Error in My Analysis of the Dietrich-Kitada Projection

[quadibloc]

I was happy to have been able to figure out where the circular arcs that made the meridians needed to go in the conventional aspect of the Dietrich-Kitada projection.
And then, when I faced the problem of determining how to draw the parallels, at first I was stuck.
Then I had what seemed to be a flash of insight: when one goes to an infinitesmial lune, the width will behave as though it were bounded by parabolic curves.
That may be true, although my logic there wasn't rigorous either. But even if that is the case, the fact that the sine curve also approaches a parabola doesn't mean an equal division of the meridians by latitude is appropriate. In a Sinusoidal projection, after all, the meridians are always the part of the sine wave that goes from zero to pi (or 180 degrees), never a smaller region around pi/2 that is closer to a parabola.
So at the least, I'll have to adjust the latitude using the same formula as used in the parabolic equal-area projection.

I remembered seeing it in an old book from the U.S. Government whose name I didn't remember off the top of my head. But then I remembered the names of its authors. Imagine my surprise when a search for the terms "Deetz" and "Adams" on Google did not turn up Elements of Map Projections as its first result, or, indeed, anywhere on the first page. However, adding "map" as a search term fixed that. Somebody connected with an Addams Family movie is apparently a punster with a knowledge of cartography.
I was able to write code in my map drawing program for Craster's parabolic equal-area projection, and for a corrected version of the Dietrich-Kitada.
From QB64, I got the error that the intermediate C++ program failed to compile.
I looked for online information about QB64 to see if there was anything I could do, without much hope. However, upgrading from version 1.0 to the current version, 1.4, fixed the problem.
Here, without further ado, is what the Dietrich-Kitada looks like after my first correction (perhaps I got the lunes wrong and will need to do some other mind-wracking mathematics...):

EDIT: Ah, my pop culture knowledge fails me. Lydia Deetz was a character in Beetlejuice, played by Winona Ryder. As some fans of the Addams Family movies also watched that, and liked her performance there, they have expressed hope she might be given in a role in a future Addams family movie. This is why the names appear together, and Google spell correction is responsible for the rest.

[Atarimaster]

Here, without further ado, is what the Dietrich-Kitada looks like after my first correction (perhaps I got the lunes wrong and will need to do some other mind-wracking mathematics...):

Nice work!
But … I hate to say it, but I think there’s still some work to do. Here is Geocart’s version (red) layered over your version (green).
I can’t tell which one is closer to the original in Dietrich’s book, my scans of the original images are too bad to tell.
(If I got that right, Kitada never claimed that his version was a 100% match.)

[quadibloc]

I'm not surprised that I may have to do more work on the part of my projection that is away from the central meridian.
At the moment, however, I cannot imagine what further correction might be required for the central meridian.
I haven't been able to find Kitada's paper online; even if it's in Japanese, I might have been able to make something out of the equations.
At any rate, at least I've added a page to my site about Craster's parabolic equal-area projection.
http://www.quadibloc.com/maps/mps0410.htm

[daan]

I have the paper somewhere, as yet not located. For some reason, I also have this in digital form. I don’t know why it’s hand-written; I don’t remember the original paper being thus.

— daan

[quadibloc]

Thank you very much. I don't think it's handwritten, even if a script font is used for the trig functions. The spacing of the kanji is much too regular for that. But perhaps I misunderstood what you meant.

[Milo]

I'm afraid that between my unfamiliarity with Japanese and the low resolution of the scan I can't say for certain for the Japanese parts, but the mathematical formulae and the Enlgish caption at the top are definitely handwritten, albeit by someone with unusually neat handwriting. The trick is to look for multiple copies of the same letter, as with "Kitada equal area circle meridian". If they all look exactly identical, then it's a font that merely imitates handwriting. If they have subtle differences between them, then it's real handwriting. In this case it's the latter.

[quadibloc]

If they all look exactly identical, then it's a font that merely imitates handwriting. If they have subtle differences between them, then it's real handwriting. In this case it's the latter.

Taking another look, you and Daniel Strebe are right. I thought that the differences were due to variances in registration: a document with English letters in a script font was then digitized at a low resolution. But now, looking carefully, I see differences between the multiple occurrences of lowercase "a" that are too large to be explained by that mechanism.