Hi,
Actually, I understood that the tables come with 10 already added.
I saw the advantage of having tables of logs of trig values but I have
struggled to understand the advantage of adding 10 to the values in the
table. When I compare that to using the logs directly, it seems more
complicated in that one has to subtract some multiple of ten from the
sum of the values taken from the table (1 x 10 when multiplying two
values, 2 x 10 when multiplying three values, etc.) My thinking was that
if the aim was to simply to avoid using negatives, the calculator-person
could simply leave off the minus sign.
But now, from looking again at the examples in your diagram, I think I
understand: it seems that one does not carry digits over into the tens
column of the summation. And dropping the tens column has the same
effect as subtracting the extra multiples of 10.
So, for example, the method involves something along the lines of 9.1 +
9.1 + 9.1 = 27.3 but don't write '2' in the tens column = 7.3.
It's nice to encounter so many strange things on the Sundial List.
Steve
On 2022-08-09 1:12 p.m., R. Hooijenga wrote:
Hi Steve, all,
Yes, the ’10-trick’ was so common because it made things very easy –
well, comparatively speaking.
But I see I have not been entirely clear: I forgot to mention the big
trick, because to me it is so obvious – the user doesn’t have to do
any adjusting, because the tables list everything ready-made.
For instance, the sines table would not tabulate sines, nor would it
tabulate the log of sines: it would tabulate the ten plus the log of
the sine.
All the computer (the person doing the computing!) had to do was look
up the angle – say, 31° 25’ from the example – and get the number
9.71705 /directly from the SIN table/. Likewise, 45° 05’ will give you
9.84885 in the COS table.
The addition of ‘minus ten’ in the example below was just to make it
clear to me, the student, what was happening. In actual practice it
was never written down.
And going the other way, still in the example below, you could just
search for ‘9.88400’ in the log-sin table and find the corresponding
angle 49°57’ 36”. (Unfortunately, there is a printer’s error in the
example here: the number should really be 9.88400 , not 0.88400.)
Of course, interpolation was most always required; there were handy
small lists for that in the margins of the table pages.
/A sight reduction form was a marvel of efficiency/. Just take your
sextant-read altitudes, determine all necessary corrections (you must
do all that even today), and enter all on the form.
Then, just proceed line by line: adding, sometimes subtracting, and
looking up in tables; and you end up with a star fix.
Later, we got the HO-249 (and similar) publications, reducing the work
even further. I bet that old first mate could work out a fix just as
fast as anyone can today on an iPad.
And if we dropped our HO-249, the worst that could happen was that we
cracked the spine (not that it ever happened); compare that to the
drama that a falling iPad might engender!
Rudolf
*Van:* sundial <sundial-boun...@uni-koeln.de> *Namens *Steve Lelievre
*Verzonden:* dinsdag 9 augustus 2022 17:43
*Aan:* sundial@uni-koeln.de
*Onderwerp:* Re: Computing hour lines for horizontal sundials
Ooof!
Did the method of adjusting all the logs by +10 really make the task
easier?
Merely negating the log seems better to me.... or simply learning to
do arithmetic on negatives.
Steve
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