The GLO surveyors (even in Nebraska) had to occasionally use trigonometry when faced with obstacles they could not measure directly across. If a right angle triangle could not be performed, the oblique triangle could easily be solved by carrying a book of logarithms. All the deputy surveyor had to know was simple addition and subtraction. This simple math was something most of the illiterate crew could not even do, so the availability of a book of logarithms was important to have.
Below is a document I put together showing how they accomplished it.
http://www.penryfamily.com/surveying/images/earlytrigonometry.pdf
Very nice! You could have a future in teaching.
I wonder if those notes were easier to read 100 years ago..
Seems like a lot of work went in to making them attractive anyway.
Memories---When I first started in this business back in '71 my chief had me carry Smoley's Log book as part of my equipment. It was the five place edition so it fit into your back pocket. Many hours sitting in the woods doing calcs long hand with that little book. When the simple calculators (add and subtract) became small enough we went to natural numbers. Still have it somewhere.
Nice job on the explanations.
> Memories---When I first started in this business back in '71 my chief had me carry Smoley's Log book as part of my equipment. It was the five place edition so it fit into your back pocket. Many hours sitting in the woods doing calcs long hand with that little book. When the simple calculators (add and subtract) became small enough we went to natural numbers. Still have it somewhere.
>
> Nice job on the explanations.
Unfortunately, I have the same memories.
I wish we had such evidence in the notes in some of the work I have done in the First and Second Meridian Surveys in NE Indiana and NW Ohio in dealing with the Maumee River.
The Maumee is wide with steep banks and can be fairly deep in some seasons. None of the transcriptions of the original notes ever mention how the distances across the river were measured, but if the Deputy Surveyor was following the instructions (of 1815) the measuring instruments were a two pole chain and a Rittenhouse Compass. The notes typically give a distance to the top of bank and the next note is the opposite top of bank. In many cases the distances from the 1819-1821 original surveys agree very closely with what we measure today. I have often wondered, standing on the top of the bank of that river, how they got over it with a two pole chain. Most likely, they did not, but we have no way of knowing. Personally, I think that they probably had no log tables or trig tables, and that they just sent the axemen out to work until a right triangle solution could be performed. I wish we knew for sure, as you do.
Thanks for the post.