Royal Scottish Geographical Magazine (5322 Byte)





V O L U M E    I:   1885









The value of cylindrical projections have been somehow overlooked; and although Mercator's is only one of several, each of which has its own peculiarities and advantages, yet, until lately, it was the only one known.
    There are three, but only three things, in which a cylindrical projection can be perfect; and these depend upon the way in which the latitudes are drawn.

    1. We may obtain perfect orientation by rectifying the latitudes throughout, as Mercator has done; and this is especially valuable for navigation. But in order to obtain perfect orientation everything else must be sacrificed.

    2. Wee may obtain comparative area with mathematical accuracy by projecting the latitudes orthographically. But in order to obtain comparative area we must sacrifice everything else.

    3. We may obtain accurate polar distance by projecting the latitudes isographically, that is, at equal distances. But, in order to obtain this, everything must be sacrificed.

    My attention was first drawn to the subject in connection with astronomy. I had published An Easy Guide to the Constellations, in which each constellation had a page for itself; and it became necessary for me to publish an Atlas of the Stars* to show their connection. In planning the atlas, it occurred to me that a magnificent panorama of the stars, including three-fourths of the heavens, might be brought into one map by using a cylindrical projection, with the latitudes drawn stereographically and rectified at the 40th parallel. The result was, that the constellations on the 40th parallel were absolutely perfect in both hemispheres, and although those at the equator were a little contracted and those beyond the 40th degree a little expanded, the errors were so small as not to be observed.

    One great advantage which this projection has over every other is, that several astronomical problems can be solved upon it, the same as on a globe.

It then occurred to me that the same, or a similar projection, would give a complete map of the world, which had never been done before; and, on drawing a projection with the latitudes rectified at the 45th parallel, I found that the geographical features and comparative areas were conserved to a degree that was very satisfactory.

    Having more closely studied the subject, I read a paper before the British Association in 1855, and exhibited the three new projections - the Stereographic, the Isographic, and the Orthographic; but I had not then thought of the supplemental diagrams, which add so much to the value of the Stereographic.

    The Stereographic projection has this advantage over all the others, that it leaves room for supplemental diagrams at the top, on the same scale and on the same projection, which take up the extremities of the general map, and show their convergence towards the pole.

For General Purposes.

Gall's Sterographic Projection (100149 Byte)

    The Orthographic projection also is a valuable map for showing the comparative area occupied by different subjects, such as land and water, as well as many other scientific and statistical facts.
It is true that the geographical features are more distorted on this than on any of the others, but they are not distorted so as to be unrecognizable; and so long as that is the, case, its advantages are not too dearly bought.

For Physical Maps, chiefly Statistical.

Gall's Orthographic Projection (42005 Byte)

    I have wondered why geographers never thought of using the Isographic projection with the latitudes rectified at the 45th parallel. Even for general purposes it is better than Mercator's, and still more for physical maps, where polar distance and comparative area are all-important. It is very simple, its geographical features are on the whole very good, although not so good as in the Stereographic; and for isothermal and other lines connected with climate, as well as for comparative area, it is greatly superior to Mercator's.

    For general purposes, however, the Stereographic is best of all; for though it has none of the perfections of the others, it has fewer faults, and combines all the advantages of the others in harmonious proportions.
It does not give perfect orientation like Mercator, bat it gives it better than the other two. It does not give exact polar distance like the Isographic, but it gives it better than the other two; and it does not give comparative area like the Orthographic, but it gives it better than Mercator, though not better than the Isographic. The consequence is, that even without the supplementary diagrams, the geographical features of the earth's surface are better conserved than in any of the others; while, with the supplementary diagrams the polar regions are as accurately and symmetrically represented as the equatorial.

    The Stereographic projection, though inferior to Mercator's for navigation, is superior to it in the following particulars:-

    1. On Mercator's projection the whole world cannot be represented, because as we approach the poles the difficulty increases; and after passing the 80th degree the map begins to run wild. For that reason, from ten to fifteen degrees of latitude are generally left out. On the Stereographic projection the whole world is represented from pole to pole.

    2. In Mercator's projection there is a great waste of room. Nearly one half of the map is occupied with a vain attempt to represent the Arctic and Antarctic regions, while the habitable world is confined to a comparatively narrow stripe in the
center. In the Stereographic there is no waste of room.

    3. In Mercator's projection, the comparative areas are grossly misrepresented. For example, Spitzbergen appears to be three or four times larger than Borneo, whereas in reality it is five or six times less. In the Stereographic they appear in their true proportions.

    4. In Mercator's projection the polar distance is not only practically bat theoretically ignored. The 9Oth degree is nowhere. This makes it peculiarly unsuitable for physical maps.

    5. In Mercator's projection the polar regions have no resemblance to the reality. In the Stereographic they are as accurately represented as the equatorial.

    It is always difficult to introduce changes when long established custom has created a rut; and for more than twenty years after I had exhibited the three new projections before the British Association I was the only person that used them. But at that time I had not added the supplementary diagrams which add so mach to the value of the Stereographic projection.

    The first to adopt it was the late lamented Mr. Keith Johnston, who introduced it into his miniature Atlas, which was, I believe, the first of his publications. The next to adopt it were Messrs. Chambers and Mr. Bartholomew, who has done more than any other to make it known. After them it was adopted by Messrs. Nelson, Messrs. Gall and Inglis, and Mr. Heywood of Manchester. The late Dr. Keith Johnston when he saw it gave his hearty approval, and said that his only surprise was that it had never been thought of before.

For Physical Maps, chiefly Meteorological and Hydrographic.

Gall's Isographic Projection (48416 Byte)

    I do not know whether there is any copyright in new projections. I hope there is not. But if there is, I wish it to be known that I make no pretensions to it, and that every person is welcome to use them. All that I would ask is that, when they are used, my name may be associated with them, and that they may be severally distinguished as Gall's Stereographic, Isographic, and Orthographic Projections of the World.

* In a series of Astronomical Charts which I drew for the Messrs. W. & A. K. Johnston, I adopted the Stereographic Cylindrical Projection for the Equatorial and Sub-Equatorial heavens.

Authors are alone responsible for their respective Statements.


Request to post this document on my homepage:

Von: "Jürgen HEYN" <>
An: <>
Betreff: Request kind permission ...
Datum: Sonntag, 16. Februar 2003 17:45

Ladies and gentlemen,

I am aware of violating the copyright is NOT a peccadillo and "ignorance does not protect me from penalty". Therefore I request your kind permission.
As my hobby I am working on a dissertation about the difference between the map projection of Rev. James Gall (1885) and Arno Peters (1967).
More than half a year ago you were so kind to send me a copy of the article from the "Royal Scottish Geographical Magazine", Volume I, 1885 in which Rev. James Gall describes his map projections.
I would like to publish this article on my homepage which is a pure private and non-commercial internet presentation.
I would greatly appreciate if you would approve my request.
Attached a *.zip archive which contains the exact layout of the intended presentation.

Best regards
Juergen Heyn, Wilhelmshaven, Germany

Von: "RSGS" <>
An: "Jürgen HEYN" <>
Betreff: Re: Request kind permission ...
Datum: Montag, 17. Februar 2003 16:36

Dear Mr Heyn
Thank you for your e-mail requesting permission to post the article from SGM Vol I on your website. I am quite happy to grant permission on behalf of the Royal Scottish Geographical Society provided the source of the article is quoted as well as our permission. I look forward to seeing the results of your research work in due course.


Dr David Munro
Director RSGS

Tel: 0141 552 3330
Fax: 0141 552 3331

The RSGS is an Educational Charity whose aims are to advance the science of Geography and create a greater understanding of the wider world in the belief that geographical knowledge makes a significant difference to the way in which we view and shape the world we live in.

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