Water Levels Versus Mechanical Levels

Theodolites are not good for running levels because the scope length is too short. Use a level for that purpose.

Your other problem has to do with the fact the the earth curves while a line tangent to a point on the earth does not.

I assume that your mechanical level is just producing what amounts to a straight line tangential to the surface of the earth at the measuring point. If this line were extended, it would gradually get further and further away from the surface of the earth. After some distance, it would become a noticeable incline, in that a ball "balanced on the line" would roll back towards the tangent point.

Don't get "flat" and "level" mixed up.

At the risk of starting a semantic firestorm, I suggest that you don't get "flat" and "level" confused with "plumb".

Flat ≡ planar

Level ≡ perpendicular to the (local) force of gravity

Plumb ≡ parallel to the (local) force of gravity

Could still drive a bus through the holes in these definitions - but I think they'll do. Feel free to improve.

Nope. They'll do just fine. No confusion here.

huge bus in that, de-finite-ly

Expand.

Neither; the curve, called entasis, was in the columns, bulging slightly outward.

(If the water level was 26 inches off, how was that more precise?)

OK so the floor was "level" or "flat" right?

Both level and flat. Over the dimensions of the floor area of the Parthenon, there'd be immeasurably small differences (in ancient Greek terms) if following the curvature of the Earth.

(Could've slipped up, but the back of my envelope reads ≈ 0.8mm in 100m. The Parthenon is about 70m long, so there'd be a bulge of less than 0.3mm in the centre with respect to the ends.)

Thanks. You are well informed re the Parthenon. Question. When engineers make tunnels through mountains working from both ends and meeting in the middle I assume they use mechanical devices like theodolites and laser levels. Does this mean that the tunnel does not follow the smooth curvature of the earth and is in reality a series of tangential flats stepping along in sections?

Out of my field, I'm afraid.

A 'straight tunnel' between two points of identical elevation, would 'gravitationally' seem; down hill, then up hill - but as the grade is so 'slight', you would need a very long tunnel to have noticeable effect.

However; in very long building sights all levels are created from a center datum - not from one end.

This, in fact may be the 'error' the OP found. I.e. optical measurement should be set in the middle, and taken relative to water level ends.

It's kinda 101 earth moving in big sites and particularly in large scale flood irrigation.

I like the question because which is right? Either device can have errors.

You can have bubbles in the water, for instance. If part of the tube was in the sun and part out of the sun some of the water might be hot, some might be cold so its density might be different at one end of the level to the other. But generally, I would trust the water level before I trust anything else.

I test laser levels sometimes by pointing to a spot, marking the dot and then transport the laser to there and seeing if the level laser hits the original place from there.

The results may lead you to return your level!

I have had customers take out their kick ass devices and overrule a wall height by half an inch or 1/4 of an inch at either end. They give themselves a great amount of stress for nothing and if they never calibrate the device, who is really getting ass kicked?

A water level at 2km might not be that accurate either.

The pipe may be heated more in one place than another causing a difference.

The error with a mechanical system can be corrected because the exact difference will be available.

Somewhere in the 1700's a surveyor started a survey of South Africa. one or more of his stations was on the slopes of Table mountain (a lone mountain) where the plumb line was of hanging skew. When he finished the task he came to the conclusion that the curvature of earth in the southern hemisphere is different from that of the north. It took almost 100 years for someone to find the error.

For any two points the water level is correct. If you add more points in the straight line then curvature will need to be calculated. If you place an optical level measurement device in the center between two connected water stand pipes you can calibrate your optical level.

My setup uses four stand pipes on 200ft dia.. Placing the device to check on a tripod at the center point lets me check and adjust level in two directions. I do this before and after using an "autolevel" which brackets my results, thus assuring the level before a concrete pour to be accurate. I realize this is double dead safe but it only has to pay off once to be justified and that risk is enough for me.

So you have the instrument at the center of a circle with a radius of 100ft and do you place each of the 4 pipes at 90 degrees from each other. What do you sight on, the meniscus in a clear piece of tubing? How do you get any bubbles out or anything else that might affect your accuracy. Due to my space limitations the best I could do would be around a 50ft radius circle.

Small bubbles (relative to the tube diameter) will have no effect on the levels, unless they are on or immediately below the surfaces, in which case it will be difficult to establish the level of the surface. The tube sightglasses should be of large enough diameter so that the surface can be clearly sighteded away from the meniscus. The diameter of the tube between the sightglasses is of much less importance.