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This a discussion of the effect of gravity on precision measurements.  
Posted by Matt Maguire <maguire@misslink.net>. Matt provided the following:

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Indsag.txt (Indicator sag text)

I've received some E-mails about "Indicator sag" So I decided to put something down
on the topic.

Indicator sag is what happens when an indicator is used for measurement and is rotated
about a horizontal axis. If the indicator is on centerline with a hole or round, it
will not "measure" the same in all positions, IE 12:00, 3:00, 6:00 and 9:00. If a hole
is bored in a horizontal plane and immediately the hole ID is swept with an indicator 
the machinist will (should) find that 6 and 9 o'clock will give the same reading and
12 o'clock will be minus and 6 o'clock will be plus, indicating about the OD of a
shaft or sphere will reverse the readings at 6 and 12 o'clock. This is our old friend
gravity at work, along with spring pressure and the stiffness of the assembly used to
hold the dial indicator.

The lathe hand may prove this by chucking a bar up, setting up a suitable rig for
holding an indicator against the OD at the back of the chuck at 12:00, setting the
indicator at "zero" and simply rotate the chuck 180 degrees. Note that the indicator
is still "indicating" the same spot on the chuck but reads minus something. The
bearings have nothing to do with this, as all you are measuring is the distance from
the center of the chuck to the outside, but the chuck just got smaller by turning it
upside down (at least the indicator says so).

The amount of sag can vary from .0025" with a light, closely coupled stiff rig, with
a lightly sprung indicator, to a whole bunch with a heavy setup, springy rig and
heavily sprung indicator. I've seen setups that sag over .030".

Now, where this might be important;

Mill operators should always be aware of sag when sweeping holes for reference of
location with the spindle in the horizontal plane.

Lathe operators need to be aware of sag when adjusting a steady rest by sweeping the
tailstock or using a live center to sweep the piece. Or just checking the tailstock to
spindle bore relationship.

Millwrights need to be aware of sag for shaft alignment in the horizontal plane,
(I've seen some real disasters occur because of poor shaft alignment.

And what do we do about it;

This is the easy part, you simply test the rig you are going to use. That is using
the indicating rig against a known reference before using it on an unknown reference.

For horizontal boring mill users referencing a hole, the spindle is extended and the
rig turned backwards with the indicator on the spindle OD, zero the indicator at
9 o'clock (3 o'clock for Lucas and TOS machines), the spindle is rotated noting the
readings at 12 and 6 o'clock. When the bore is indicated (using the same rig) the
noted readings are REVERSED. For dial test type indicators such as "Last Word" with
a jig bore attachment and small holes I have fashioned a set of right angle bars to
test for sag off the machine if I need to work to close tolerance. Every once in a
while I'll just indicate a bore just machined with one of my dial test indicators,
I find that my last words usually sag about .003" and my interrapid about .002" TIR,
if they are more I'll adjust the joint tension on the indicator.

For lathe work this type of sweep indicating is usually done with a mag base or the
"C" clamp found with test indicator sets. In this case the rig is tested back over
the workpiece, or if clamped on the live center swept around the tailstock quill.
Readings are then noted and when the rig is reversed to do the actual indicaing the
readings are retained. IE if the indicator was +.002" at 12 o'clock and -.002" at
6 o'clock while testing sag, then the indicator should read +.002" at 12 and -.002"
at 6 when testing, or setting is done with the workpiece.

Shaft alignment is done the same as for lathe work, however there are usually sweeps
taken from 4 locations with at least 2 different rig setup lengths to account for all
variables. I'll not go into all the variables and calculations here for shaft aligning.

Rules;

1 rig setups are the same for testing and indicating, IE if you're reaching out 8"
then you test back 8".

2 If testing OD and Indicating OD all noted readings and offsets are the same.

3 If testing OD and indicating ID then all readings and offsets are reversed.

None of this addresses the problem of shaft deflection, but in my experience this is
only a concern with heavy long shafting in a lathe and almost never an issue in day
to day operations with the machinist.

If there are any tech writers out there that feel they can clean this up a bit,
please be my guess as I consider this info to be in the public domain.

Respectfully submitted
Matt Maguire