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Re: Measuring Dip in the 18th Century
From: Bruce J. Pennino
Date: 2013 Dec 26, 14:55 -0500

I agree with FER's comments . I did the same thing with the Table in the Mariner's Compass Rectified by Wakely. t I understand this to be a 1781 publication, but gather the data is from 70-80 years earlier...sorry having trouble following the references?

But, I took the Wakely table for dip and just calculated an average dip coefficient of about 1.15. (minutes of arc and height of eye in feet). This is clearly geometric dip . But the dip coefficient depends very much on the radius of the earth which early mathematicians and surveyors were working on. I believe by 1750 (I've seen a table somewhere) that the French and English astronomers had settled on an average radius that was good to a couple of percent? About this time or somewhat earlier a "true" vertical could be established, and then a true horizontal could be obtained. I don't know when angles could be precisely measured (dividing engine and all that), but that is when correct dip values were measured by an astronomer and he corrected the geometric dip equation. That's my theory and I'm "sticken to it". I've got to find my dip analysis where I "derived" a geometric coefficient of 1.06 using a modern earth radius. I suspect changing the radius 1 or 2 % value can easily change geometric dip coeffiecient by few percent. The pure beauty of the onshore theodolite measurement from the vertical is the simplicity of the measurement...... just sight the horizon and subtract 90 degrees. The early astronomers figured this out...simple compared to the other things they were doing. The astromers had to wait for the instrument makers to "catch up".

Bruce

----- Original Message -----

From: Frank Reed

To: bpennino.ce@charter.net

Sent: Thursday, December 26, 2013 2:07 PM

Subject: [NavList] Re: Measuring Dip in the 18th Century

Brad, you wrote: "I suspect that there are navigational dip tables for the earliest of instruments that measure altitude vis the horizon. So for the cross staff at sea, there must have been a dip table. I wonder, what is the earliest published dip table? " Those early dip tables fall into the category of "advice to future generations". You can't measure angles with a cross staff or a backstaff or any other handheld pre-double-reflection instrument to better than maybe +/-10' accuracy under excellent conditions. So unless you're observing the sea horizon from well above a hundred feet altitude (maybe from a cliff?), these dip tables served no practical purpose ...yet! This is an example of something that mathematicians and other "natural philosophers" understood from a very early era (try Ptolemy), and they just couldn't hold their tongues waiting for it to become useful. The dip table from 1599 that Gary posted is easy enough to reverse-engineer. You can calculate nearly matching values using the simple formula dip=1.10*sqrt(h) with dip in minutes and h in feet (with that constant the dip calculated for 90 feet altitude rounds to 10 instead of the listed 11 but the difference is only half a minute of arc in any case). Since the mathematical details of refraction were unknown, we can safely conclude that this was a geometric dip table for a slightly over-estimated radius of the Earth. -FER ---------------------------------------------------------------- NavList message boards and member settings: www.fer3.com/NavList Members may optionally receive posts by email. To cancel email delivery, send a message to NoMail[at]fer3.com ----------------------------------------------------------------

: http://fer3.com/arc/m2.aspx?i=125928

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