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ference of his sphere was not divided in 360 degrees,
but in 60 parts, each of 4,200 stades ; which, how
ever, amounted to the same thing.

(100) Page 92. Navarrete, vol. ii., p. IOI.

(101) Page 92. We propose to ascertain where,
according to the theory of Jaime Ferrer, the meri
dian of the Line of Demarcation should be placed
on the terrestrial globe as it is known to-day. 1

Our inquiry will be prosecuted on the basis of
data borrowed from the Parer of that cosmographer,
which, in their original Spanish text, are as follows :

1st. The starting point, to commence counting
the 370 leagues westwards, is "la isla del medio de
las que estan delante del Cabo Verde" (Navarrete,
vol. ii., p. 103, line i).

2nd. " Cada un grado en este paralelo comprende
veinte leguas y cinco partes de ocho" (Op. V.,
p. 99, line 3o). 2

1 We are under the greatest obligations to our esteemed
friend, Mr. E. Bauvieux, a retired officer of the French navy,
without whose obliging and scientific aid we certainly could
not have devised the necessary methods, and carried out the
difficult computations in this as well as in other technical dis
quisitions and notes of the present work.

2 It is from this datum 2nd that we infer Ferrer s league
to be of 21^353 to a degree of his equator.



Notes 179

3rd. " Es menester dar por cada un grado sete-
cientos stadios segun Strabo, Teodoci, Macrobi,
Ambrosi, Euristenes " (Op. cit. y p. 101, line

51-53)-

4th. " Es de notar que las 370 leguas partiendo
de las dichas islas [del Cabo Verde] comprende diez
y ocho grados y cada un grado en este parallelo
comprende 20 leguas y cinco partes de ocho " (Op.
at., p. 99, line 28).

5th. " Cada un grado de los tropicos es veinte
leguas y cuatro partes de trescientos sesenta " (Op.
at., p. 102, lines 34-36).*

6th. " En el cerclo equinoccial cada un grado es
de veinte y una leguas y cinco partes de ocho " (Op.
at., p. 102, lines 33-34). 3

yth. " La circumferencia de la tierra es doscientos
cincuenta y dos mil stadios segun Strabo, Alfira-
gano, Ambrosi, Macrobi, Teodosi, y Euristenes, los
cuales doscientos cincuenta y dos mil stadios a razon
de ocho stadios por milla son treinta y un mil y
quinientas millas, y a cuatro millas por legua son
siete mil ochocientas setenta y cinco leguas" (Op.
at., p. 1 02, lines 9~i5). 4

8th. " Es menester dar por cada un grado sete-
cientos stadios, segun Strabo, Alfragano, Teodoci,

1 It is from this datum that we draw inferences identical
with the data drawn from Nos. 7 and 8.

2 It is from this datum 5th that we infer Ferrer s league to
be of 2 1 ,8 1 3 to a degree on his equator.

3 It is from this datum 6th that we infer Ferrer s league to
be of 2i J ,625 to a degree on his equator.

4 It is from this passage that we draw inferences identical
with those drawn from Nos. 3 and 8.



180 Notes

Macrobi, Ambrosi, Euristenes, porque Tolomeo
no da por grado sino quinientos stadios " (Op. /., p.
loi, lines I-4). 1

We will now proceed to carry out our investiga
tion in the following method, thus :

First: By accepting for the actual sphere the
meridian which, on Ferrer s sphere^ passes 37 of
Ferrer s leagues on the parallel of 1 5 latitude, west
of the easternmost extremity of Fogo Island (one
of the Cape Verde Islands). According to Ferrer,
the arc of the parallel of 15 latitude comprised
between those two meridians is 18.

Second : By verifying the calculation by means of
which Ferrer came to fix that arc of longitude
of 18.

Third: By determining the meridian which, on
our aftual sphere^ would traverse the parallel of
15 latitude at a distance stated in actual marine
leagues (of 20 to a degree) equal to 370 of Ferrer s
leagues.

FIRST.

Relying upon his data relative to the dimensions
of the terrestrial globe, Ferrer, in 1494-1495, calcu
lated that 370 of his leagues represented the length
of an arc of 18 on the parallel of 15 north latitude.

1 It is from this datum 8th that we establish the relation
existing between the real dimensions of the terrestrial globe
and those ascribed to it by Ferrer (in valuing the stade at
i92 m ,2y). From this passage can also be inferred the value
of Ferrer s league in our marine leagues of 20 to a degree of
the equator (the stade also equal to i92 m ,27).



Notes 1 8 1

He proposed, therefore, that the divisional line be
tween Spain and Portugal should pass on the sphere,
such as it was then believed to /><?, 1 8 west of the
starting point, which was the most eastern extremity
of Fogo Island in the Cape Verde archipelago.

Whatever may be the dimensions adopted by
Ferrer for the terrestrial globe, the meridian of 18
on his sphere will always be 18 for all the spheres
possessing the same centre as his own, and, conse
quently for the terrestrial sphere as it is known
to-day. On the latter, the meridian adopted by
Ferrer would be in 24 25 west (Greenwich) -f- 18
= 42 25 west (Greenwich), accepting 24 25
west (Greenwich) as the starting meridian. 1 This
divisional meridian would thus pass, on the parallel
of 15 latitude, in 348^ 138 (marine leagues of 20
to a degree) west of the starting meridian, which, as
already stated, was the easternmost extremity of
Fogo.

1 In calling * the length of the arc of 18 (in marine
leagues of 20 to a degree on the equator) on the parallel of
15 latitude, and knowing besides that the arc of 18 of the
equator is equal to 18 x 20 = 360 leagues, we have the
relation :

X COS I C ,

- = -, whence x = 360 x cos 15 .

360 i

Log 360 = 2,55680*5
Log cos 15 = 9,98494.38

Log* = 2,54.174.63
x = 348 ,! 38.



1 82 Notes

SECOND.

Let us ascertain whether the meridian calculated
to pass, on Ferrer s sphere, 370 of Ferrer s leagues
west of the starting meridian, is really a meridian
situate 18 west of the starting meridian.

For that purpose it is necessary to determine the
value of Ferrer s league in the equatorial degree
in his sphere.

Ferrer in his Parer says :

" Es de notar que las 370 leguas partiendo de las
dichas islas comprenden por Occidente 1 8 grados, y
cada un grado en este parallelo comprende 20 leguas y
cinco partes de ocho." " It is to be noticed that the
370 leagues, from the said islands [the Cape Verde
Islands], comprise westward 18 degrees, and each
degree in that parallel comprises 20 leagues and | "
[ 20 1 , = 20 1 ,625].

If on Ferrer s sphere one degree of the parallel
of 15 is of the length of 20^625 of Ferrer, one
degree of the equator of the same sphere will be
2 1 ,353 of the same leagues. 1

1 In calling x the length in Ferrer s leagues of the arc of
i of Ferrer s sphere at the equator, and knowing that on the
same sphere the arc of i of the parallel of 15 latitude is
equal to 20^625 of Ferrer, we have the relation :

, whence x = 20 6z 5



20,625 cos 15 cos 15

Log 20,625 = 1,3143940
Log cos 15 = 9,9849438

Log#= 1,3294502



Notes 183

In the same Parer we find the following state
ment :

" Y cada un grado de los Tropicos es 20 leguas y
cuatro partes de trescientos sesenta : And each
degree of the Tropics is 20 leagues and four parts of
three hundred and sixty" [20 1 , T o = 2O 1 ,oii].

This valuation of 2o 1 ,oi I of the arc of I of the
tropical circles (23 27 lat.) gives 2i 1 ,8i3, for the
length of the arc of I of the equator in the same
sphere. 1

Again, in his Parer , Ferrer says : " Es de notar
que en el cerclo equinoccial cada un grado es de
veinte y una leguas y cinco partes de ocho : It
should be noticed that in the equinoctial circle, each
degree is of twenty-one leagues and |-" [2i l ,5|- =
21 ,625].

Finally, it appears from several passages in the
same Parer, that Ferrer ascribes 700 stades to a
degree of the equator in his sphere ; 8 stades for a
mile, and 4 miles for a league.

1 In calling x the length in Ferrer s leagues of the arc of
i of the equator in Ferrer s sphere, and knowing that the arc
of i of the parallel of 23 27 latitude is equal to 2o l ,on of
the same leagues, we have the relation :

20.011
-, whence x = - -^



20,011 COS 23 27 COS 23 27

Log 20, on = 1,3012688
Log cos 2327 = 9,9625624.

Log* = 1,3387064

X = 2I 1 ,8l 3 .



184 Notes

According to these data, Ferrer s league in his
Equator would be :

700_7oo_ lg
8x4-^

We consequently find, according to Ferrer him
self, four different valuations for his league in the
equatorial degree, viz :

21^353 ; 2i 1 ,8i3; 21^625; 21^875 ;

(A) (B) (c) (D) "

If we at once set aside A as being the widest of
the mean valuation, there remain B, c, and D, of
which B and D differ but little from each other.
This leads us to reject c. Finally, we adopt D, or
2 1 ^875, because it was obtained directly from the
relations between the units of length generally ad
mitted in Ferrer s time, instead of being derived
from astronomical valuations which in his days were
not very exact.

If we carry 370 of these leagues (of 21^875 to a
degree of Ferrer s equator) on the parallel of 15
latitude (of Ferrer s sphere), the arc thus obtained
will be 17 3iV

The difference between this valuation and that
of 18 is insignificant, especially if we take into con
sideration the little precision with which the starting
meridian was determined. We thus see that Ferrer s
calculation was sufficiently exact, and that his 370

1 In calling x the length of arc of the equator of Ferrer,
which is of the same angular value as the arc of 370 of



Notes 185

leagues on the parallel of 15 latitude in his sphere,
intercepted about an arc of 1 8.



THIRD.

Let us now find which is the meridian which, in
our sphere, would cut the parallel of 15 at 370
of Ferrer s leagues west of the meridian of Fogo
Island.

To that effecl: we must first know the value of
Ferrer s league in our marine leagues of 20 to the
degree of our equator.

According to Ferrer, the circumference of the
earth was 252,000 stades.

But there were several kinds of stades. From
Ferrer s references to certain Greek authors as au
thorities, it is evident, however, that he employs the
stade used by Strabo, Eratosthenes, and Macrobius

Ferrer s leagues in the parallel of 1 5 latitude, we have the
relation :



x



, whence x = ^-

370 cos 15 cos 15

Log 370 = 2,5682017
Log cos 15 = 9,9842438

Log x = 2,5832579



The value of the arc in degrees, at the rate of 21^875 to the
degree is given by the relation :



- 7 s " "



1 86 Notes

in their estimates. This was the stade commonly
used in Greece, that is, the Olympic, which at
present is known to measure exactly I92 m ,27, as we
have already said. 1

Ferrer s circumference of 252,000 stades x I92 m ,27,
is equivalent therefore to 48,452,040 metres, in
stead of 40,000,000 metres, which is the real
value.

Ferrer s equatorial degree of 700 stades, 700**
x I92 m ,27, is, for the same reason, equivalent to
134,589 metres, instead of iii,iu metres, which
is the value accepted now by all metrologists.

The relation of the circumference of the earth,
such as Ferrer computed it to be, to the circumfer
ence of the globe as it is admitted to be, is conse-

. 48,452,040
qUe " tly 40,000,000 = VI 13010, or approximately,

1,211. That is, Ferrer increased the circumference
of the earth by -Jy^. of its real value ; that is, ap
proximately, by \.

As the arc of i of the equator of Ferrer s sphere
was 2 1 ,8 75 (see above) of his own leagues, the arc
i of the equator of the real sphere, as known to-

1 Supra, note 97, where we give the measurement made of
the stadium of Olympia, after it had been cleared in 1881 by
the commission of German archaeologists. As regards the
facl that until at least the fifth century of our era the Greek
scientists employed exclusively the Olympic stadium, see
Boeckh, " Metrologische Untersuchungen," Berlin, 1838, 8vo,
pp. 288-90, and particularly Th. Henri Martin s valuable
critique of Letronne s " Recherches sur les fragments d Heron,"
in the separate issue of the " Revue archeologique," Paris,
1851, 8vo, pp. 15, 20, 21, 32, and 112.



Notes 187



day, will be represented by a number of those leagues

equal to - ? = 1 8*0598 of Ferrer s leagues.

1,2113010

On the other hand, as the same arc of I on our
equator is equivalent to 20 of our marine leagues,

Ferrer s league is equal to ~ - ~ = I l ,i074

marine leagues of 20 to the degree of our equator.

The 370 leagues of Ferrer, consequently, amount
to 370 x i ,1074 = 409^738 marine leagues of 20
to the degree.

An arc of the parallel of 15 latitude, of a length
equal to 370 of Ferrer s leagues, that is, equal to
409^738 of our marine leagues, corresponds on our
actual sphere, 1 with an arc of the equator of the same
angular value equal to 424 ,! 92.

That is, at the rate of 20 leagues to the degree,



equal to > = o 2I = 2I _ I2 _o"6.

20

The meridian required is, therefore, the one which
cuts the parallel of 15 latitude in 21 12 longitude

1 In calling x the length of the arc of the equator of the
same angular value as the arc of 409^738 on the parallel of
1 5 latitude, we have the relation :

x _ 409,738
Cos 15

Log 409^738 = 2,6125070
Log cos 15 = 9,9849438



Log* = 2,6275632
x = 424^192.



1 88 Notes

west, starting from the meridian of Fogo. That is,
in taking 24 25 west (Greenwich) for the longitude
of Fogo, the meridian which we are endeavouring to
ascertain is 24 25 west + 21 12 west = 45 37
west (Greenwich).

CONCLUSIONS.

It follows from what precedes that to ascertain
where the Line of Demarcation would have passed,
according to Ferrer s theory, we must first adopt for
our sphere the meridian of 18 west of the mean
meridian of the Cape Verde Islands. This we have
shown to pass on his sphere very nearly 370 of his
leagues on the parallel of 15 latitude west of the
starting meridian in Fogo. This meridian of 18
on his sphere will always be the same meridian of
18 on any other concentric sphere, whatever may be
its dimensions ; but with this difference : On any
other sphere than Ferrer s, it will no longer pass 370
of Ferrer s leagues west of the starting meridian, on
the parallel of 1 5 latitude. It will pass at a distance
proportional to the dimensions of that other sphere.
This meridian, on our actual sphere, would be the
meridian of 42 25 longitude west (Greenwich),
passing at a distance of 348^1 38 of 20 to the degree,
west of the meridian of Fogo, on the parallel of 15
latitude.

This unexpected longitude of 42 25 , which is
nearly 8 further east than the longitude assigned to
the Line of Demarcation in the Weimar plani
spheres (judging from its appearance on those maps),
finds its explanation in the fac~t that Ferrer increased



Notes 189

the dimensions of the terrestrial globe by about
^y^ or, approximately, \ of its real value. 1

Ferrer s meridian would cut the north coast of
Brazil about 75 miles east of the entrance of Mar-
anhao, and 10 miles west of the entrance of the
western mouth of the Rio Paranahyba.

It would also cut that part of the Brazilian coast
running westward from Cape Frio, at about 23
miles west of Cape Frio, or 40 miles east of the
entrance of Rio de Janeiro^ south of the laguna of
Jucurutia, near the great laguna of Araruama.

But if the Spanish and Portuguese pilots had
possessed the means of measuring exactly the distance
of 370 of Ferrer s leagues westwards on the parallel
of 15, starting from Fogo; also, if when they had
arrived at the extremity of that distance, they
had been able besides to determine in a precise
manner the longitude of that extremity, they would
have ascertained that this longitude was the one
which on our sphere is in 21 12 west of Fogo,
45 37 west of Greenwich, and not 42 25 accord
ing to Ferrer s theory.

This meridian of 45 37 would have cut the north
coast of Brazil at Pirucaua point, situate between
the Bay of Maracasume in the east, and the Bay of
Pirucaua in the west, about 23 miles west of the Bay
of Tyryassu, 85 miles west of the entrance of Mar-
anhao, and 120 miles east of the Para river, on the
east coast of Marajo Island.

1 Ferrer s league is equal to 1^1074 f our marine leagues
of 20 to the degree. This league is about 18^06 to the
degree of our aftual equator.



1 90 Notes

It would have also cut the Brazilian coast extend
ing west of Cape Frio, about 150 miles in the
entrance of Rio de Janeiro, 8 miles west of the channel
separating the island of St. Sebastian from the coast,
and about 25 miles east of the entrance of Santos.

(102) Page 94. "John Cabot, the Discoverer of
North America, and Sebastian his Son," London,
B. F. Stevens, 1896, 8vo, pp. 296-308.

CHAPTER XIII.

(103) Page 98. " Discovery of North America,"
pp. 412-415. There is, however, a map added after
1512 to Corumberger s edition of Peter Martyr s
first Decade, but it is a small, rough woodcut, omit
ting also the Line of Demarcation, and placing our
Amazona, therein called " rio grande," in the longi
tude of the Canary islands ! (Op. /., No. 94, pp.

474-477)-

(104) Page 100. "Les Corte-Real et leurs voyages

au Nouveau Monde," pp. 73-96, and the " Dis
covery of North America," pp. 422-25.

(105) Page 100. See the King s chart, Kunst-
mann, No. 2, etc.

(106) Page 1 02. Method which we adopted to
ascertain the positions in Cantino s mappamundi,
according to its geodetical data :

For the latitude. After determining the distances
from the equator to the Tropic of Capricorn and
to the Polar Circle, which, on the Cantino map

are, respectively, 2o8 mm and 56o mm , or about -7-



Notes 1 9 1

4 (or 8 mm , 4 for the length of each de



gree of latitude), we measured the distance in milli
metres from the point to the equator, and divided
that distance by 8, 4. The quotient gave the num
ber of degrees of latitude.

For the longitude. The degree of latitude multi
plied by the cosinus of 45 having shown the de
gree of longitude equal to 6 mm , the distance from
the point to the meridian of Paris was measured in
millimetres. In dividing that number by 6, the
quotient was the number of degrees of longitude
according to that meridian.

We then assumed that the cartographer who con
structed Cantino s prototype gave i6-| leagues to a
degree on the equator, according to the measure
generally adopted by the Portuguese pilots of the
time, 1

Judging from the difference in longitude between
Cape San Roque and South Guinea, which is 55 in
the Cantino map, instead of 45 as in reality, we
may assume that in the opinion of its maker the
radius of the globe was equal to five millions of
metres instead of six.

We should also take in consideration that in the
Cantino map the latitude of the tropics is 20 40
instead of 23 27 .

The object of this technical explanation is simply
to show that no reliance is to be placed upon the

1 " La ragione perche io do 16 leghe e due terzi per ogni
grado," says Vespuccius, in his letter of July 8, 1500 (Ban-
dini, Vita di Vespucci, p. 72).



192 Notes

metrology of that map, and that the figures which
we have set forth in our Corte Retl^ should not be
invoked, as has been done recently, 1 to determine
the longitude of that meridian. We must be guided
in that respect only by the geographical position of
the Line in the Cantino map, which is fixed therein
eastward from the Maranhao. 2

CHAPTER XIV.

(107) Page 103. Navarrete, in his " Optisculos,"
vol. i., p. 66, says that " hallabase en un Registro
de copias de c6dulas, provisiones, etc., de la Casa de
la Contratacion desde 5 de febrero de 1515 hasta 6
de marzo de 1519."

( 1 08) Page 1 03. " Suma de geographia que trata
de todas las partidas y provincias del mundo : en
especial de las indias, y trata largamente del arte del
marear : Juntamente con la esphera en romance.
. . ." Sevilla, 1519, folio; "Bibliot. Americ. Vetust,"
No. 97, pp. 167 ; "Discovery of North America,"
pp. 502, 716.

(109) Page 104. It must be noted, however, that
in the windrose added to the a Suma," the difference
between two points of the compass seems to have
been calculated on the basis of 17^ leagues. But
logic requires in the present discussion to adopt the

1 London "Times," February 6, 1896, p. 8, and March 7
following, p. 6.

a That which shows that it is the Maranhao, and not the
Maranon or Amazona, is the delineation of a large estuary
west of the Line, and bearing the well-known inscription :
" Todo este mar he de agua doce " (all that sea is fresh water) .



Notes 193

data which Enciso himself explicitly sets forth for
his computation of the circumference of the earth.

(no) Page 105. This is impossible. Enciso
probably wrote 57 instead of 117, and 950
leagues instead of 1,950.

(in) Page 105, Those 400 leagues of Enciso
are equal to 443 of our leagues ; but the real distance
is 520 of our leagues of 20 to a degree.

(112) Page 105. Enciso makes the following
statement : " Porque cada un grado es tassado en
l6J leguas y un sesmo de camino todo el Mundo
tiene en derredor 360 grades que montan 6,000
leguas" (As each degree is fixed at 16^ leagues, and
one-sixth in space [16 -f- ^ + TT = 1 6,666], the cir
cumference of the entire world [globe] is of 360

, \ r 6,OOO

degrees, amounting to 6,000 leagues) [again . =

1 6 leagues, 666 to the degree of Enciso s equator].

According to Enciso, who wrote in 1518, the
value of an equatorial degree was, therefore, on his
sphere, 1 6^666.

We have shown that according to Ferrer, who
wrote in 1494, the value of an equatorial degree, on
his sphere, was 2I 1 ,875.

The probability is that the league, which is
always a unit usual and fixed, was the same for
Enciso and for Ferrer ; that is, at the rate of 32
stades for one league. We shall therefore adopt the
same value for the league of both cosmographers,
and ascribe the difference in the valuations which
they give to the equatorial degree only to their
different valuations of the dimensions of the earth.



194 Notes

Let us ascertain the relation which the equatorial
degree on the sphere of Enciso bears to the equa
torial degree on our sphere.

According to that cosmographer, the circum
ference of the globe is 6,000 leagues ; that is, at the
rate of 32 stades per league, 6,000 X 32 = 192,000
stades. If we adopt for Enciso, at we did for Ferrer,
the stade as being equal to 192 metres, 27, the cir
cumference of Enciso s sphere is 192,000 X 192,27
= 36,915,840 metres, instead of 40,000,000 metres,
which is the value admitted to-day.

The sphere of Enciso therefore bears to the real

sphere the relation of 3 >9 5? 4 = o,Q2?, and his

40,000,000

equatorial degree bears of course to the actual equa
torial degree the same relation of 0,923.

The equatorial degree on Enciso s sphere being
of 16^666, and the 0,923 of our actual equa-

. , , . 16,666

tonal degree, the latter will contain



i8 ,O57 of Eerrer s and of Enciso s leagues. 1

Our actual equatorial degree being equal to 20 of
our leagues, it follows that Enciso s league is equal

to ^ - = i ^107 8 of our marine leagues of 20

to a degree, or i,io8. 2

In short, the circumference of Enciso s sphere is

1 We found nearly the same result when discussing Ferrer s
data, viz. : 18,0598 of his leagues to our equatorial degree j
and it could not be otherwise.

2 We found for Ferrer s league, i 1 ,io74 marine league
of 20 to a degree.



Notes 195

equal to the 0,923 of the circumference of the real
sphere; that is, he makes the latter smaller by 0,077
than its real value.

Ferrer s sphere, as has been shown (supra^ p. 186),
is 1,21 1 of the circumference of the real sphere ; that
is, Ferrer makes the latter larger by 0,21 1 than its
real value.

Consequently, Enciso commits an error of 0,077
less, Ferrer one of 0,21 1 in excess.

The difference shows, to a certain extent, the geo-
detical progress accomplished between 1495 and 1518.

Those figures can be verified as follows :

We have shown that the relation of the circum
ference of Ferrer s sphere to the circumference of our
aclual sphere is 1,211 ; now, the relation of the
circumference of Ferrer s sphere to the circumference



of the sphere of Enciso is = I ?3 I 3 j 1 conse



quently the relation of the circumference of the
sphere of Enciso to the circumference of our actual

. 1,211

sphere is - - = 0,023.



We must also notice that Ferrer ascribes 7,875
leagues to the circumference of his sphere ; whilst
Enciso ascribes to his own sphere a circumference
of 6,000 leagues. The relation between these two



circumferences therefore is l 1-213. But we

6,000

1 This relation is that of the size of Ferrer s equatorial
degree with the equatorial degree of Enciso, and is evidently


1 2 3 4 5 6 8 10 11

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