petition for naturalization you cite is digitized and available through Ancestry.com. (Though a subscription database, you can access Ancestry for free at National Archives locations as well as many public libraries.) You can view the record by searching the index "New York, State and Federal Naturalization Records, 1794-1940," on Ancestry. Unfortunately, the index card available on Family Search contains all of the information on the actual petition. Pre-1906 naturalization records are not very detailed and contain little information.
If you are unable to access Ancestry, or have additional questions, please contact the National Archives at New York City directly for assistance. They can be reached via email at firstname.lastname@example.org