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Dear Ms. Ink,
Thank you for posting your request on History Hub!
It has been our observation that there is not great deal of consistency in the use of things such as "3d" vs. "3rd" in the records from the time period. You maybe interested in U.S. Army Center of Military History (CMH) publication CMH Style Guide, which includes a section (1-12) on "Designations of U.S. Army Units and Organizations." Additionally, you may wish to contact the CMH for questions about historic practices.
We hope this is helpful. Best of luck with your research!
Perhaps this may be of use from the U.S Army Center for Military History:
In my experience using this as a resource, it has almost always been correct.
Best of luck!