Did you just suck that out from your thumb? When constructing those straight bars needed for the rectilineator you would make them all from the same template. However, when finally using the bars you would turn one's face downwards and the next bar's face upwards. By doing so you would reset any error in the template that would otherwise cause the drawn line to bend in either direction.

Inverting the rectilineator section top/bottom doesn't help either, for the structure will still sag in the same sense, with ends drooping. Could this be the systematic error that accounts for the results? With the materials used in the rectilineator, the sag can't be very large. But a sag of only 0.000003 degree in each section, multiplied by the 1045 sections in a four mile length, gives a cumulative error of 0.003 degree. That would be about the latitude difference between the endpoints of the survey. Such a small error was far too small to be measured or detected in just one, or even a string of a few, rectilineator sections.

This is a subtle source of systematic error. The preliminary tests of the rectilineator were done with only a few of those sections they had (four). The systematic error for these would be far beneath detection level during those tests. An individual section's cross arms might deviate from parallelism in one of two directions, or might, by sheer accident be nearly parallel for one orientation of the rectilinator. If it deviated in one direction, then when the section was inverted, the deviation would flip in the other direction and still be such as to cause the ends to bend downward. Even if by pure accident the first few rectilineator sections were aligned exactly parallel, the procedure of "recycling" sections and inverting them would ensure a systematic error from that point onward of about the same amount over the entire length of the survey.