When viewed from the front, one can most clearly see the position of the soldier's left hand -- it is never higher than the breast. The second soldier appears to have it as low as his abdomen. Also note how straight and vertical the piece is carried in each instance -- it is not listing towards the rear. This is further illustrated in the next set of images.
In the first two images, when viewed from the rear, we can see that the rifle is not resting at all on the top part of the man's shoulder. In the third and fourth images, we can see this even clearer -- all the "support" occurs at the small of the stock and the left breast. This will cause the piece to rest in a straight manner. When the soldier is viewed from the right, as in the fifth image, the stock should not be visible forward of the hips. If the 1st Sergeant were to look down a line of men at support arms, he should not see one rifle stock protruding to the front.
Some years ago, Cal Kinzer wrote an article entitled
"A Dozen Inexpensive Ways to Improve Your Personal Impression" which contained tips on how to present a better soldier's portrayal without burning a hole in your checkbook. To this list of twelve, I would like to submit that spending quality time reviewing the manuals for little details you may have missed, and reviewing photographs showing how these manuals were put into practice are one of the biggest (and cheapest) steps a re-enactor can take in the quest to "be like them." Likewise, re-enacting officers would be best advised to drop the arrogance of "I've been doing this since the '70s, there's nothing new you can teach me" and go back to the basics, and encourage their men to do the same. Just as in the game "Telephone," the quality of the information diminishes the further away from the original source it gets, such that decades of re-enactors learning from re-enactors results in the folks of our hobby looking like just that -- hobbyists. There are no better teachers of tactics than those who authored and mastered them in the 19th century. Their writings, drawings, and photographs are readily available. Use them!

Federal soldiers at the Elk River Bridge, Tennessee, 1862.

26th New York at Fort Lyon, VA.

Soldiers in the crowd at the Grand Review, 1865, showing slight degrees of variation among individuals, though staying somewhat true to the manual.
Sources
Baxter, Col. D. W. C.
The Volunteer's Manual. Philadelphia: King & Baird, 1861.
Casey, Brig. Gen. Silas.
Infantry Tactics. New York: D. Van Nostrand, 1862.
Gilham, Maj. William.
Manual of Instruction. Philadelphia: Charles Desilver, 1860.
Hardee, Brig. Gen. W. J.
Rifle and Infantry Tactics. North Carolina: 1862.
Library of Congress, Prints and Photographs Division, Civil War Photographs.
Stillwagon, John.
Right Shoulder, Shift: A Reexamination. Southern Guard Living History Association.
Special thanks to: Amanda Bradley, Bo Carlson, Ed Hermann, and Jason Wickersty.
This article may be distributed freely, but credit to the author must be given.
Updated Nov. 17, 2005.