This is how the 1873 Upton's Manual describes the motions of "salute"
"18. The instructor commands: 1. Right (or left) hand, 2. SALUTE.
Raise the right hand smartly, pointing in the same direction as the right foot, the palm of the hand down, the thumb close to the forefinger, the arm extended, and horizontal. (Two.) Bring the hand around till the point of the thumb and the side of the forefinger touch the lower edge of the cap or visor, at the same time turn the head a little to the left, look toward the person to be saluted, and retain this position till the salute is acknowledged. (Three.) Bring back the hand and arm to the position of the first motion, at the same time cast the eyes to the front. (Four.) Drop the arm quickly by the side."
So it would appear that the salute changed in or by 1873(the army manual was by Upton in 1868 as wel,l but I can't put my hands on my copy of the '68 manual right at the moment).