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Log tables
Posted by davekaroly on November 17, 2022 at 3:24 amI got the old log table book off the shelf. I figured out the logs fine but there??s a mysterious set of angles at the bottom. The explanation at the front of the book is about as clear as mud. Nothing I do produces those numbers.
The writing is in some strange dialect, most of it I figure out eventually but this is baffling to me.
It has S=4.685 on every page of the entire set of tables. Than the numbers after. Same with T=4.685.
davekaroly replied 1 year, 7 months ago 5 Members · 15 Replies 
15 Replies

One thing I??ve learned about the precalculator era is they would add negative logs to 10. Found that in the slide rule book. So that cleared up why they have positive logs with a characteristic greater than zero for the logarithmic sines, etc.
The USCGS book of sines, etc. has no instructions but I figured it out after some effort.

There was a time when I knew all of that but it has been too many years since then. Good luck.
For beginners.

I believe those numbers at the bottom are a method of finding log sin and log tan for small angles more accurately than would be directly in the table. The CRC Standard Math Tables book has a description using table entries called CS (correction to sine) and CT (correction to tangent) with the formula
log sin theta = log theta(seconds) – CS etc. Those numbers 4.685…. seem to check out as the CS and CT correction for angles around 2700 seconds= 45 minutes.
I have no idea how to do similar with 27000 seconds, as CS and CT would differ from those for 2700 seconds in the 3rd decimal.
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I believe those numbers at the bottom are a method of finding log sin and log tan for small angles more accurately than would be directly in the table. The CRC Standard Math Tables book has a description using table entries called CS (correction to sine) and CT (correction to tangent) with the formula
log sin theta = log theta(seconds) – CS etc. Those numbers 4.685…. seem to check out as the CS correction for angles around 2700 seconds= 45 minutes.
The T correction doesn’t seem to work for me and I have no idea how to do similar with 27000 seconds
Thanks.
My slide rule book (1955) which I downloaded was written by a couple of Northwestern University Engineering Professors and they are fairly easy to follow plus they give plenty of examples so if the text is not clear, the examples help figure it out.
But the Logarthm (1947) book by Dr. Bruhns, Professor of Astronomy in Leipzig reads like it was written by a German Poet then translated into English. “The number you seek.”

written by a German Poet
I hope everyone has a great day; I know I will! 

Note that I edited my post after you quoted it.
The log of sine 1? doesn??t quite match my calculator:
But the log of sine 3?ø26??01? does match. The line over the 5 has something to do with rounding, I think.

On my 40yearold HP 15C I get 10+ log sin 1″ = 4.685 574 867
Excel gives me 4.685 574 866 82 in good agreement.
I think your complaint is against the calculator app, not the table.
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On my 40yearold HP 15C I get 10+ log sin 1″ = 4.685 574 867
Excel gives me 4.685 574 866 82 in good agreement.
I think your complaint is against the calculator app, not the table.
I paid $15 for the hp 15c app on my work phone. Seems like it was worth it.

I have a free app on my phone called RpnCalc that doesn’t use any particular HP layout, and I find that confusing, but it agrees with the HP on log sin 1″ and anything else I’ve checked.
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I have a free app on my phone called RpnCalc that doesn’t use any particular HP layout, and I find that confusing, but it agrees with the HP on log sin 1″ and anything else I’ve checked.
I tracked the problem on the RLM 11c app to the DMS to DD converter. It misses on a couple of digits out 7 or 8 to the right.
if I do 1/3600 then sin then log then 10+ it matches the book and my genuine hp15c app which has a correctly working DMS to DD routine (>H).
The other thing at the bottom of the pages of the log tables is to get a log small angle to X.XX?. You look up you angle in minutes and seconds and convert to seconds only (most of the time will have to interpolate). Then you look up the log of that number on the page and add it to the number at the bottom. I tried it and it works.
The book is written by an Astronomer and there is a lot of focus on fractional seconds which usually wouldn??t be a concern to Land Surveyors.
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