I set up to measure cant yesterday, to answer the question:"Do we really need S.L. front sights?"
Here's the results so far.

A Stanley vial has 2 lines a little wider than the bubble. 
From center to touching the bubble = 1/4 degree
From center to all the way to the end of vial = 1 degree

My Maynard S.L.F.S. bubble could not be centered with screw adjustments to the test rig.
These are tests of my leveling the rifle, looking through the sights, not using a spirit level. Just eyeball.

Maynard, 20 tests, looking at a blank piece of white paper
Standard Deviation .73 degrees
Max Left Deviation  .86 degrees
Max Right Deviation 1.52 degrees

Sharps 1875, 21 tests, Iron sights, looking at gray sky
Standard Deviation .41 degrees
Max Left Deviation  .93 degrees
Max Right Deviation .69 degrees

Sharps 1875, 20 tests, 30X STS, looking at gray sky
Standard Deviation .30 degrees
Max Left Deviation  .39 degrees
Max Right Deviation .61 degrees

I think that this agrees with the previous article, that the human eyeball can repeat level pretty well. Most of the time to within +/- one degree. And that a flat or straight surface at the front sight aids that repeatability.
If there's anyone out there willing to make some tests, I'll be happy to describe the test setup which costs about nothing and takes about fifteen minutes to construct. 
Until next time, don't throw away those S.L.F.S.s, even if you may not need them.
joe b.

Joe & Forrest,

  The point Joe makes seems to me to be good on first glance, but like Forrest I'm wondering what these small "errors" amount to the further out you shoot.

  Someone correct me if I'm wrong on the following, but, I've always been under the belief that if you are .001" off your aim at the muzzle you would be aprox. 1/8" off at 100 yds.

  Now considering the errors Joe reported it would make it seem possible at the shorter ranges that a spirit level front sight might not be of much use as you shouldn't be able to tell if any errors were caused by so slight a cant.

  But the further out we go these errors increase at an exponential rate, and along with sighting errors induced by not being able to resolve differences in lining the sights up, these errors, to me at least, just seem to compound themselves.

  As an example...... I personally don't feel I'm all that much handicapped at 100 yds. using iron sights against a scope, because I can "shade" the sights as I need to for rapidly changing wind & mirage. But at 200 yds. my eyesight isn't good enuf to be able to shade less than a 1/4"- 1/2", so am not able to "hold off" for conditions as a scope would allow me to do.

  To get back to Joe's test..... Since he gave his errors in degrees, I would like to see someone with the math skills figure out what they would amount to in inches in 100 yd. increments out to a 1000 yds. I think that would be very interesting! Offhand I would think the results would indicate the very real necessity of using a spirit level sight the further out you go.

PETE

First, for dbm. The effect of cant has nothing to do with sight height, it only has to do with drop of the bullet. 
For Forrest et al. I don't know the B.C. of your bullet, with it it's easy to look up the drop. Canting a rifle moves the point of impact 1.745" per 100" of drop, per degree. A 1250 fps bullet with BC of .4-.45 drops about 360" at 500 yards, 1700 inches at 1000 yards. 3.6 X 1.745 = 6.28" per degree, 17 X 1.745 = 29.7". Everything I've tested so far says that without S.L.F.S. the human can hold within +/- one degree most all the time. I don't know how close to zero degrees cant we can hold with a S.L.F.S. And I don't know how important 6.28" at 500 yards or 29.7" at 1000 yards is-note that most of the time the error would be substantially less than one degree and these numbers. I originally suggested that a horizontal bar on the front sight made "level" much easier to hold, unconsciously, without looking at the bubble. Maybe a 2" long horizontal bar. See the scope results for a suggestion that this may be true. It's much easier to hold level with that horizontal crosshair.
joe b.

David,

 Well, as far as I can see you answered your own question when you said if you tip the barrel left or right the bullet strike will go left or right. That was my point. Vertical isn't the only error there is. Canting the gun in any direction induces error which, as you know, has been felt for over a 125 yrs. to be best corrected with the use of a spirit level sight.

 Now, whether this can be mathematically figured I don't know, as I must have missed that class when they taught it.

Joe,

 If, as you say the angle of departures you listed amount to approx. 6" at 500 yds. that will, if everything else is perfect, score a 10 instead of an X. In Shilouette shooting where it is figured that a load with an accuracy of 2 MOA or 10" at 500 yds. is the minimum needed to hit the Ram. Add this 6" of error to minimum load requirements and it's not hard to see you're getting pretty close to a miss.

 Another point I think you are missing. That is personal sighting error (PSE). The ability to resolve a given distance at any given range. I mentioned in my last post that I did not feel handicapped much against a scope while using irons at 100 yds., but felt a scope would beat me out at 200 yds. and further.

  A simple test for PSE is to mount your gun solidly on the bench, and at any given distance you choose, have an asisstant move a box around, with target attached, until, looking thru the sights, you determine that the sights are lined up perfectly. The asistant marks a point thru the center of the target, then moves the box and you start all over again, until you have 10 points marked. Measure the group at it's widest point and that is your PSE. With training this can be reduced, but there will always be some error, and this must then be added to any of the other "personal" errors you induce into the shooting equation.

 For arguments sake lets say you have a PSE of 1" at 100 yds. Just running this out on a straight line increase will get you 5" at 500 yds. But, as any eye doctor will tell you this isn't necessarily the truth, because that would mean that at 500 yds. you can resolve the difference between 5" and 6". The truly great shooters probably can, but most of us can't, and the older we get the worse it gets. That's the reason the black on a 600 yd. target is so large. If only the 6" X ring were black many people would have a hard time seeing it.

 The point I'm trying to make is that fixating on whether a spirit level sight is really necessary or not, just doesn't cover even a small part of shooting. A spirit level sight isn't all there is to shooting well at any distance. It is just one of the tools a shooter can use in their quest for a perfect score. If you can eliminate even a part of the canting error this equates to a slightly better score.

 Your idea of a bar set horizontally to some arbitrary point might work out ok. But, many of us believe that the spirit level sight would allow you to more easily line up the rifle correctly. Your argument that noticing whether a bar is level is quicker than a spirit level sight, or not, might be valid, altho I still think you would have to check it at some point in your shot consciously to be sure it is level. It would seem to me that glancing at both it would be easier to tell if the bubble was centered than if a bar was level.

 Good discussion. Gets me thinking about the various possibilities.

PETE

To dbm. If you draw a picture of the rifle, target, sight line and bullet path, then imagine it rotated 90 degrees, it helps. The only thing that affects displacement per degree of cant is bullet drop.
To Pete. Cant makes the bullet shoot off in W and E. The E is insignificant at small = <15 degree cant angles. (1-cosine theta) 
PSE was treated thoroughly in a Rifleman article probably thirty years ago. I was going to do the test, searched the literature, found the article and quit. PSE is small, tiny, approaching zero, no matter iron or scope.  Has almost nothing to do with distance between sights. 
I didn't say that the angle of departure is anything. I said that with my Sharps and irons, the S.D of cant is .41 degrees, means that 95% of shots within +/- .82 degrees or something under 5".
Now, how precisely can you repeat with your S.L.F.S.? It ain't perfect! Why not test?
Next, errors don't add nor subtract simply. The square root of the sum of the errors squared is the total error. One must do the arithmetic, or remain confused.
And, the results of my survey-"Do we need S.L.F.S.s?" is far from unanimous.  I know that you are unanimous, but others differ. There have been some fairly good scores and groups shot in the past 125 years without a bubble to watch. 
My Maynard uses a Winchester sight. I'd contend that most of the 1885 Winchesters, indeed most of the schuetzen rifles, were used at short range, mostly offhand. Here the S.L.F.S. is of no use, just another whistle to confound the opposition and get rid of a few bucks.
Cant affects bullet displacement as a function of drop, so any short range or higher velocity work reduces the effect of cant to the minute.
Use 'em if you want, but you ain't fooling me!
joe b.
I suspect that a horizontal bar maybe even an inch long, would do the job.
 

David,

  I don't recall ever reading anywhere that a vertical line is easier to position than a horizontal one. Personally I use whatever horizontal lines are available in the scope or the apperture if no bubble level is attached. If the apperture is just attached on the bottom then I will use the flat surface of the cross slide. But, in all cases I feel that a bubble sight is the best.

  But your idea of rotating the insert might be of interest altho all the inserts on globe front sights I've seen will only allow you to rotate them 180 degrees.... maybe. Most seem to be set up with studs of two different sizes that fit notches on the side of the globe, so even rotating it 180 degrees isn't possible.

  I suppose tho if someone wanted to try the idea out they could cut these studs off....... but don't do it on your favorite size! 

PETE

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Oh, I favour the bubble as well. It is a more sure way of eliminating another variable. They just take some training with to devleop an awareness of, without constantly switching the eye from the foresight element to the bubble.

David

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