Random scatter and shared bias
Independent repeat readings can estimate scatter. A tilted angle reference or an incorrect height datum shifts several readings together and will not disappear in their average. Record both effects rather than treating every discrepancy as random noise.
Propagate what the formula is sensitive to
For C = 360d/Δz, independent standard uncertainties give u(C)/C = √((u(d)/d)² + (u(Δz)/Δz)²). Two independent equal angle uncertainties contribute √2 times each reading’s uncertainty to their difference. A shared angular zero bias cancels only when it truly affects both readings equally.
Choose a separation that resolves the models
A tiny angle difference can make a circumference estimate unstable. A larger meridian baseline improves its angular leverage, while adding sites tests the form of the angle-versus-distance curve. Keep raw observations and state the uncertainty type; one standard uncertainty is not automatically a 95% coverage interval.