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Cahill 1909

B.J.S. Cahill's World Map Variants:
1) Conformal

In the 30 years after Cahill published his initial Butterfly map in 1909, he also produced several "Variants" as well as other false starts, with a confusing array of nomenclature and neologisms. However, besides the 1909 original, Cahill settled on three main types, the clearest illustration of which is in this [1934] offprint from Nelson's Encyclopedia:

Source: B.J.S. Cahill, "Projection"(Nelson's Encyclopedia, [1934], offprint;
 also in Cahill, "The Butterfly Map: Octahedral System of Projection" (Pacific Marine Review, 1938-09) p. 42-43.
Scanned and enlarged by GK from a duplicate offprint received from
B.J.S. Cahill Collection at The Bancroft Library, University of California, Berkeley.

Note: on an earlier page, I showed a smaller enlargement of this image at the same scale of
1/200 M as a set of other Butterfly maps. Here, I have made it yet larger for emphasis of the Three Variants.  

A conformal map is one in which meridians and parallels cross one another at right angles — as on a globe, but much more problematic when it comes to devising a flat world map.

On Cahill's earliest map, the graticule was a very well-drafted custom-made assembly — he was an architect, remember —, but it was derided by ultra-mathematical cartographers. So Cahill set about making some more rigorously mathematical variants, and even hired the prominent mathematician Oscar S. Adams to compute their graticular distributions at five-degree intervals for all three main variants. Meanwhile, Cahill had not forgotten what I consider his foremost principle:

The creation of a master plan of the world is a matter of design first and foremost, the design of a frame within which intensive mathematical details shall be afterwards subordinated. (1928)

In most of his examples, Cahilll's Conformal is embedded in equilateral triangles, unlike the truncated ones of Variant 2, the Equal Area (and the curvilinear octants of his 1909 original).  Below is an undated [mid 1920s?] Cahill Conformal draft in the North Pacific Butterfly orientation, one of a number of illustrations ["Fig. 5"] for an unpublished article or book manuscript. Like his earlier maps, it has his dubious 7.5 x 10º graticule, which conceals the split geocells along the perimeter meridian. (By 1927, Cahill was at last showing a 5º graticule.)

Source: B.J.S. Cahill Collection at The Bancroft Library,
 University of California, Berkeley;
Xeroxed, then scanned and reduced to 98% of original for a scale of 1/200 M
by GK.

The next one [mid 1920s?] is done at 5º resolution, betraying the sore-thumb two-and-a-half-degree geocells along the outer perimeter. (In this version, however, Cahill has omitted the internal northern triangle sides, concealing the half-degree problem.in those areas.)

Source: B.J.S. Cahill Collection at The Bancroft Library,
University of California, Berkeley;
Xeroxed, then scanned and reduced to 75% of original for a scale of 1/200 M
by GK. (Larger copies further below.)

This 1924 drawing is perhaps the only instance in which Cahill showed a Conformal graticule inside curvilinear octants, whereas his other Conformals were all done with equilateral triangles. So far as I know, he did not develop this version, nor add the continents, etc., unlike the triangulars. Here we see his excess nomenclature: three other titles (unused) besides Conformal.

Source: excerpt from a 36 x 57 cm (14 x 22") broadsheet. "The Butterfly Map"
at The Bancroft Library, University of California, Berkeley;
Xeroxed and spliced, then scanned and enlarged to 175% for a scale of 1/200 M by GK.

As I've mentioned elsewhere, Cahill seemed to "steal" my ideas before I was born, including the "M" layout instead of his predominant Butterfly. Below is an unpublished Cahill draft, n.d., ca. 1927, of the Conformal variant in an "M" shape. I do not know the purpose of the internal scaffold lines, but the four diagonals across the triangles' altitudes once again show what I regard as his design mistake of dividing the meridian-perimeter geocells in half, e.g., at 22.5º W instead of 20º as I did (and Steve Waterman independently). Using 20º, the altitude of each octant would be a central meridian 45º from either edge, instead of a column of bisected geocells. But at least this draft has the far preferable 5º geocells.

Source: Xerox from Cahill collection at The Bancroft Library,
University of California, Berkeley;
scanned, spliced, and cleaned by GK.

The next item [1928] is similar to Cahill's double piece* in the April 1929 Monthly Weather Review, but not entirely.

* (as copied from my Cahill Resource): 1928-12-28 / 1929-04 Cahill, B.J.S., "Projections for World Maps" —and text continued in separate pdf, plus illustrations:— Cahill, B.J.S., "A New Map for Meteorologists: Equally Suitable for Small Areas, Continents, Hemispheres or the Entire World" – both from Monthly Weather Review, 57/4, 1929-04) p. 128-133; illus. Has Cahill's only published [partial] world map with a one-degree graticule, except on land areas; as well, one of his only published five-degree world maps, regrettably discontinuous on two pages. See similar map in [1934] below, octants together, but in an awkward north-south spread, which I also show enlarged; and cf [1940] below, in Butterfly layout.

It is a broadsheet, 30 x 47 cm (12 x 18.5"), packed with tiny print because it was reduced from an original five times larger. [I have a complete scan of the small one, shown here, but only a Xerox-splice portion at the original size.]. So I re-enlarged the reduced typeface in separate frames below, to make its important content legible, especially the lower right section, "All Synoptic Charts from One Base Map", where Cahill again voices themes that I was discussing 45 years later, before I found he too had raised many of the same concerns.

The map itself is in still another layout, a North and South zigzag spread, which Cahill thought might be apropos for a consolidated world weather map.

Above is the map's broadsheet which I scanned and uploaded at its actual 1/5 size version.. In the next frame are detail-enlargements of its text portions. In the first subtitle cut below, we again see Cahill's confusing nomenclature: unillustrated mention of his otherwise unused terms "Authalic", "Orthometric". and "Graticular Scale". (I was also confused at first by the character "V", thinking it was a Roman numeral for "5" among Cahill's versions; but it is an abbreviation for Variant.) Note also the credit to Dr. Oscar S. Adams, the prominent mathematician whom Cahill hired to calculate all three Variants subsequent to the original.

Below is the same text detail as the last piece above, but at its original size, as Xeroxed and spliced from the original at the Cahill Collection in the Bancroft Library, then scanned in two parts and spliced in ClarisWorks by GK. Notice that the "E PLVRIBVS VNVM" sheets are more distinct in this original size image:

Source: Monthly Weather Review as indicated,
April 1929; jpeg screenshot of pdf, enlarged by GK

Source: The Bancroft Library Cahill Collection. (Listing items 19 and 20.)