On page 33 of the 1864 manual, "Field Artillery Tactics". It states that "A horse travels the distance of 400 yards at a walk in 4-1/2 minutes; at a trot, in 2 minutes; at a gallop, in 1 minute."
On page 34;"Average daily marches at natural rates are,
for infantry, 15 miles, preformed in six hours;
for cavalry, 17 miles in six hours;
for artillery, 16 miles in ten hours"
this would be over common ground, if the ground was rough or no roads present, the rate of travel would be longer.