A. F. McGahey mentions the train accident in this letter to his wife dated January 7, 1863. January 7, 1863 was a Wednesday as was December 31, 1862.
"Vicsburg is the largest sity that I ever saw. Thare was a grate ascident happened on the rale road on last Wednesday about 14 miles from hear. The cars run off the track and killed nine men and wounded forty one more. They nearly all belonged to the 35 Miss Regiment, the same regiment that Tom belongs to, but I learn that hee was not on that train."
See this post from George Purvis.
Hope this helps,