My understanding is that by the 1850s, the enumerated were supposed to
provide the answers to all of the questions asked by the enumerators.
The specific instructions to the enumerators in 1850 with regard to
color are as follows:

"Heading 6, entitled 'Color,' in all cases where the person is white,
leave the space blank; in all cases
where the person is black, insert the letter B; if mulatto, insert M. It
is very desirable that these particulars be carefully regarded."

These instructions become more emphatic by 1870:

"Color.-It must not be assumed that, where nothing is written in this
column, ''white'' is to be understood. The column is always to be
filled. Be particularly careful in reporting the class mulatto. The word
is here generic, and includes quadroons, octoroons, and all persons
having any perceptible trace of African blood. Important scientific
results depend upon the correct determination of this class in schedules
1 and 5."

That said, I have worked extensively with three counties in Georgia
where I followed the populations from 1850 through 1910, and I have
found significant variation in the way color is reported within families
over time - some or all of the members will be described as black in
1860 and 1870, some described as mulatto in 1880, and then reported as
black in 1900 and 1910.  This change leads me to believe that
enumerators may have ignored the "official" instructions and offered
their own assessment of race.  

Historians have long been aware of the reporting problems with the
pre-1920 decenniel censuses, particularly the 1870 and earlier
enumerations.  Much of the criticism revolves around how marshalls and
enumerators were appointed with the locality and the fact that they were
paid on a quota system which placed a premium on visiting as many
households as possible, usually at the expense of accuracy.

This is a good opportunity to share a couple of sources related to the
U.S Census.  The U.S. Census Bureau has put historic census data online
going back to 1790 - the official reports from 1820 forward are scanned
from the originials in their entirety.  Unfortunately, they do not have
the manuscript census returns scanned as yet - that, I imagine, would be
a massive undertaking.  You can find all of that here:
http://www.census.gov/population/www/censusdata/hiscendata.html
 
While I imagine that you can find the original enumerator's instructions
somewhere on that site, they do have a PDF publication called "Measuring
America: The Decennial Censuses From 1790 to 2000" which provides
transcripts of the instructions for most if not all of the censuses.

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