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Going to need more information. I went to the free website familysearch.org and as a for instance in the 1870 census there are 20 Alford/Alfred Stone's on the first page and continues.
Need a year, a state, perhaps a family member, and etc.
Dear Mr. Rush,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Population Schedules for the 1830 Census, Population Schedules for the 1840 Census, Population Schedules for the 1850 Census, the Population Schedules for the 1860 Census, the Population Schedules for the 1870 Census, and the Population Schedules for the 1880 Census, in the Records of the Bureau of the Census (Record Group 29) that may contain information about Alford/Alfred Stone and his family. For access to the non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at firstname.lastname@example.org.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT1. We apologize for this inconvenience and appreciate your understanding and patience.
For information about the U.S. Census, see the Census Bureau technical documentation and questionnaires.
You may wish to search Ancestry.com or FamilySearch.org for the U.S. Census. There may be a fee for using Ancestry. Instead, check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
Even though the census before 1850 only listed the head of the household by name, and the rest of the family members by sex & age, you can often use that information along with comparing the names of neighbors between each census schedule to infer the correct household for prior years.
We suggest that you search the FamilySearch index for Tennessee Births and Christenings, 1828-1939 for the birth record of Alford/Alfred Stone and contact Tennessee State Library and Archives to inquire about any probate files, land, judicial or other records that may give more information about the Stone family. In addition, the FamilySearch Research wiki for Tennessee Genealogy may be helpful
We hope this is helpful. Best of luck with your family research!