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A New Earth Instrument -- The Ge-Organon -- By The Prolific Mathematician, Mapmaker and Inventor of Navigational Objects Benjamin Donn

Fascinating "new instrument invented by [Donn] for the study of geography," one of a number of map and navigation objects created by Donn during his career in Bristol in the second half of the 18th Century. 

Benjamin Donn was both a prolific writer, mathematical instructor and seemingly an inventor of new devices for navigation and the use of maps, globes and similar instruments. He taught courses to mariners and published several works on mathematical instruction.  As noted by van Poelje:

A number of articles from his hand have appeared, in the “Gentleman’s Magazine” and the “Mathematical Repository”, during the second half of the 18th century on subjects like a Davis’ Quadrant, an Orrery, lunar and tidal instruments and an “Analemma”, “Panorganon” or “Georganon” for solving “Problems of the Globe”. In his 1796 book “An Essay in Mechanical Geometry”, he informs the reader that " ...from 1766 to the present time I have invented mechanical aids to the most important propositions in Geometry, 50 schemes and models in card-paper, wood and metal."

Donn was active in designing, and also in selling his instruments at his Academy: the production of his designs he had delegated to instrument makers and engravers.

While best known for his award winning 1765 County Map of Devon, Donn produced a number of other maps while in Bristol.  Among his more fascinating undertakings, Donn proposed improvements on the Analemma, a variation on what is known as the Standard Gunter Rule for recurring navigational calculations, and a Panorganon and Ge-Organon, intended to be reliable means of calculating geographical distances and times without the use of a globe.

His Ge-Organon would seem to be a continuation of his prior work on a Panorganon ("for Solving the Common Problems of the Terrestrial Globe) The Panoragon (a type of horary quadrant) seems to have been described as early as 1672 in William Leybourn's Panorganon: or, an universal instrument, performing all such conclusions geometrical and astronomical as are usually wrought by the globes, spheres, sectors, quadrants, [&c.] .  Like the Ge-Organon, it seems not to have been a commercial success, with the only recorded surviving example being in the collection of the Clements Library at the University of Michigan.

Published in about 1770, the Panorganon seems to have received sufficient interest that it was also advertised as being sold by Robert Sayer, along with B. Law, and Heath & Wing.  The advertising on the the Panorganon notes that Donn's Improved Analemma was then being sold by Mount & Page.

By 1788, it seems that Donn had significantly enlarged and refined his original Panorganon and re-imagined it as a Ge-Organon.  Donn has now incorporated the voyages of James Cook, as well as two patrons (who were also sisters), the Countess of Talbot (Charlotte (Hill) Talbot (1754-1804) and the Countess of Salisbury (Emily Mary Cecil) (1750-1835).

The Ge-Organon seems to provides a detailed explanation of its use.  A note at the bottom left of the 1st Sheet states:

This Instrument, Price 6s. 6d. Sheets will not only serve the common purposes of a Map of the World, but will also solve several Problems of the Terrestrial Globe, more accurately then the Globe itself.  It may be fitted up in a general manner with moveable plates for 3sh, and 6d. additional expense.  A Description and Use is published, pr. 1s.

The work was first advertised in the Bath Chronicle on May 1, 1788:

"The Ge-organon" or World Delineated" on 2 sheets Royal paper by Benj Donne, teacher of Maths & Philosophy at Bristol, 6s 6d in sheets, or on pasteboard, with hour circles & painted 10s. From Mr Bull, Mr Hazard, Mr Marshall (all Bath)

The use of the Ge-organon was described in The Critical Review, or Annals of Literature, Volume 66 (1789) and Deutsche Zeitschriften des 18. und 19. Jahrhunderts, Volume 1 (1789) The Critical Review review is as follows:

The Use of the Ge-Organon and Improved Analemma; or, Substitutes for the Terrestrial and Celestial Globe. Invented by B. Donne, Teacher of the Mathematics and Natural Philosophy at Bristol. Price of the Ge-Organon in Sheets , 6s. 6d. but if fitted up with moveable Hour Circles, &c. 10s. Of the Analemma, 35. 6d. and of this Pamphlet, 1s. Published by the Author.

THE instrument described in this pamphlet, and here called a Ge Organon, consists principally of maps, on two sheets of royal paper, each containing an orthographic projection of a hemisphere, namely, the northern and southern hemispheres, on the plane of the equator, and consequently having the pole in the middle, the meridians as radii from the pole or centre, and the parallels of latitude as concentric circles. Besides these two principal maps, there are, at the corners of the sheets, two smaller ones, being charts of the eastern and western halves of the torrid zone ; and from other appendages; as first, in the upper right hand corner of the hemispheres, are scales for shewing, by inspection , the sun's declination, answering to any day of the month ; secondly, in the right-hand corner, at the bottom of the northern hemisphere, is a scale, made in form of a carpenter's square, for finding the distances of places; with a quarter point of a compass for finding the courses, which, as it is there made, answers the end of a whole compass ; also to the pole of each hemisphere, one end of a fine silken cord is fixed, serving the purpose of a general meridian ; and the hemispheres, when fitted up, have also moveable hour-circles, for more readily resolving problems concerning the difference in time between two places, &c.

Without the equator are several concentric circles, contained in a kind of ring, or hoop, called the equatorial ring, and coloured, for sake of distinction. In this ring the longitude is counted several ways, to answer different purposes: it has the longitude counted from the meridian of London half round each way, viz. 180 degrees east, and the same west, according to the method followed by most of the English: it is also counted all round east from London, agreeable to captain Cook's last voyage: and in the outermost part it is counted all round the world east from the island of Ferro, to agree with the method chiefly followed by the French, and some among the English. The equatorial ring is also divided into hours and minutes. And Captain Cook's tracks, in his three voyages round the world, are laid down on both hemispheres, and distinctly coloured. 

The title Ge Organon, is from two Greek words, Ge, the earth, and organon, an organ or instrument ; thereby intimating that it is a machine representing, and for resolving problems relating to, the earth: indeed it performs this office, for the most part, as readily as the globes themselves , and sometimes even with more accuracy than these do.  On docount of their portableness they are, on many occasons, preferable to the globes. The general principles of working problems are the same, both on the globes and the ge-organon; only, as the general or brazen meridian is fixed, and the globe moveable, the given place is brought to that meridian; but in the ge-organon, the plates being fixed, and the silken cord, which represents a general meridian, being moveable, it is brought to the place. Also, on most globes, the hour-circle being fixed , and the index moveable, the index is set to the given hour; but here the hour-circle itself is moveable, and carries the index, which is set to the hour.

There is, however, one thing in these maps which we cannot approve of, namely, that, from the nature of the orthographic projection , and the great extent of the maps, being each half the surface of the earth, the places near the equator are exceedingly distorted , and thrown out of their natural position and true shape. The author, indeed, was aware of this objection: he \says , It may perhaps be objected , that the degrees of latitude diminish very much towards the equator, and consequently the places near it will be much shorter from north to south, than they are with respect to their breadth from east to wet, on the globe. In answer to this, it is well known to those who are well acquainted with the subject , that it is impossible, on any principle of perspective, to observe the real proportional magnitudes in a delineation on paper. That we must judge of their length and breadth by the number of degrees they extend, and not from their apparent magnitude.  If the stereographic projection had been made use of, the degrees would have been shorter near the pole, and wider as they approached the equator. There is an arbitrary projection sometimes used , called the globular projection, not founded on any principle of perspective ; but to make the places appear nearly of the same apparent magnitude as they are on the globe; and if it had been designed only to have made a picture, this would have been preferred. The preference has been given to the first, or orthographic progression, in constructing the ge-organon ; principally, because the degrees of longitude, or distance of meridians, decrease in this as they approach the pole, in the same proportion as they really do on the globe, which is peculiar to this projection, and very naturally explains the nature of parallel sailing in navigation. I have said thus much, to take off the cavils of some ignorant critics; who, not seeing the advantage of this projection, might possibly be glad to point out its defects. However, I think it not worth while to spend any more time on this head; and therefore shall only observe farther, that as it is principally near the equator that the degrees of latitude are much contracted in this projection, making the land appear very different in figure, &c. from what it is on the globe, I have, to remedy that defect, given two charts of the torrid zone, as above mentioned, containing all the land between the parallels of 23 degrees 28 minutes north latitude, and 23 degrees 28 minutes south, in as true proportion as on the globes; which \serves also to \shew how the two hemispheres connect together.

We have thus given the author's own reasons for preferring this sort of projection, which so much distorts the figures of many places, that, so far from conveying a true idea of the figure of them, they occasion one that is incorrect; and we recommend it to the author's consideration, whether, as such instruments are only intended to give ideas of the figure, size, and position of places, as well as an approximate solution of problems relating to geography and navigation, rather than true ones, for any real practical uses; whether, we say, these things being considered, it would not be best to use the globular projection, or some other convenient method, by which the deviations from the truth may not only be as little as possible, but also nearly equal both in all parts of the map, and the same in longitude as in latitude. As to the uses here described , of the Ge-Organon and Analemma, they are numerous, distinct , and well explained in a variety of problems, which may be as easily performed on them as on the globes themselves. And, we may add, some of these problems are new and curious.         C.


While the Ge-Organon seems to have enjoyed a robust sponsorship, it appears no known examples survived until the discovery of this example in 2022.

We note no record of the object at auction or in dealer catalogs.

Hans: New Trends in Education in the Eighteenth Century (2013).
Van Poelje: The Navigation Scale, Improved by B. Donn, Journal of the Oughtred Society, Vol. 14, No. 2 (2005).

Benjamin Donn Biography

Benjamin Donn (aka Benjamin Donne), was a British cartographer, surveyor and mathematician

Donn was born into a family of respected mathematicians, including his father and older brother.  Gentleman's Magazine (No. 74, p499) called his father George "one of the best teachers of arithmetic, navigation and dialling, in his time."

In 1768, Donn was elected librarian of the Bristol Library, where he unsuccessfully proposed to convert the library into a mathematical academy.  Late, he founded his own private mathematical academy in Bristol.

Donn’s is best known for his 1765 large wall map of Devonshire, based a survey which he undertook at his own expense, and which won the award of £100 from the Royal Society for the Arts. He produced a number of other local and regional maps, as well as several "scientific" charts, including The Analemma Improved by B Donn, in 1770, and his virtually unrecorded Ge-Organon.

He also published mathematical texts likely related to his mathematical school in Bristol.