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© 1878 Nature Publishing Group

J1t7te 6, 1878] NATURE 1 49 

However complex the curves described by them may be, 
the points will be found to form a circle on the upper 
plane; and if we give to A different values, the corre-
sponding circles will be found to be all concentric. 
Further, if we call the circle corresponding to the value 
A = o the zero-circle, the area of the ·curves described by 
the points on any other circle of the system equals N 
times the ring inclosed between that circle and the zero-
circle. It is remarkable that such a singular point as the 
centre of the circles should exist. 

In the special case in which N=o, i.e., where there 
has been only an oscillatory movement of the upper 
plane and no complete rotation, the system of ~oncentnc 
circles is replaced by a system of parallel straight Imes, 
the area of the curves described by the points on any 
straight line of the system being proportional to the 
distance of that line from the zero-line. 

It should, perhaps, be pointed out that the ;_irea_ of a 
figure 8 is zero, as the two halves are of opposite signs; 
also that when a point reciprocates on a curve the area 
inclosed by it in its path is zero. For example: if we 
take the interesting _case of a circle rolling inside another 
of twice its diameter, every point on its circumference 
reciprocates on a straight line, and consequently the 
circumference is the zero-circle. 

This theorem was suggested to me by reading a paper 
by Mr. C. Leudesdorf in the Messenxer of Mathematz"cs, 
where I have already enunciated it. It seems, however, 
to be one which, from its somewhat startling simplicity, 
may interest a larger class of readers than a purely 
mathematical one. 

The proof is simple. Let P, P' be two points on the 
moving plane, and Jet A, A' be the areas described by 
them. Let PP'= r, and let the total movement of P' 
perpendicular to P P' = n. 

Then A-A'=nr-f-N1rr2, 
If we take P' as origin and the position of P' P in which 
1t is a maximum and equal ton' as initial line, n'=n cos 0. 
Thus A-A'=n' cos 0 · r+N 1r r2, the equation to a family 
of concentric circles. Transforming to the centre, we 
have A = N 1r (r2·- a 2), 
where a is the radius of the zero-circle. 

A. B. KEMPE 

OLD MAPS OF AFRICA 

M R. STANLEY, in the paper which he read at the Geographical Society on Monday, spoke of Africa 
being brought to light after an oblivion of 6,000 years. 
Notwithstanding the somewhat confused phraseology, Mr. 
Stanley's meaning is clear enough : Central Africa, with 
its great lakes and rivers,. is now known, he means to say, 
for the first time. But recent investigation seems to show 
that the oblivion of Africa must be counted by hundreds 
and not thousands of years; that, in fact, it is only within 
two or three centuries that a knowledge of Central Africa 
has been allowed to lapse. A more rigorous search may 
show that between the fourteenth and the seventeenth 
centuries the great features that have been placed on 
modern maps within the past few years were discovered 
and recorded on the maps of the time. 

We have recently referred, on more than one occa-
sion, to two very curious globes that have been brought 
to light, one in the National Library in Paris, and the 
other in the Library of Lyons. On the Lyons globe, the 
date of which is 1701, the Congo is made to issue from a 
great lake, and wind its way westwards to the Atlantic, 
in a direction to some extent coincident with that recently 
discovered by Mr. Stanley. As a sort of preparation for 
the work of the great traveller, so soon to be issued, some 
account of the data on which these maps may have been 
constructed, may not be uninteresting. Our information 
is based 01~an article in La Nature, and on a report by 
a commission of the Lyons Geographical Society, ap-

pointed to investigate the value and origin of the Lyons 
globe. 

The discovery made at Lyons is, in reality, no surprise 
to those who know the history of geographical exploration, 
Not only in the seventeenth century, does the Zaire-
Congo appear on most of the maps with the direction 
definitely assigned to it by Stanley, but nearly all old 
documents, from the fifteenth century-and the date 
should be noted-make the great river issue from a con-
siderable mass of water far in the interior of the African 
continent. 

Already, in the year 1500, the famous majjemonde of 
Juan de la Cosa, the pilot of Christopher Columbus, gives 
the same indications ; the picturesque majjemonde 
known as that of Henry II., repeats them with some 
variations, as also the master-work of Mercator (1569), 
the founder of modern geography. All the old geo-
graphers, or nearly all, repeat the same data :-Forlani 
( 1562), Castaldi (1564), Sanuto ( l 588), Hondius ( 16o7), 
Nicolas Picart (1644), Blceu (1569), Sanson, &c. There-
fore there need be no surprise to find on a globe of the 
eighteenth century information which for more than 200 
years previously had been registered on the map of 
Africa. 

Whence, however, came this knowledge which our 
fathers had of certain regions in Central and Equatorial 
Africa? The reply is simple : from the Portuguese, who,. 
since the fifteenth century, undertook not only extensive 
maritime voyages, but several times crossed Africa from 
west to east and from east to west. It is even very pos-
sible that they discovered the sources of the Nile, the 
great equatorial lakes; thus, in the midst of the simplicity 
and incoherence of their tracings we find, in their old 
parchments, the great lines of African geography almost 
as science now represents them. Most of these Portu-
guese, with the exception of some missionaries, were but 
poorly educated; they travelled much oftener as traders 
than as experienced explorers ; nevertheless, we have 
almost the certainty that before the year 1500 they had 
furnished very precise information on the centre of Africa. 
In nearly all these maps, and in that of Lyons, the Congo 
Bows in a nearly straight line from Lake Zaire or Zembre 
to the Atlantic ; it bends only a very little to the north, 
and does not pass the equator, as we now know it does. 

As a sort of exception, there has been found among the 
riches of the National Library at Paris, a Spanish globe 
of copper (without date, but probably between 1530 and 
1540), which is not content with presenting the same data, 
but which reproduces, with wonderful closeness, the 
course of the Congo as discovered by Stanley. The 
river issues from a lake, Bows towards the north, de-
scribes a large curve well to the north of the equator, 
then turns west-south-west to the Atlantic. This is indeed 
a summary of the last journey of the intrepid American 
correspondent. Fig. I gives a perfectly accurate idea of 
a portion of this valuable globe. 

From all this it must not be concluded that Stanley 
has discovered nothing new. These discoveries of the 
ancient travellers, if genuine discoveries they were, seem 
to have ben forgotten as soon as they were recorded; and 
although the maps referred to above have been known 
for generations, no one ever seems. to have taken them as 
trustworthy guides to the lines of African exploration. 
Indeed, it is only now that Stanley has made a discovery 
never to be forgotten that these old maps have come to 
have a real interest, for we suspect that till now geo-
graphers regarded the tracings as having their basis 
in the cartographers' imaginations. The glory of being 
really the first discoverers of the two Nyanzas, Nyassa, 
Tanganyika, Bangweolo, and the course of the Congo 
cannot be taken away from Speke and Baker and Burton 
and Livingstone and Stanley; or if so it must be by soz:ne 
ancient Arab or possibly Egyptian, many, many centuries 
ago, for there can be no doubt that long before Europe 

G 2 



© 1878 Nature Publishing Group

NATURE 

awakened to modern geographical enterprise, these great 
features of Central Afri ca were known; Herodotus had 
an inkling of them, and Ptolemy all but located the cen-
tral lakes. The se mf.ldern explorers de serve the glory of 
first discoverers as much as Columbus deserves that of 
discoverer of America. 

Without then detracting from the originality of the 
work of modern explorers, it is evident that from the 
fifteenth century onwards some travellers whose names 
have fallen into oblivion but who may have been com-
panions of Diego Cam and Martin Behaim, ventured into 
the heart of Africa; followed certain arteries of com-
munication and discovered the course of the Congo ; 
geography kept possession of these discoveries for two 
centuries and gave them as articles of faith; besides, in 
the sixteenth and seventeenth centuries many Portu-
gue se, Capuchins or simple traders, entered anew the 

interior, published the same facts, sometimes with cor-
rections and additions. 

Father Ricioli, a Jesuit and very intelligent man, 
furnished the Fathers Placide, of St. Amien, and Cres-
pinien, two laborious monks, with documents to prepare 
the Lyons globe, in I 7or. The actual constructor of the 
globe seems to ha ve been the celebrated Lyons me-
chanician, Henri Marchand, in religion P ere Gregoire, 
a Franciscan, with the help of the Venetian Contarini, 
a pupil of Nolin, belon~ing to the Flemish cartographic 
system. Evidently this was the last word of science. 
Fig. 3 is a much reduced copy of the facsimile made from 
the globe by M. Deloncle, the reporter of the commission 
we have alluded to. 

How came it that just about the same time, about 1700, 
one of the princes of modern geography, Guillaume 
Delisle, was so badly inspired as to reconstruct an alto-

F1c. x.-Pvrtion of a Span ~~h Globe of 15 30-40, f Jund in the National Library, Pa ris . 

get her New Afri ca in which he accumulated heresy on 
heresy? The Central lakes, the imm ense reservoir s 
of the Nile, disappear a t one stroke of the pen ; as to 
the Congo it is no longer connected with the lakes of 
the interior, although it is allowed to retain a little of its 
semicircular direction. The error accredited by a cele-
brated geographer like Delisle made way. The old map 
of Africa was demolished stone by stone, so to speak. 
I n short the work was so well done that, after having piled 
nonsense upon nonsense, for tbe sake of peace, all was 
ex punged; aft er having believed in tribes with docr-
heads, placed a few anthropopbagi everyw here a nd co~-
founded countries situated a thou sand miles from each 
other, they ended by m ak ing a tabula rasa and leaving a 
white space where formerly were rightly placed the great 
lakes and sources of the Nile. Yet a few years and here 
was geography doubting, denying, and ridiculing th e 

follies of our predecessors. The students of geography 
of the period of 1840-50 were too much on their guard to 
commit the colossal blunder at that period of making the 
Nile issue from the lakes to the south of the equator.. 
"So far as concerns a part of Africa," to quote M. R . 
Cort am bert, in the article in La l\lature, "the past has 
been resuscitated: 'old things have become new.' That 
which was laughed at yesterday is taken seriousl y to-day. 
Then, my friends, these good ancestors of the fifteenth 
and sixteenth centuries, who counted among them 
Columbus, Gama, Magellan, and many oth er conquerors 
of the world, have not, perh aps, left altogether to their 
descendants of the nineteenth century the glory of invent-
ing geography." 

From the r eport of the Lyons Commi ssion ,ve learn 
that the following works were probably acces s ible to the 
Flemi sh map-makers, and lat er to the constru ctors of the 



© 1878 Nature Publishing Group

:June 6, 1878] NATURE I 51 

Lyons globe :-r. The Geography of Ptolemy; 2. The 
"Portuguese Asia" of De Barros (r552); 3. The "De-
scription of the Congo," by Pigafetta, according to 
Lopez (r592); 4- The" Historical Description of Ethio-
pia" of Dom Francesco Alvarez" (1558); 5. The 
"Africa II of Leo Africanus (1556); 6. And the old maps 
and portulans. 

Among these old maps and portulans, those which 
appear at this period to have had a certain influence 
are :-r. The Medicean Portulan (1351); 2. The Catalan 
Atlas ( 137 5); 3. The Map of Mecia de Viledestes (1413); 
4. The Map of Johannes Leardus (1448); 5. TheMappe-
monde of Fra Mauro; 6. The Ambrosean Map (1480); 
7. The Mappemonde of Juan de la Cosa (1500); 8. The 
Map of Diego Ribera; 9. The Spanish Mappemonde of 
the National Library, Paris (Fig. 3) (1540); IO. The 

1701". 

F1G. 2. 

Maps of Ramusio, of Pigafetta, and of Hugues Lina 
schoten. 

In the detailed report which the Lyons Commission 
will communicate to the Society will be shown to what 
extent each of the above documents contributed to the 
establishment of the Flemish maps, on which probably 
the Lyons globe was more immediately based. The 
same Report will contain an investigation into the travels 
known or unpublished which, from the tenth century, 
have contributed to the progress of the African geography 
of the Middle Ages and of the Renaissance. This inves-
tigation will include the following :-1. The Arab voy-
ages and Compendia ; 2. The voyages of the mendicant 
Spanish friar of the fourteenth century; 3. The expe-
dition of eight dominicans of Montpellier to the sources 
of the Nile (1317-1350), unpublished; 4- The travels of 

F1G. 3· 

FIG, ,.-Map of Stanley's Recent Journey Across Africa. FIG. 3.-Portion of a Globe of 1701, belonging to the Lyons Library, from a copy by M, Deloncle. 

the brothers Vivaldi, thirteenth century; 5. The expe-
dition of the Catalan Ferrer in l 346, unpublished; 6. 
The voyages of Diego Carn; 7. The itineraries of the 
early pombeiros; 8. The "Eastern Ethiopia'' of Joan dos 
Santos; 9. The travels of Barbosa; 10. The exploration 
of the Dutch Jan van Herder, in the country of the 
Akkas, unpublished; l r. The Derrotero desde Lisboa 
Al Cabo de Bueno Esperanza y India Oriental, anony-
mous and unpublished; 12. The description of the 
Congo, by Martinus Abarca de Bolea et Castro (1601), 
unpublished; 13. The "Universal Book of the Navi-
gations of the World 11 (1590 ?), Spanish, unpublished; 
14; The Travels of the Belgian Pierre Farde from 
Al?;iers to the Congo (1686), unpublished; 15. The 
"Travels of Manoel Godinho" (1663); 16. The Letters 
of Father Mariano, the Jesuit, on Kaffraria, &c., &c. 

The work undertaken by the Lyons Geographical 

Society is creditable to them in the highest degree and 
will result in a valuable addition being made to historical 
geography. Their work, as . the Commission rightly 
maintain, is to some extent international, and deserves 
the countenance and assistance of geographers a[l the 
world over. 

COSMIC METEOROLOGY 1 

I I. 

I NFLUENCE of the Moon on the Earth's Ma[;nelism.-There is a fact in connection with the moon's influence 
on our earth for which an explanation is necessary, and M. 
Faye has proposed for this end a hypoth7si~ in ad_van_ce. 
He had already pointed out Dr. Lloyd s mvest1gat10n 
which showed that the diurnal magnetic vanat1ons could 

l Continued from p, , 28, 


	OLD MAPS OF AFRICA