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Re: H.O. 203/204, Littlehales, Hydrographic Engineer
From: Brad Morris
Date: 2017 Mar 22, 23:25 -0400

Frank

Thank you for the paragraph on Littlehales. That was instructive.

Mixer estimates 500,000 values in those tables. In the days prior to digital computation, several (3?) human computers were independently utilized such that confirmation of each resulting value could be obtained. Say 1.5M spherical triangle solutions. That's a mind numbing mountain of tedium! That would be 3 human computers going at the rate of a solution every minute, non stop for nearly a year. No bathroom breaks, please!

Mixer also says they became unpopular by the mid 1930s. I understand that. These volumes are huge and heavy. Compared to the other, much smaller tables which came after, the volumes are almost ridiculously large. I've heard that complaint about 229, which is much larger, but the complaint still fits on 203/4. Very large and heavy.

I didn't get the horary bit until you mentioned the sextant as a sundial solution. Worsley does that when he rated his chronometer on Elephant Island, yet that was a multiple table entry solution, obtaining several logarithms. The logarithms are manipulated such that the last table can be consulted, where the arc sine of the logarithmic manipulation was turned into time by table lookup. The column in that table merely divided the arc sine result by 7.5°/hour, yielding hours since noon. But that's hardly a single lookup to find the result of the spherical triangle. It was a multi-step, multi table entry solution.

So those early references must have greatly differed from the common method practiced by Worsley. Has anyone had a look at them?

Brad

On Mar 22, 2017 10:50 PM, "Frank Reed" <NoReply_FrankReed@fer3.com> wrote:

Brad Morris, you wrote:
"In fact, the three references you specify are specified by Littlehales."
Yes, and I think it's extremely likely that Cotter got those references from that very footnote. Cotter was a library researcher, not a primary source historian.
And you asked:

"If you are a French speaker, would you mind translating the lengthy title of the Lalande work."
I'm sure others will offer their versions. There are "literal" translations and "sense" translations. Here's mine which is somewhere between:
"Epitome of Navigation: historical, theoretical, and practical, in which are found the principles of maneuver and piloting, the most simple methods of voyaging at sea by latitude and longitude, with horary tables for determining the true time by the altitude of the sun and stars at all times of the year and at all latitudes up to 61°"
I had to think for a bit on the translation of that first word "Abrégé" but when "epitome" popped into my head, I realized it was ideal (and an echo of all those discussions of Worsley's epitome!). The expression "horary tables for determining the true time" is what we know today as "tables for local apparent time" or "sundial time". These were lookup tables for "time sights" in other words. Certainly no big deal though a lot of work for the compiler.
There's a brief description of HO 203/204 in Mixter's famous Primer of Navigation which was first published in 1940. He describes them as "popular when first published" but "obsolete" at the time of writing (late 1930s). See attached chapter from his Primer.
Frank Reed

Attached File:
Mixter-on-methods-(1940).pdf

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