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332 THE ARGONAUT

November 23, 1912

A NEW PORTRAIT OF MOTHER EARTH.

The First Map of the World Drawn in Truth.²

"The three corners of the world." — King John.

"When I see on one side this luxuriant foliage of sand, the creation of an hour, I am affected as if in a peculiar sense I stood in the laboratory of the artist who made the world and me — had come to where he was still at work, sporting on the bank, and with excess of energy strewing his fresh designs about. I feel as if I were nearer to the vitals of the globe, for this sandy overflow is something such a foliaceous mass as the vitals of the animal body. You find thus in the very sands an anticipation of the vegetable leaf. No wonder that the earth expresses itself outwardly in leaves it so labors with the idea inwardly. The atoms have already learned this law and the overhanging leaf sees here its prototype. Internally, whether in the globe or animal body, it is a moist thick lobe, a word especially applicable to the liver and lungs and the leaves of fat³ (labor, lapsus to flow or slip downwards, a lapsing; globus, lobe globe; also nap flap and many other words). Externally a dry thin leaf, even as the f and v are a pressed and dried b. The radicals of lobe are lb, the soft mass of the b (single lobed or B double lobed) with the liquid l behind it pressing it forward. in globe, glb, the gutteral g adds to the meaning of the capacity of the throat, the feathers and wings of birds are still drier and thinner leaves. Thus also you pass from the lumpish grub in the earth to the airy and fluttering butterfly. The very globe continually transcends and translates itself, and becomes winged in its orbit." — Thoreau's Walden."

[Diagram, "ORBIS TERRARUM, a butterfly map of the earth at the north pole]⁴

FIG. 1. The new land map of the world, nicknamed the "Butterfly Map." This is shown to the same scale as the four cuts in Fig.2.

No doubt the commentators have their explanations, but just why Shakespeare speaks of the three corners of the earth, when a sphere has no corners and the accepted notion of dividing the great space of outdoors has always been in four cardinal quarters, is one of those mysteries of poetic prescience that all can wonder at and none explain. Whether Shakespeare knew the geographical facts or not, no scientist could have expressed the truth more accurately. The world is literally three-cornered — that is to say, the dry, habitable part of it is. Careful study of a globe reveals this fact to anybody prepared to look for it. One corner ends in America, one in Africa, and one in Asia — that is to say, the Austral part of Asia. But it is difficult to realize this because of the quite baffling fact that you can never see more than about a third of a globe at the same time, and as fast as new regions appear on one side the old ones recede on the other. The published maps of the world do not make this matter clear at all. From none of them in common use does one get the notion that the land radiates from the North Pole on one side of the world in three streamers about equally spaced and well hooked under the sphere as though three fingers grasped an orb and the opposing thumb but touched it in a spot.

And this brings us to consider a curious and quite remarkable fact. In spite of the profound calculation of cartographers. the diligence of map-makers and the accurate knowledge we have of the earth in detail, no one yet has seen a true picture of the world as a whole in one continuous map. Such a thing does not exist: is nowhere in print. You can not find it in any geography, atlas, or encyclopaedia. on Mercator's chart (Fig. 2) the land is preposterously exaggerated towards the poles. In Mollweide's map it is cramped at the poles and quite absurdly twisted and drawn out at the edges, as though viewed in a comic mirror. Yet both these are gravely engraved from one generation to another as authentic portraits of the face of the earth! As each is so unlike the other it is not surprising that neither of them resembles the thing it represents, to put the Euclidian axiom to an inverted use. Other familiar maps show the world in twin small discs or one big disc. All these so-called projections have been solemnly worked out with an amazing amount of mathematics but a ludicrous disregard of the consequences. Far be it from me to speak flippantly of the sublime science of mathematics in its loftiest reaches, but your mathematician can and often does take that extra fatal step the poet speaks of. In this very matter of map projection the results of mathematicians have always seemed to the writer to have a large element of what is really ridiculous, They remind one of the tortured reasonings of mediaeval metaphysicians: all kinds of profound logic culminating in all kinds of foolish conclusions. Our world maps have too much science and too little sense. Does the reader doubt it? If so let him answer this question: Is there any relation between a disc, a rectangle, or an ellipse on the one hand and the surface of a sphere on the other? There is none whatever. If the reader is still doubtful, let us put the question in another form. It is a poor rule that won't work both ways. The problem of laying out the surface of geometric forms is termed by the older writers on stereography "developing the coverings of solids." The word "covering" is here used in a strictly scientific sense. Let us reverse the problem then, forget the scientific side, and inquire how one would cut a piece of leather to make the covering of a baseball? As every one knows, there are several practical ways in which this could be done. The leather might be cut in gores like the markings of a muskmelon or in lateral strips as when one peels an apple, or, best

[Diagram: peeled globe]⁵

THE GORES OF A GLOBE

[Diagram: rectangular Mercator projection of the world]

Mercator 1569

[Diagram: circular van der Grinten projection of the world]

Van der Grinten 1898

[Diagram: elliptic Mollweide projection of the world]

Mollweide 1805

FIG. 2.

The uppermost cut represents the world as it actually is, land and water. The lower three cuts are various versions of the same. Compare the facts as shown in the top cut with the other four versions as to size and shape.

of all, in two sections shaped somewhat like dumb-bells. There are thousands of forms that might be used if the number of seams and the consequent amount of stitching was a matter of no concern. But the few forms that one would not think of trying, the forms that are on the face of it impossible, are, if you please, the circle, the ellipse, and the rectangle, the very forms which the mathematico-geosophical experts have used for generations, and which are still used in our geographies, atlases, and encyclopaedias.

In no conceivable way can you wrap a circular, an oval, or a square-cornered piece of leather around a ball. A child attempting it would excite amusement. If a learned person were to carefully calculate the exact area of the surface of the ball and then cut a leather ellipse so cunningly that the long axis just went round the centre and the short axis reached from top to bottom and the surface had the same number of square inches as the ball to ten places of decimals, could the trick be done then? Of course not. And the learned person solemnly attempting it would be an object of ridicule this time — not amusement. Yet this is precisely the way Mollweide's projection is made. To work out the calculations and equations needed to produce this projection is a task likely to drive one frantic, yet the shape of the continents developed by it, when all is said and done, are for the most part fantastic, form being so utterly sacrificed to formulas.

It is doubtful whether any one gets any real use out of Mollweide's map except those who print and sell it, because the eye is so outraged by its marginal distortions. The attempt to cover a ball with a rectangle is overcome by geographers in a way that is truly surprising when you come to think of it. Unable to make the leather covering fit the ball, they make the ball to fit the leather — and the sphere becomes a cylinder — as though one should play baseball with a paste-pot!

As a matter of fact Mercator’s projection does not yield us a map, but a sort of sailing diagram, a wholly artificial albeit extremely helpful graphic instrument for the use of mariners — ad usum navigantium as the old title reads to Gerhard Kremer's original engraving. Its deliberate use was to enable one to steer a course, by the use of the compass. from one port to another. The constant and growing use of this seaman's chart for landsmen's purposes is really a sort of cartographical scandal — an abuse that almost calls for legal deterring enactments. Americans should resent this map, and particularly Californians, as will be seen later on. Professor J. Paul Goode of the Chicago University says "the constant use of the Mercator projection tends to teach untruth of form and area, so that we of North America come to have some excuse for a sort of geographic "big head," as the phrase runs; and I suspect that nine out of ten of us would answer off hand that North America is a great deal larger than Africa." What virulent form of megalocephaly will inflict Greenlanders or the White Esquimaux when they learn the use of maps à la mode is appalling to think of.

It is said that Emperor Wilhelm enjoys pondering over world maps, and of course all the chancelleries of Europe are well stocked with them. Who can tell but what the overwhelming preponderance of the Russian Empire, on the map, has held the rest of Europe in awe for a couple of generations. But while Russia shrinks enormously when drawn on an accurate map, lndia, Africa, and Australia remain much the same.

Consequently they seem much more important in comparison with the rest of the world. If, however, the dominion of the Bear in the Old World is diminished, that of the Lion is enlarged.

In the New World the mainland of Canada on a rational map will shrink to something less than the mainland of the United States, instead of showing more than twice its size. And in comparison with North America our sister republics of the south. though remaining the same absolutely, will, in a relative sense, appear much larger and more important. But the gigantic and wholesale illusions of Mercator's map — now used in every school house, textbook, atlas, and transportation office throughout the entire world — are not confined to exaggeration and distortion of the land areas. On this map, for example, an actual mile of ice floe at the pole would have to appear as wide as the equator — that is, twenty-four thousand miles long.

A sea trip from Norway to Labrador in latitude 60 appears to be exactly the same length as one from the west of Africa to Yucatan in latitude 20. At least this is the impression that one gets from the Mercator chart. In reality the southern trip is four thousand miles, while the northern one is but two thousand miles — just twice the distance; an error of 100 per cent. If the true great circle curve were shown on the map the error would be still further exaggerated, because the curve of this course increases as you go north, and the bigger the loop the longer the voyage looks.

This brings us to consider another feature of this wholly misleading map. We of San Francisco are now nearing one of the great events in our city‘s short but stirring history. The International Exposition of 1915 to celebrate the opening of the Panama Canal is a world event that should surely express itself somehow on a world map. As a matter at fact if you turn to Mercator’s version — and that is about the only one that you can consult at present — you will, if you trust your own eyesight, come to some very curious conclusions. You will see that the Hawaiian Islands lie directly in the line between Panama and Yokohama. Now since the Islands are some 2000 miles from San Francisco you will naturally wonder in what relation, if any, San Francisco stands with reference to the sea-born trade between the ports of the Atlantic and the Orient. Honolulu appears to be the natural port of call for all this trade, and San Francisco is not only not on the route to Japan, but decidedly on the route by at least one thousand five hundred miles. If the map, however, is marked with bold red steamer routes linking up the southern ports with San Francisco and thence passing across to Japan one may reasonably suspect some form of faking due to the boomer's enthusiasm or the guile of crafty transportation companies. In truth it is the map that is guilty of deception, and not the men who mark the routes. The real course that a bird or an airship would take to get from Panama to Yokohama does not go out west into the Pacific at all. It passes through the Gulf of Mexico to Galveston, thence in a northwesterly direction through Texas, hundreds of miles east of San Francisco, out into the ocean somewhere along the coast of Washington, up to Alaska, nearly, thence southwesterly down to Japan! This great circle route can be clearly and accurately traced on the map shown at the head of this article by drawing a pencil line straight from the Canal Zone to the Japanese coast. On a map made on these lines one sees at a glance that every Pacific seaport from Panama to Portland lies on the direct shortest and cheapest route between all ports of Europe and the Eastern, Atlantic, and Gulf states and the Pacific coast of Asia via Japan. Greater San Francisco is the largest and most important [3]

November 23, 1912.THE ARGONAUT333

of all ports on this run, with the best harbor and cheapest fuel, and of course the natural centre to celebrate the completion of the government's wonderful work at Panama. But you would never suspect this from a study of Mercator's misleading map.

[Photograph of a butterfly]

Picture of a butterfly found in India, showing lines of latitude and longitude and called the "Map Butterfly." — Illustrated London News, November 2, 1912.

II.

lt was the inadequacy of the world maps now in use that started the writer, an architect by profession, in quest of a rational projection. It can not be too plainly stated that the preceding criticisms of world maps are in no way directed against the makers of regional maps. This work, to which the profoundest scientists have contributed, is now brought to a state of perfection absolutely above criticism. It was, then, to the problem of showing the whole world in one continuous map that the author addressed himself. Three times in five years victory seemed to be at hand. In each case the result was abandoned and the quest begun again. The long, unsuccessful road has been tedious and discouraging. Finally the search came to an end in complete success. Some account of the author‘s essays and the final solution has been published in the Scottish Geographical Magazine. In a subsequent number a writer in the same magazine who so far mastered the map as to point out a minor error (which the author, too, had meantime discovered) printed the following:

Every one who is interested in the teaching of geography should hail with satisfaction the production of a map of the world based on the method suggested by Mr. Cahill in his paper in the September number of this magazine. No projection of the hemispheres, stereographic or globular, no equal area projection of the whole of the earth's surface, no gnomonic and no cylindrical projection can give at once such a comprehensive and accurate representation of the globe as the map which is there shown. — "A New Land Map of the World," by Stephen Smith. B. Sc., F. R. S. G. S. — Scottish Geographical Magazine, November, 1909, page 600.

It is of course impossible to lay the surface of a globe flat on a plane. The compromise in this case was constructed by considering the problem from the viewpoint of a "covering" on a sphere that must be so cut as to allow its development in a plane with the minimum of distortion. It was this departure from the purely mathematical method that probably led the president of the Carnegie Institution of Washington to remind the author that he was an amateur — Dr. Woodward forgot that an architect's whole career is concerned with projections from morning until night. Every drawing an architect makes from first sketches to final details is some form of projection. so that he is necessarily very much more familiar with the idea than the geographer, who may not concern himself with the subject at all. Moreover, the dome, the vault, the cupola, and the rotunda are all globular problems that he has to tackle sooner or later in his career. Finally an architect must have a highly developed sense of form, whereas it is not essential and may be lacking in the geographer or mathematician. Barring this specimen of faint praise, encouragement and appreciation have come to the author from cartographers and professors of the leading universities of the world, including London, Paris, Berlin, Oxford, Edinburgh, Harvard, Yale, Columbia, Chicago, and California.

Fortunately the method of projection has been made most easy of explanation by simple mechanical means that a child can grasp in an instant. While the projection took five years to invent, the toy that explains it took but five minutes. An explanation of this will be the best explanation of the map and the general method of its construction.

Let the reader imagine that he holds in his hands a child's hollow rubber ball a couple of inches in diameter. On this the lines of latitude and longitude are drawn every twenty-two and a half degrees apart and the world's outlines filled in as correctly and minutely as you please. It is now a miniature rubber globe differing in no respect from the standard geographical ones. Now let us conceive that the equator is shown in red ink, also that longitude 22½ degrees west of Greenwich is shown in red all the way round. Let us also mark in red another line of longitude at right angles to this one. These three great circles in red will be found to cross one another at right angles at six different points or nodes. Two of these are the poles; the remaining four are all on the equator, and let it be noted, all well out in the ocean.

We now have the surface of the globe divided by these red lines into eight absolutely equal parts, four north and four south of the equator, each exactly 90 degrees of latitude⁶ wide and 90 degrees of longitude⁷ high. It must be noted that it is impossible to draw more than three great circles around a sphere that intersect each other at right angles. On the red "lines of scission" the reader is now supposed to cut with a sharp knife a Latin cross at each of the six points of intersection. Each arm of these crosses must extend 22½ degrees from the centre — that is to say, that each cut reaches to the next black line of latitude or longitude. Four more cuts are made to liberate the southern lobes from each other and one cut on any of the four northern red meridians, and the rubber globe can be laid out on the table exactly as shown in Figure 1. The globe is literally laid flat with so little distortion that it does not even crack the color on the surface. The illustration may be homely and mechanical , but it is absolutely convincing. On releasing the pressure necessary to flatten the eight lobes the rubber map jumps back to its spherical form and once more becomes a globe.

B.J.S. CAHILL

SAN FRANCISCO, November, 1912.

[Further newspaper content omitted from transcription]

[4]⁸

[1]

SOME EXPERT OPINIONS

NEW LAND MAP OF THE WORLD

by

B. J. S. CAHILL [2]

SOME EXPERT OPINIONS

New Land Map of the World Invented by B. J. S. Cahill

(PATENT ALLOWED)

(1) J.G. Bartholomew, FG.R.S.W., F.R.G.S., etc., of Edinburgh commended the author's account of the New Projection for publication to the Royal Scottish Geographical Society of Edinburgh.

In a letter dated Edinburgh, Feb 23, 1909, he says:

"It seems a pity that such a geographical enthusiast and cartographic idealist as yourself should not be in a more congenial atmosphere of Geographic culture than San Francisco."

(2) Dr. Cleveland Abbe, of the United States Climatological Service of Washington, in a letter from Baltimore dated May 14, 1909, says: "Your conclusion seems to be in favor of the system of gores shown in your diagram (see frontispiece). The result makes quite an attractive picture of the globe and may very likely be very useful in many studies."

(3) Dr. G.K. Gilbert, the well-known geologist, read the memoir on the new projection with much interest and is in full sympathy with the author's work and heartily in favor of its publication.

(4) Professor Edgar Luciean Larkin, Director of the MS. Low Observatory, Los Angeles, says of the map that is is a "very ingenious concept of projection of the earth's surface," and wishes the author full success.

(5) Professor W.H.Davis, of Harvard University, in a letter from London, England, finds the plan ingenious and suggests publication to take its chances with similar projections in the struggle for existence. Later, in a letter from Cambridge, Mass., dated may 19, 1909, he says: "I am glad to see the favorable comments your work has excited from various geographers, several of whom are much better informed on cartography than I am...... I am glad to see that my suggestion to Dr. Groll, as a qualified expert in the matter, lead you to profitable correspondence.

(6) "The reasons given for the proposed change in making a map of the world cannot be controverted. The presentation of your argument appears to be strictly logical."

John N. Baldwin, Expert Mathematician,

Pacific Grove, California.

(7) "Most ingenious, interesting and I am confident, valuable."

John de Witt Warner,

Warner,Wells, & Korb,

Counsellors at Law,

60 Wall St., New York.

(8) Extract from a letter from Prof. J. Paul Goode, Chicago University.

"I have gone over your account of your new projection of a land map of the world with much pleasure and I am very much pleased with your final projection. Your discussions with illustrations of the errors of the various projection is illuminating and valuable. I hope you will offer your paper for publication in some geographical magazine where it would be referred to and made use of in college and normal school work with maps. It is extremely instructive … I can answer that it could be a very effective [3] map for atlas use. I have had under consideration the preparation of an atlas for schools use and I should be glad to have the use of this projection for that atlas if it could be arranged.

"Permit me to congratulate you upon this very successful device…"

In another latter dated Chicago, July 7, 1909, he says "I am glad that Dr. Groll gives approval to you map projection. If you publish an account of your projection, I should be pleased to know where it is to appear so that I may obtain a copy of the account. I should rather like to write a note in regard to it for the Journal of Geography if you would be willing."

(9) Washington D.C., July 3, 1909.

"Dear Mr. Cahill: I have read the lecture on your Land Map of the World, and find much to commend in it. The illustrations throughout are good, and your criticisms of the Mercator and other existing projections in their inadequacy for the purposes of anthropogeography are in the main, well founded."

Yours very truly,

G.W. Littlehales."

(10) Extracts from a letter form Richard E. Didge, Professor of Geography Teachers College, Columbia University, N.Y., May 21, 1909.

"Your projection.... from certain standpoints for advanced students will be extremely helpful....

"A map of your projection drawn on a large scale would, it seems to me, be very efficient for the study of certain large problems....I hope some authoritative geographical publication will help you put it before the country."

(11) Extracts translated from the German text of a letter from Dr. M. Groll, "Kartograph and Lektor" of the University of Berlin, dated Wilmersdorf, April, 1909.

"Dear Sir: Accept my thanks for yours of the 13th of April. The beautiful sketches are of the greatest interest to me. The development is exceedingly original.

"Considering the small size of the map diagrams I am sorry that No.s 10 and 11 are not to exactly the same scale. The more pleasing is without doubt No. 12 (and, of course, No. 14). This map reproduces the surface of the earth with but little distortion...I believe that these projections for certain purposes may be useful and will be employed.

"I shall be very glad and much interested to see large plates of this projection, particularly as wall maps and anthropogeographical insertions.

With highest esteem,

Dr. W. Groll.

(12) At first it seemed like a jig-saw puzzle, but when I was able to get into it fully, I began to see light and appreciate its import."

H. A. Gwynne, Editor "London Standard,"

104 Shoe Lane, Fleet St.,

London, England

(13) The geometrician and the professional cartographer have naturally a prejudice against any representation of the earth's surface or a part of it which is not constructed on strictly mathematical principals. So also have those, as for instance, navigators, to whom the accurate determination of distance or [4] directions from a map is essential. But not one in a hundred individuals, perhaps hardly one in a thousand of the children who are daily being taught geography in our schools will ever belong to those classes, and to the ordinary child or man, a map produces its impressions of size, of shape, and of proportion, entirely by the eye, and without any consideration of meridians, parallels, points of view, perspective or system of projection. Undoubtedly, the only true method of studying the geography of the world as a whole is by the use of a globe, but a globe is too expensive and perhaps too unwieldy an article to find its way into every household, and even when used in schools it does not lend itself readily to the purpose of demonstration to a class, as a map hanging on a wall does with great facility. For those reasons, every one who is interest IN THE TEACHING OF GEOGRAPHY SHOULD HAIL WITH SATISFACTION THE PRODUCTION OF A MAP OF THE WORLD BASED ON THE METHOD SUGGESTED BY MR. CAHILL IN HIS PAPER IN THE SEPTEMBER NUMBER OF THIS MAGAZINE. NO PROJECTION OF THE HEMISPHERE, STEREOGRAPHIC OR GLOBULAR, NO EQUAL AREA PROJECTION OF THE WHOLE OF THE EARTH'S SURFACE, NO GNOMONIC AND NO CYLINDRICAL PROJECTION CAN GIVE AT ONCE SUCH A COMPREHENSIVE AND ACCURATE REPRESENTATION OF THE GLOBE.....

"It is much to be deplored that the conservatism of our map publishers has so long perpetuated the use of such a deceptive representation of the world's land surface as Mercator's map. If Mr Cahill's and the present article assist to arouse the dissatisfaction of teachers of geography and of all who take any interest in the subject, with the maps provided for their use, and make them demand from the publishers a map constructed on rational principles which he who runs may read, these article will not have been written in vain."New Land Map of the World"

by Stephen Smith B Sc. F.R.S.G.S.

Scottish Geographical Magazine

Nov. 1909, Page 600.

(14) W. Bissiker, Editor of the "British Empire Atlas," writes in part from 10 Chicester Rents, Chauncey Lane, London.

"....As regards the projection, for any map of the world where it is essential that the land should be shown on a equal area projection, yours is admirable, and for graphical and statistical comparisons, on land, it would be most useful as there is not much distortion.

(15) From the Literary Digest of June 18, 1910, "Roosevelt Number," "The best maps are those made for seamen; in these the form of projection is selected that represents best the form of the great oceans, sacrificing where necessary, accuracy in delineation of the continents. For charts Mercator's projection is generally used, and this is particularly inaccurate when applied to land maps of world wide extent....

"Obviously we need a landsman's map. Mr. Cahill works this out mathematically, and the curious form of map that he finally adopts is shown in the accompanying illustrations."

(16) From an editorial on "Making Maps" in the Portland Oregonian of July 31, 1910.

"The new plan of map-making which Mr. B. J. S. Cahill of San Francisco has devised, is interesting, because it portrays the entire surface of the earth with something like accuracy.

The polyconic projection has been widely adopted for the representation of large land areas, but now it may give way [5] to Mr. Cahill's method which, in some respects, appears to be more accurate."

(17) From the San Francisco Chronicle. Full page illustrated article, March 6, 1910.

"San Francisco is destined to acquire added fame by reason of the fact that one of her citizens, B. J. S. Cahill, has, for the first time, succeeded in evolving a correct single map of the land of the world."

(18) "A very ingenious and for many purposes a very useful projection....I thank you for pointing it out to me,"

H.J. Mackinder, Prof. of Geography,

London University.

(19) "A wonderful projection... It has all the simplicity of genius."

Austin Lewis, B.A., Oakland, California.

(20) THE CAHILL PROJECTION OF THE WORLD

"I have carefully examined the very ingenious projection which Mr. Bernard J. S. Cahill has worked out, and I am convinced that for showing the continents of both hemispheres in their respective positions and with a minimum of distortion, there is no better method available."

"A land chart of immense area may be shown with greater relative accuracy by this method than by any other known to me.

"It is well known that it is impossible to represent the surface of a sphere, or a larger area of it, upon a plane without distorting it. The usual methods for plotting land areas are applicable with sufficient accuracy for a comparatively small portion of the earth's surface, but, if the surface to be represented be a large one, the difficulty of retaining a unit scale becomes apparent at once, and increases with the size of the area to be developed.

"There are a number of mathematical projections in use, each of which may well serve its intended purpose.

"Mercator's projection, for instance, solved a great problem, and simplified navigation by an artifice deserving our fullest admiration. Yet its purpose is not to show the relative land areas, but to show relative bearings of land localities bordering the sea. Valuable as such as chart is for navigation, no one would recommend a Mercator projection for geographical land work. It is the most distorted deformity one can imagine.

"The Polyconic projection, which has its application in geodetic work exclusively, serves its purpose better than any other, and very large areas may be represented by this method. The area of the United States, for instance, is covered by 25 degrees of latitude and 50 degrees of longitude; in such a chart there is little distortion. At the central meridian, say, at Council Bluffs, the scale is true; but at the borders, say, at Boston on the east, and between Cape Blanco and Eureka on the West, the scale elongation is about 7 percent. The greater the area covered, the greater the marginal distortion becomes. This projection is not applicable fo representation of a map of the world.

"Mr. Cahill's projection overcomes the main difference, and lends itself primarily to land maps covering immense surfaces. It will show the areas of the world's continents and their relative positions, with less deformation than by any other method. The author accomplishes this by adopting a segregation of the globe into uniform gorings of 22½ degrees. [6]

This particular method was chosen after many empirical trials and his result is such, that it seems as though the continents of the world were made by design to fit that particular division and goring which Mr. Cahill finally adopted as the most suitable.

"It is doubtful whether a better scheme could have been worked out to give the same satisfactory solution.

"While a globe will always represent to the eye of the young and the untutored the best explanation of the relative location of its continents, landmaps, showing comprehensive groupings become necessary in connection with it and there is perhaps nothing that gives as clear an oversight of the situation as Mr. Cahill's projection, after its main points have once been grasped.

Otto Von Geldern

M. Am. Soc. C.E.

Member of California Academy of Sciences.

(21) Regarding the split rubber globes which illustrate the principle of the new projection in the manners explain on page Prof. J.Paul Good of Chicago writes in part as follows:—

Chicago, Aug. 3, 1912.

Dear Mr. Cahill;

Permit me to thank you most sincerely for you kindness in sending the very interesting dissected globes. It seems to me that this device is the best object lesson that has ever been prepared for connecting in the beginner's mind the relations between the map and the globe. I hope you will put those little rubber globes on sale where they can be put into use in every primary school in the country....

(22) From Rand McNally & Company, Chicago, Feb. 12. 1911.

......."From the description and the fine letters you have from geographers, we have no doubt that you have made a real discovery."

(23) From Rudyard Kipling:

....."Your idea of a really comparative map of the British Empire is a sound one......"

(24) John Swett, late Superintendent of Schools, San Francisco, states that:

"The projection is a very useful and ingenious invention; that such a map and globe could probably be used to great advantage by careful and painstaking teachers and should be so user."

He wishes the author "every success with this meritorious addition to carthography [sic]" and hopes "that the teachers will take to it."

(25) Translated from the French text of Prof. Emmanuel de Martonne of the Universities of Lyons and Paris:

........"So far I have not had time to study in detail your projection which seems to me very interesting. I shall not fail to do so when I get to Paris. I have devoted a chapter of my Treatise on Physical Geography to the problem of projections. I am wholly in accord with you as to discarding the use of Mercator's projection, certainly the very worst (la plus mauvaise) for geographers......

......"Some progress has been made with star projections, such as those invented in Germany and of which you can find a notable example on the cover of Petermann's Mitteilungen. You are still more advanced with your butterfly projection.....If, however, we decide to cut out the surface of the globe....I cannot see why [7] we should not have recourse to a system such as yours which seems to me very attractive, and very well studied out." (tres seduisant et tres bien etudie.)

(26) From Alan Grant Ogilvie, School of Geography, Oxford University: "There can be no doubt whatever as to the great value of the projection in the use for which it is primarily intended, viz., to give a proper idea of the proportions and in this respect is is particularly valuable for use in British Empire Geography."

(27) From E.A.Reeves, Map Curator, Royal Geographical Society, London. "As regards Mercator's projection, we are all of course aware of its defects for educational and general purposes."

(28) From a government report entitled "Charting Storms in the North Pacific" by Professor Alexander McAdie, official Forecaster, San Francisco, California....

......."In charting storm areas on the Pacific it is apparent that the Mercator map gives a considerable distortion inasmuch as the zone of maximum storm frequency lies between 45° and 55° north latitude. The distortion is so great that the Mercator map may well be eliminated from further consideration. Nor can regional maps be used to advantage, i.e., maps which are approximately accurate for given areas, because meteorologists now require reports from extended areas. Radio communication has made possible the girdling of the globe. And the necessity for long range forecasts, leading in time to seasonal forecasts, is now pressing. For the successful accomplishment of this the atmosphere must be charted and studied as a whole. It is a interesting fact that the daily weather map now issued at Washington contains reports covering the area from Nome, Alaska, to Seisfjord, Iceland; and there is every prospect that in the coming years the daily weather map issued at various National Central offices will contain data for an entire hemisphere. It is particularly important then that some method of representing the earth's surface, suitable for the presentation of weather reports over the greatest possible area, and with the least possible distortion, be devised,. And such a map must show the most important steamer routes "in absolute integrity", and the earth's globular dimensions in proper proportion. A projection which meets these requirements has been devised by Mr. Bernard J.S.Cahill, an architect of San Francisco, after seven years of study and experimentation.

"The map has been call the papillon or butterfly map from a fancied resemblance to the outstretched wings of a butterfly. The fundamental difference between this and other maps is that the latter are geometric projections upon a plane, normal to the line of vision whereas the new map is essentially the result of ingenious unfolding or peeling of the surface which is so spread as to give a minimum of distortion while preserving the proper ratio of areas, angles and distances."

(29) From Ambrose Bierce, Army and Navy Club, Washingon, D.C. "Cahill's projection is indubitably the right one."

(30 From Dr. David Starr Jordan, President Leland Stanford Jr. University, Palo Alro, Cal.

"Dear Sir;

Your map article in the Argonaut was so charming and promising that I violated my usual rule of sending anything printed to the nearest available professor......I am very strongly impressed with your statement and with your maps, and I believe there is latent in them a possibility of real gain to the intelligence of the world....I wish you all success in developing your plans. [8]

(31) From Luther Burbank, Santa Rosa, Cal.

"I take pleasure in saying that your map of the world without exaggeration or distortion should be of value.... I am with you in anything which helps make a better knowledge of the earth available."

In addition fo the above written opinions are many verbal expressions of approval and enthusiasm from a large number of men who have had the projections explained to them,. Among such are Prof. Childs, teacher of Geography in the Oakland schools, C.F.Weber of the house of Weber & Co., (Globes and Maps) Chicago and San Francisco, Prof. Alex McAdie, U.S. Meteorological Service, Prof. Harlan H. Burrows, Geographer, Chicago University, Professor Holway, Geographer, University of California, Marsden Manson, F.R.G.S., Dr D'Evelyn, the late Prof. Davidson of the Coast Survey, the lae Edward Wesson, Assyriologist and Astronomer, and scores of others. [9]¹