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1912 October: B.J.S. Cahill elaborates the Butterfly World Map:
B.J.S. Cahill, "A Land Map of the World on a New Projection"
(Journal of the Association of Engineering Societies, 1913-10; orig. 1912-10)
p. 153-207, with 50 illustrations. Reformatted in HTML by Gene Keyes.
Part 2 of 2: illustrations.   [Go to part 1 of 2: main text.]

Illustration notes by Gene Keyes, 2008-04-16:

For the article itself, I did an OCR scan from old Xeroxes*, and reformatted it in HTML. The 33-page text (p. 153-185 of the Journal) is all in the other file. I have scanned its 50 illustrations (p. 185-204) into this separate file, which should be opened together with the first one. These pictures are hotlinked from the text file.

Note: because of the captions' tiny print — and because the original artwork was bigger than in the Journal article — I have enlarged the scan versions of both by 40%.

* Early Xerox could hardly reproduce areas of solid black, so the continental silhouettes don't show up very well in some of the figures here. My first Xerox of this article was from the Library of Congress in 1975. Having marked up that one so much, I got another somewhat improved Xerox copy in 1982 from the Bancroft Library Cahill Collection, University of California, Berkeley, plus other research material copies when I examined those archives for nine days in 1983.

My picture scans from either Xerox version still don't do justice to the print-quality original, which I lack. In a few cases, I have been able to compile better images using offprints of other articles or duplicates from that Cahill Collection; and I had re-inked Fig. 43 by hand in 1975. I have also re-typed some of the captions, in lieu of scanning.
For help during my 1982-1983 Cahill research project, many thanks to Mary Hardy, then at the University's College of Environmental Design Documents Collection, and Philip Hoehn, then Map Librarian at U.Cal. Berkeley.
Comments below in italics are by me, GK; all the rest are Cahill's.


Fig. 1-2, Stereographic Projection  

Figs. 3-7: Gnomonic, Orthographic, & Globular Projections  

Figs. 8-14: Cubical, Cylindrical, & Conical Projections

  Fig. 15, Pacific Ocean on Gnomonic Projection

    [In this instance, the globe-circle is smaller than the others. — GK] 


Cahill, fig. 15
 Fig. 15, caption


Fig. 18, Gores of a Globe

Fig. 18.  The Gores of a Globe.

   The paper gores of a globe peeled off and laid side by side. This maps tells the truth about the globe as to the actual shape and size of the land masses. By carrying the sizes of Alaska, Greenland and Scandinavia in the mind's eye and comparing them with these areas in the maps below, one can compare the various projections with the normal facts. See also Fig. 8, 26, and 36.

Fig. 19, Mercator Projection
Fig. 19.
The World on Mercator's Projection.

   Note the enormous exaggeration of Alaska, Greenland, Norway, Sweden, Siberia, etc. See Fig. 49.

Fig. 20, Mollweide Projection

Fig. 20.
The World on Mollweide's Projection.

   All the above maps are drawn to the same scale. Both 19 and 20 are meant to represent the facts shown in Fig. 18. Neither the rectangle nor the ellipse can be made to cover the sphere.

Fig. 21, Van der Grinten projection
Fig. 21.
The World on Van Der Grinten's Projection.

   Note — This map is a compromise between the exaggeration of Mercator and the distortion of Mollweide's. But it does not remedy either defect sufficiently, while it sacrifices the  advantages of equal angles and equivalent areas which make the first two scientifically valuable.
   The above version of this projection is almost identical with one patented in England on July 13, 1889, by H.B. de Beaumont, of Geneva.

Fig. 22, Whole world on Polyconic Projection

Fig. 22.
The Whole World on the Polyconic Projection.

   This projection for limited areas is the most accurate of all. For the whole world it is practically useless. See Fig. 10 and 48.


Fig. 23, Polar Radial Map

Fig. 23.
Polar Radial Map, Six Extensions.

   Note. This map is published by the American Book Company, and shows both the need of a new type of projection and the fact there is a tendency to supply the need.

Fig. 24, Polar Radial Map, 5 extensions

Polar Stellar Projection, 4 extensions
Fig. 26.
A Polar Stellar Projection with Four Extensions.

Published by J.G. Bartholomew & Co. In this projection the gorings extend above the equator and the world is divided below the equator into four parts, a decided improvement on all preceding maps of this type to date.

Distortions in polar map
Fig. 27.

Showing necessary distortion of a polar map carried down to 25° north latitude, as in the projection shown in . Fig.26.
Note: this is a larger version of the same illustration as used in Cahill's 1909 article in the Scottish Geographical Magazine, with Xerox black-fade somewhat corrected by GK. (Figure's left edge impaired due to binding.)

Continent-distortions on a polar map
   Note. — Fig. 28, 30 and 32 show Africa, Australia and South America twisted and distorted as they come on the equal area polar map shown in Fig. 26.
   Fig. 29, 31 and 33 show normal region maps of these continents to about the same scale.
   When drawn on the new projection these continents assume forms indistinguishable from Fig. 29, 31 and 33. See Figs. 37, 38, 42, 43, 44 and 45.

8-piece orange peel

Globe gores assembled at temperate zone

Cahill map with repeated  lobes

Geometrical principle of new projection

Cahill map joined at Atlantic

Fig. 42: The World on the New Projection.

   Note — In this map the Pacific Ocean is separated, while the Atlantic is shown complete. The clef or key which carries Kamchatka on the right upper lobe suggests pictorially that it is meant to fit the corresponding gap opposite Alaska.

  Cahill Butterfly Map, Pacific view

Fig. 43: The World on the New Projection.

   Note — In this map the Atlantic Ocean is separated, while the Pacific is shown complete. See Fig. 45, which shows mechanically the method of projection.
   If the map be slewed around another sixth of a revolution, and the African lobes are thrown over to join the American ones, we have the world with America in the center and the Atlantic and Pacific on either side, an excellent arrangement for school use. In all these changes the actual map-sections remain the same. Only one drawing of all parts of the world is needed, the various arrangements being merely mechanical.


Cahill's rubber-ball globe
Cahill's ball globe, spreading out

Fig. 44.  Experiment With a Rubber Ball

   Note — The world is drawn on lines of latitude and longitude 22 1/2 degrees apart. When it is cut through in six crosses at the poles and on the equator, and these cuts are connected, the adhering lobes can be spread out into a plane and laid flat exactly like the map, Fig. 43.

Cahill's ball globe, flattened to a map

Fig. 45.  Showing by Mechanical Means How the New Projection Literally Lays Flat the Surface of the Sphere.

   Note — The rubber globe half displayed in Fig. 44 is here flattened behind glass. The strain is so slight that it does not crack the ink. When the glass is removed the butterfly map jumps back and resumes the spherical form.

[GK note: I have added a sharper scanned photo of the large octant below, as well as a Xerox of the octant as it appears in the article, with the dotted lines indicating nine sheet sets of the International Millionth Map, mentioned in the caption below.]
One octant of the new world map

Same octant, with IMW outline

Fig. 46.  One Octant of the New World Map

   Note — This is reduced from a large drawing made originally to the scale of a 36-in. globe. The coordinates are drawn every two degrees and every fifth degree in between. The small shaded sections show the actual positions and relative sizes of the sheets of the International Millionth Map. The dotted spaces show groups of nine sheets as shown on the polyconic diagram, Fig. 48.

  IMW sheet N-K-W 19

Fig. 47.  Sheet "North K 19" of the International Millionth Map.

   Note — The only one published in the New World. Fig. 46 shows its actual position on the new map and the position of the eight other sheets that go around it.
[GK note: thanks to the magic of the Internet, I am taking the liberty of adding this color copy of that same 1912 IMW N-K-19 sheet, from the Boston Public Library. http://maps.bpl.org/id/M8800/ .]

IMW sheet N-K-19


Polyconic principle of IMW

Cahill map and meteorology

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