Talk:Gerardus Mercator

Length of quotes

This article has complete or extensive sections of pamphlets or letters that do not fit the model of short, pithy, quotable quotes. ~ Ningauble (talk) 17:37, 17 January 2018 (UTC)

A Pamphlet to the emperor Charles V -- Part I

• The original latin text and a german texts may be found in may be found in volume 3, pp 99-333 of Ad Maiorem Gerardi Mercatoris Gloriam. This english translation is a slightly edited version of the Google translation

Declaratio insigniorum utilitatum quae sunt in globo terrestri : coelesti, et annulo astronomico ad invictissimum romanum imperatorem Carolum Quintum

A description of the most important applications of the terrestrial and celestial globes and the astronomical ring. For the most invincible Roman Emperor Charles V

Part I: About some problems and the use of the earth globe

Chapters:

1. That there is a certain magnetic pole and where it exists
2. The study of the the latitude and longitude of the magnetic pole.
3. How to find the longitude (of a place)
4. How to find the Magnetic Deviation at any location
5. the spheres of influence of Portugal and Spain
6. On the correction of the length of Europe

Author's preface

Much would be said about the use of the magnet, invincible emperor, if anyone wanted to explain all his secrets. But since they require greater effort, experience, and more in-depth investigation than many-even difficult-problems of mathematical reasoning (speculation), I will now only discuss its utility in the question of location length, a matter of which little is yet heard Has. However, as your Majesty desires, I will devote myself with zeal to the exploration and disclosure of the most hidden and useful features of the magnet in geography.

1 ESSE POLUM ALIQUEM MAGNETIS ET UBI SIT
That there is a certain magnetic pole and where it exists.

First, it has been well established by philosophers that whatever moves, moves toward any goal. If the movement takes place in a fixed location, the target is also located in a fixed location. The tip or the tip of a magnetized [magnet-swept] needle moves locally [ie at a fixed location], so the intended target [of this motion] is also some [fixed] location. This place is a solid, as the tip of the magnetic needle is always directed in the same direction in any city. By no means, however, is it always distracted to the north, deviating from north to west or from north to east. However, since each point in the sky unlike the North Pole evidently moves [around the pole], this place [to which the magnet needle points] can not be in the sky, because it would follow that the tip of the magnet in a [certain] city or to deviate from north to east, now from north to west, at a certain place, following the non-fixed place [in the sky], which is not right, as the day-to-day experience shows. So it is this place where the magnet is moving, not in the sky, but on the earth, whose places are all unmoved.So it actually seems that this [fixed] place [on the earth] can be rightly called "magnetic pole".

2 LINQUISITIO LONGITUDINIS AC LATITUDINIS POLI MAGNETIS
The study of the the latitude and longitude of the magnetic pole.

However, in order to accurately determine the length and the width of the magnetic pole, one must have observed the deviations of the magnetic needle from the north direction at two points of known latitude and longitude difference. From these deviations it will be easy to calculate the latitude and longitude of the magnetic pole as follows. I know that a magnet or the magnetic needle on the island of Corvo actually points north. I have also know that in Leuven that the deviation is 9°59 east; I also know the latitude of Leuven is 50°54' and the longitude difference between the Leuven and the island of Corvo is 36°31'. From all this, I conclude that the latitude of the magnetic pole is 73°2' and the longitude difference between Leuven and the magnetic pole is 143°29'. Now Leuven is at a longitude of 26°5' so the longitude of the magnetic pole will be 169°34'. Using these calculated values of latitude and longitude, I have shown the magnetic pole on the celestial globe, because there would be no proper use of it on the terrestrial globe because of the celestial sphere enclosing it. (Editor's note: Mercator is describing the double globe presented to Charles V wherin the terrestrial globe is enclosed by a celestial globe.)

3 INVENTIO LONGITUDINIS BY MAGNETEM
How to find the longitude (of a place) with the help of the magnet

(Editor's note: this obscurely worded section is an attempt to describe the inverse calculation to that of the previous section, ie given the latiude of a point and the deviation at that point calculate the longitudinal difference from a reference point (Corvo).)

If, therefore, the longitude of any place is to be determined by means of the magnet, one must first know the latitude of the place, then find the meridian, and place on it the needle (coated with a magnet, i.e. the magnetic needle) then look for how many degrees and minutes it deviates from the north at this point and determine the direction [of the deviation]: to the east or to the west.

If one has now determined the latitude and the deviation of the magnetic needle, one must set up the globe accordingly and adjust the height squares in the same way. Then, from the northward intersection of the meridian (ring) and the horizon (ring) [i.e. the degree of the intersection], one has to count and account for as many degrees and minutes as the magnet deviated from the north, east or west.

On this [resulting] statement in degrees and minutes you have to adjust the Meßschenkel the Höhenquadranten 4 . After attaching a flag there, you have to turn the globe until the magnetic pole lies directly below the measuring leg of the elevation quadrant. The true length of the given location is then determined in equator degrees and minutes below the meridian.

It should be noted, however, that the magnetic pole - after fixing the height quadrant - will come twice below the height quadrant. In the case that the longitudes of the two points of contact differ greatly, it is easy to specify which longitude should be determined from both; in the other case, if the deviation is small, not so easy.

The greatest differences between the longitudes of the two points of contact are at the places near the meridian which goes through the island of Corvo, and near the opposite side. Otherwise, they diverge almost everywhere, except in places very close to the lengths of 80 ° and 260 °, where both points of contact coincide almost with the longitude in question.

However, anyone who travels east or west or sails and tries more often, by means of a compass or a magnetized needle - whether or not he can avoid a very large deviation of the magnet from the [earthly] North Pole - will find himself at the latitude of his itinerary of longitude are not wrong (even very close to 80 ° or 260 °) : as long as he is not past this, the deviation of the magnet will increase, but as soon as it is over, it begins to decrease.

4 INVENIRE MAGNETIS DECLINATION QUODLIBET LOCO PER GLOBUM
How to find the Magnetic Deviation at any location with the help of the globe

If you have set the meridian to latitude of a given location and rotated the globe until the longitude of the location is below the meridian, place the height quadrant over the magnetic pole. The height quadrant will then show on the horizon ring how many degrees and minutes and in which direction the magnet deviates from the meridian line at that location.

5 DE CONTROVERSIA QVAE EST DE LNSULIS MOLUCCIS DIRIMENDA
About the controversy with the "Moluccenfrage" (the separation of the spheres of influence of Portugal and Spain) accompanied

The dispute over the islands of the Moluccas could easily be decided, always provided that on the island of Corvo the magnet indicates the true (magnetic) North Pole. If there too the magnet would indicate the correct Norpol, they would lie on the same meridian; but if the magnet deviated to the east, they would be more western than the meridian of Corvo; and if he deviated west, they would be more eastern than this meridian. And since the Moluccan islands are not much more easterly than this meridian - as far as one can conclude from the sea voyages - it would be easy - as already mentioned - to determine their longitude.

6 DE LONGITUDINE EUROPAE CASTIGANDA, ET QUOD MERIDIANUS INSULAE CORVI NON TRANSIT BY NOVAM INDIAM SED SIT ORIENTALITER
On the correction of the length of Europe, and that the meridian of the island of Corvo does not pass through New India, but is further to the east

The errors of Ptolemy concerning the length of the countries of both Africa and Europe, which lie at the western ocean or at the beginning of the longitudes, have caused most of the [later] researchers to discover otherwise in dividing the earth into two parts, as it behaves (actually): they cut off the meridian that passes through the island of Corvo, a large part of [South] America or New India, namely Brazil, although it is more easterly than Brazil, so that he even the Cape St. Augustin is not touched.

The reason for the error of Ptolemy is that he believed the coasts of Africa extended directly from the Pillars of Hercules to the south, just as the old sea route of the Carthaginian Hanno entails. Since he allowed [Ptotelmus ] to begin the longitudes of the Canary Islands, he was forced to extend Gaul, and especially Spain, far to the west, so that Africa's shores from the pillars of [Hercules] could reach that extent to the south. But that he would successively extend Africa from Carthage, Gaul, and especially Spain to the west, will be plainly seen by anyone who correctly compares all the voyages made by our seafarers around Europe, both in the Mediterranean and in our northern sea (the North Sea) as well as along the African coasts to the Pillars of Hercules (Strait of Gibraltar) as to the extreme tip of the Canary Islands, which is called "Ferro" (Hierro) - and there is no southern route like Ptolemy's but [all lead] to the southwest or even to the west.

For who, according to this deliberation, painstakingly presents everything by drawing, will find that Western Africa, as far as and beyond Carthage, and Europe, as far as Gaul, reaches the lengths indicated by Ptolemy fairly accurately, but that the more western ones are crowded together To which certainly - no wonder - the sea routes and the distances between the places force. If someone then additionally in Strabo , Antoninus Pius , in Arrian s Navigatio Pontica (sea voyage on the Pontus Euxinus / the Black Sea), read by Herodotus and other absolutely reliable authors of the same time, and if he - where these (namely: old certificates) are not present - adds later route descriptions, and if he became attentive to the description of Europe with the adjoining regions of Asia and Africa from the great amount of distances of places collected from all over, so that these authors with each other and all the routes with each other and the authors with the routes as accurately as possible Brings harmony, so, the find out that the lwidth of Europe is greatly shortened to the east, such that the length to the west coast of Spain - that is, up to Finisterre - amounts to 20°9'. Ptolemy set s the longitude of Cape Finisterre as 5.1/4° in length; Cabo sets Sao Vicente at almost 2° longitude as against Ptolemy at 3 °.

We have inferred from this description of Europe at that time that everything that was useful from ancient or modern testimonies, from testimonies of travellers, from maps and nautical charts, so united that everything fits together as logically as possible , Therefore, I do not doubt that this [the length extension of Spain shortened by 6 degrees of longitude] is as accurate as possible the longitude of of Spain.

However, in our depiction, the lengths of the places are not smaller than those of Ptolemy , except from Cologne and then from Italy to the west, but not so much in Gaul, so that the old English island is still the longitude of Ptolemy Spain, however, is smaller (by 6°). Also the island Ferro [Hierro], the outermost of the Fortunatae (the formerly so-called 'happy islands) retains the length as with Ptolemaeus.

After these observations, we want to calculate how far the island of Corvo is in the distance from the extreme [west] coast of Spain [Cape Finisterre]. However, since the island of Corvo is 300 leagues [miles] from the nearest coast of Portugal - which is near Lisbon - that is approximately 39.5 ° in longitude approximately parallel to it, these 300 are about include the longitude [extension] of 21.1/2°. Therefore, the island of Corvo lies in the length of 349.1 / 2 °, because the nearest coast of Lisbon is about 2 ° long.

But now Cape St. Augustin is in Brazil - according to the distance from Africa, which all have credible maps - on longitude 348°.

So the meridian that goes through the island of Corvo runs 1.1 / 2 ° further east of Brazil.

Postscript

Haec tuae Maj ti breviter pro nostro captu significare volui, ut super hac re by opportunitatem altius cogitare possit.

I wanted to briefly explain this to Your Majesty, so that you can think about the problem on occasion.

A Pamphlet to the emperor Charles V -- Part II

• The original latin text and a german texts may be found in may be found in volume 3, pp 99-333 of Ad Maiorem Gerardi Mercatoris Gloriam. This english translation is a slightly edited version of the Google translation

Declaratio insigniorum utilitatum quae sunt in globo terrestri : coelesti, et annulo astronomico ad invictissimum romanum imperatorem Carolum Quintum

A description of the most important applications of the terrestrial and celestial globes and the astronomical ring. For the most invincible Roman Emperor Charles V

Part II: The exquisite use of the celestial globe

Chapters:

1. The use of the globe with regard to the sun
2. The use of the globe with regard to the stars
3. To the knowledge [of the position] of all stars get
4. The use of the height quadrant
5. About the dwell time of the stars over the horizon
6. How to find the midday line
7. How to determine the latitude of an area
8. How to find the ecliptic sign and the height of the sun
9. How to measure the height of any star above the horizon measures
10. At what time of the year is any star around Midnight in the meridian
11. At what hour does each star stand in the [place] meridian
12. How to determine the size of dusk

1 The use of the globe with regard to the sun

Almost the entire use of the celestial globe consists in the that [that] someone has all its constituents in all similar understanding how to harmonize physical qualities in the sky; d. H. the horizon [ring] the [true] horizon [1], the meridian [ring] the sky meridian, the globe buspol the sky pole, the ecliptic [ring] of the ecliptic, the height came to the zenith [the pole of the horizon] as well as the latitude of the [question] region.

The horizon - represented by the horizon ring - is represented by a pendulum, which is located in the foot [of the celestial globe], fixed as soon as that hovering directly above the vertically underlying point. The meridian - represented by the meridian ring - is Needle in the foot [of the globe stand] with the help of which one then visit the other [true] meridian. As soon as this meridian fits send is to be established first, the ring [the meridian ring], the is inside [the celestial sphere], on the [meridian] line to turn, which is attributed to the misappropriation - by [exactly] so much of that [by the magnetic needle in the bottom of the glove-stand detected] meridian removed as the magnet at the relevant location fails [d. H. deviates from the geographic north direction]. The GE- according to the light of point 4 in the previous chapter [= I.4, p. 101]. The [celestial globe] pole is applied to the celestial pole, by turning the [Globe] meridian so that the globe pole closes Least as many degrees above the horizon as the latitude of the the area concerned.

In the end, the [globe] ecliptic must follow with the help of the sun- so set up: the hour hand 12) may the degree [up] correspond to the ecliptic on which the sun stands on that day. This is exactly the case if that degree is just below the meridian is brought as the 12th hour of the hour ring. Then the will Pointer of the ball-gnome 13) placed above the said degree and the globe with that turned until the rod [of the ball Gnome] no Shadow casts more.

If this is the case, the [globe] ecliptic corresponds to the [sky] ecliptic as well as the degree concerned then the state of the sun of the [true] Sun, the Arcturus 14) [the celestial globe] the [true] Arcturus, the Goat [the celestial globe] the goat [in the constellation of Fuhrmanns] and accordingly the individual stars of the globe fenden stars in the sky, - how ever [in this case] the whole [Heaven] Globe matches the whole sky.

The index [horarius = hour hand] 12) shows the [day | Night] hours at. And if the sun [the model of the sun] to the touch with the Horizon is turned to the east, one gets the Sun's rise recognize this day [the azimuth of the rising sun], d. H. at what time Degree of the starting point on the horizon [ring] from the eastern intersection the horizon with the equator [where the equator, so to speak rises: the eastern point] deviates - as well as the relevant direction [after North: early, south: post-sunrise]. The index marks while the time of sunrise; and so can the length of the day. In the same way - if the [model] sun [the degree of the ecliptic, in which the sun stands] until the contact with the Horizon [ring] is turned to the west - can the evening range of the sun, the hour of doom is determined as the length of the day. [2]

2: The use of the globe with regard to the stars

The ecliptic can also be adjusted using the stars as follows: (a) Choose any star - of course on the celestial globe like in the sky itself is the same; (b) measure its height above the horizon by means of a quadrant, an astrolabe or an astronomical ring and (c) observe in which direction it deviates from the meridian: against East or west. (d) Turn the star in this direction Globe using the height quadrant and thus the globe itself as long as the star and the height of the star [d. H. the point ('the height') on the height quadrant] - the quadrant (Astrolab or Ring) - exactly coincident. Then also the Hour hand - considering the position of the sun - the sidereal time Show. Accordingly, then take the individual stars their position in the sky, and then it will be easy with such a thing established celestial globe to find all [other] stars. [3]

3: To the knowledge [of the position] of all stars get, although no Star is given

If one considers it necessary - although no [single] star is given [see. II.2, p. 111] - to get to know [the position] of all stars, the hour hand should be set [as follows] to the level of the sun After the time has been determined by using any clock is, turn the celestial globe until the hour hand is the same Hour indicates. After then horizon and meridian [meaning the relevant rings] and also the other circumstances [of the globe] their [cosmic] counterparts are set correctly, the Celestial globe sufficiently accurately correspond to the sky.

4 The use of the height quadrant

But now, as soon as the globe - be it with the help of the sun, be it with help of a star, as described above - anywhere on the Heaven-oriented, one becomes from any star or from the sun in Experience how far they rise above the horizon. Of the You will also be able to see the sun, how far below the horizon stands.

This is determined by the height quadrant, placing it on the star or adjust to the level of the sun - stand it above the horizon or (in the opposite case) under the horizon. The ones on the quadrant marked degrees will show how far the star or the Sun above or this in turn is below the horizon. Then the quadrant will also have the azimuth on the horizon as well Area [in the east, west] in which the star or the Sun stands at this time.

5 About the dwell time of the stars over the horizon

If you want to know in how many hours any star will be Run above the horizon from its rising to its sinking This will be indicated by the hour hand [index horarius] as follows. If the [relevant] star [on the celestial globe] first on the touch is set in the east, so the index shows the hour and also the width of his rising. Will you then the same star [up the celestial globe] on its contact with the horizon in the west set, the index will be both the hour and the width of the Sinking, but also the time passed by the index [span] show, - and that is just the dwell time of the star over the Horizon. [4]

6: How to find the midday line

Adjust the pole height according to the latitude of the location. In the morning, set the position of the sun by means of the gnomon in the one The area going from south to east; is it afternoon, so in the area that lies to the west. If the stand of the globe is set up [with the help of the solder], turn it Globe back and forth until the shadow of the gnome falls on the globe, and Although equidistant above the horizon with respect to the position of the vertical circuit.

Then you turn the stand - without taking the globe under the meri- dian move - until the gnomon casts no shadow any more. Once this happens, it is certain that the meridian [ring] is the true one [Place] meridian equals.

In the same way, the meridian of a high astrono- mix ring the true meridian, as soon as the one [with a hole provided] visor plate of the inner ring - on the state concerned set the sun - the sunbeam through the hole of the exact dropping opposite visor plate. [5]

7 How to determine the latitude of an area

Horizon, meridian and pole should be correctly set up. As- then according to the state of the sun, in the ecliptic, the gnomon placed and brought to the meridian - if the sun in the south stands. Now turn the meridian [ring] within the horizon [d. H. for his perpendicular to the horizon] and raise or lower the pole until the gonomon no longer casts a shadow. The pole height, which is now shows, then in fact the latitude of the place. If the hour of [the day] is known, you can do it the following way determine the width [of a place] at any time: set the globe like this, that the hour hand, which indicates the state of the sun accordingly, on shows the current [hour] hour; and there - without the globe under to move the meridian [ring] and after you have the gnomon set up the sun - turn the meridian [ring] [around its axis perpendicular to the horizon] until the gnomon has no Shadow casts more. Then the pole height is according to the location [the Width] has been set.

8 How to find the ecliptic sign and the height of the sun

If the horizon, meridian and the rest are set correctly with Regarding the latitude and the corresponding season - as there are spring, summer, autumn and winter -, move the gnomon Up and down next to the meridian until he no longer casts a shadow - the Sun stands in the south - and the height [on the meridian] is marked where the gnomon touches the meridian. Now turn the globe: the part of the ecliptic quarter where the sun is at this time of year stands and during the passage [through the meridian] exactly this [marked] Degree touches marks the location of the sun that day.

9 How to measure the height of any star above the horizon measures

Adjust the hour hand and list the meridian [ring] exactly the star or the planet you want to measure Has. The meridian is now moved up and down as long as [quasi to Hourly circle 'converted'], until the highest point of the hour circle [the Himmelspol, which now works as a substitute zenith '] the seems to lean towards the targeted star. Then the meridian degrees, which lead from the equinox [ring] towards lying on the Antarctic pole to the touch with the horizon, the Height of the relevant star.

10 At what time of the year is any star around Midnight in the meridian

Place the star under the meridian and mark the degree of the ecliptic [using a marker index], which is at the same time below the meridian: If the sun then the this location opposite [on the ecliptic] (which you can easily find out with the help of the ephemeris board), then the star will be in the meridian or very close to Meridian.

11 At what hour does each star stand in the [place] meridian

The hour hand is set to the [declination] degree of the sun. Now turn the globe until the [relevant] star under the Meridian [ring] stands; the hour hand then displays the hour.

12 How to determine the size of dusk

The hour hand points to the [declination] degree of the sun. you Now bring the degree opposite this degree to the 18 ° mark of the height quadrant: Then the degree of the sun is 18 ° below the Horizon, where he is the beginning of the morning twilight and the Marked at the end of the evening twilight. Mark the hour the hour hand indicates. Then bring the marker index Exactly on the horizon and mark again the relevant hour: The The intermediate time swept by the hour hand then gives the length of the [respective] twilight

A Pamphlet to the emperor Charles V -- Part III

• The original latin text and a german texts may be found in may be found in volume 3, pp 99-333 of Ad Maiorem Gerardi Mercatoris Gloriam. This english translation is a slightly edited version of the Google translation

Declaratio insigniorum utilitatum quae sunt in globo terrestri : coelesti, et annulo astronomico ad invictissimum romanum imperatorem Carolum Quintum

A description of the most important applications of the terrestrial and celestial globes and the astronomical ring. For the most invincible Roman Emperor Charles V

Part III: The order of the rings of the annulus

Chapters:

1. How to find the character and the (equatorial) length, in where the sun is
2. How to find the pole height
3. How to determine the time of day
4. Likewise the night hour
5. About the length of the day, . . sunrise, . . . sunset
6. About the height of a star above the horizon
7. The use of graduation of vertical circuits
8. The use of vertically or horizontally mounted marks
9. How to find the size of dusk

The annulus first has two rings: the meridian on the one hand and the Horizon on the other hand. Above these two is the ring attached to the Represents vertical circles, and that turns in the cones of Zenit and Nadir. The zenith has a small ring attached to it. is hanging. In turn, there are two other rings in the first two rings. One is an equatorial hour angle ring. The other is a merit dian, firmly attached to the first meridian, but nevertheless movable in it is appropriate. He carries the world poles, which are [usually from the zenith] are offset out so that in the same way the equator by one Sliding certain angle over the horizon [in the first meridian] is moved.

Inside there is still a wide circle left over, which decorates the declinations of the Bears zodiac signs and the most significant stars, d. H. their distance from Equator.

Furthermore, there are movable reticles inside this ring, which for any declinations [dioptric = diametrical] are adjustable. On the movable [wide] ring are the degrees of the ecliptic as well such of the more significant stars according to their right ascension, so that [the position of the] stars and the degrees are reciprocal correspond.

I call "right ascension" any degree of ecliptic or of a star the degree of the equator, by pointing to it [degree or star] in the meridian [ascending vertically]. [6]

1 How to find the character and the (equatorial) length, in where the sun is

Search for the current day on the inner side of the equator. The degree recorded on the [upper] side of the equator is that in which the sun moves on this day. He also designates the same time Degree of that sign in the heavens, by the equatorial Character is displayed.

2 How to find the pole height 2. Bring that part of the wide ring on which the declensions [the sun in] the ecliptic, under the meridian, and point straight that wide ring a diopter on a position of the sun on this day.

When the sun is at noon, turn the moving [second, inner] meridian so back and forth - by changing the pole height -, until the sunbeam passes through the opposite opening. On this way, then the pole is set as it is the circumstances of the required location.

3 How to determine the time of day

Set the Pole and attach a Absehe on the current state of the sun. Turn this to the sun and move the wide ring back and forth until the sunbeam pierces the hole of the intersected [diametrically] opposite Absehe. Than then the line, which runs in the middle of the curved wide ring, the hour on the Show equator and the [second] meridian then represents the "true" Meridian.

4 Likewise the night hour

Use a descendant to set the declination of the star that you have want to use; the second Absehe one fastened [diametrically] opposite. Now turn the wide ring until the corresponding one Reticles have been set to the star. Then the line that is in the Center of the curved wide ring runs, on the equator the indicate the hour and the minute. Then look for this one line of the star in question the ring with the movable absehe is registered and that the rectal of the star in question indicates which one - such a line and at the same time give the number attributed to the declination of the star After reading this line on the hours and once found set their minutes (the hours are on one side of the broad ring), the current position of the sun, the one finds with the help of the other Absehe, which indicate correct hour.

5 About the length of the day, about the hour of the sunrise and the sunset as well as their size

Connect the present state of the sun [of the degree of the sun], on the outer side of the wide ring at the point of contact with the middle line, with the horizon from the east, and it becomes the middle line of the outer side the hour of sunrise on Show equator.

If one has the same position of the sun [the same degree of sun] with the Horizon from the west connects, you will see the hour of sunshine learn about downfall. From either - or both - you open up the length of the day. From the respective degree of the horizon If you open up the respective azimuth of the rise or fall.

6 About the height of a star above the horizon

Bring the World Pole to its zenith, one overseer, the other [diametrically opposite] below the horizon until you see the star through the sees through corresponding openings. The Absehe, over the Horizon is lying, the height is [the degree of height of the star] above the Displaying horizon on the wide ring.

7 The use of graduation of vertical circuits

If, according to Chapter 3, a sunbeam passes through the [diametrically] opposite reticles or if you go according to sentence 4 a star through the corresponding holes of the reticle sees, then one can the height of the sun or the height of the concerned Stern's above the horizon and the direction he's taken from us viewed: to the east, to the west). In fact using the top ring as follows: Bring the sight line - course on the graduated page - on the current position of the sun [solar degree], which is in the middle of the curved wide ring is marked, or on the there likewise marked Declination. The degree that depends on the declination of the sun or the star the height in question [the sun, the star] is above the horizon - exactly how the cut of this ring with the horizon will show where he is leaning from our point of view.

8 The use of vertically or horizontally mounted marks

But to know when the vertical circle of the sun or star declination is well approximated, as well, which height with the degree of the sun or the star declination, you have the vertical index the Approximate the index of the vertical circle so that the line of sight of the index (the nige, which touches the vertical circle) on the degree of sun or the star declination points;

in the same way - if, according to Chapter 4, the degree of the sun approaches the horizon - one must approach the horizontal index so the horizon that the Sight line, when it touches the horizon, coincides with the degree of falls.

9 How to find the size of dusk

Set the present (current) degree of sunshine, which one on the Center of the back of the wide ring finds, at 18 ° below the horizon A, then the line is in the middle of the back of the wide circle the beginning of the morning twilight or the end of the evening show, depending on the degree of sun to the east or west is aligned. Then, according to chapter 5, search for the hour of sunrise. or sunset. The time in between then becomes the duration of dusk be. The degree of sunshine is determined by means of the vertical circle to 18 °, by directing the sighting line to the 18th degree of the vertical circle and turn the wide circle either way until the line of sight with the degree of Sun coincides.

His Holiness's Majesty most humble servant Gerhard Mercator - native of Rupelmonde

Mercator to Perrenot, 23 February 1546

From (out of copyright) Terrestrial Magnetism, vol48, 1943, pages 200–203. With an introduction by H. D. Harradon

SOME EARLY CONTRIBUTIONS TO THE HISTORY OF GEOMAGNETISM-VI

By H. D. Harradon

Gerardus Mercator (Latinized for Gerhard Kremer) was a Flemish mathematician and geographer, born at Rupelmonde in Flanders, March 5, 1512. He studied at Herzogenbosch and Louvain. In the latter place he established in 1554 his Geographic Institute from which was issued in 1537 the first of the important list of maps and globes which brought him fame. In 1552 he moved to Duisberg where in 1568 he published his first map (Nova et aucta orbis terrae descriptio ad usum navigantium accommodata) with meridians and parallels at right angles -the so-called "Mercator's projection." This projection was later improved by Edward Wright and came into general use in the first half of the seventeenth century. Mercator died at Duisberg, December 5, 1594.

In the letter to the Bishop of Arras, a translation of which is printed below, we find for the first time the view expressed and substantiated that the Earth has a magnetic pole. Before this time, it was generally believed that the magnetic needle pointed towards the pole of the heavens or towards the Polar Star. Thus Petrus Peregrinus stated in his Epistola (Part I, Chapter X) "From the poles of the heavens the poles of the Earth receive their Virtue."

Mercator's interest in terrestrial magnetism is shown in the following statement by Hellmann: "Since later Mercator repeatedly expressed his ideas regarding the Earth's magnetic pole, his studies in this connection did not remain without influence on the further development of geomagnetism, as, for example, in the case of Georg Hartmann. In an explanatory document for the various globes which Mercator constructed for Charles the Fifth (1552) he devoted the first four chapters to questions like the following: The existence and position of a magnetic pole; investigation of the latitude and longitude of the magnetic pole; determination of longitude with the magnet; finding the magnetic declination at any place on the Globe-and on his world-chart he drew zero-meridians through the magnetic pole. That Mercator laid great weight on de­termining the position of this pole is shown by his fine picture, which was executed at the instance of his friend F. Hogenberg of Cologne in which, with a pair of compasses, he fixes the position of the magnetic pole on the globe.

A word may be added in explanation of the remarkable position obtained by Mercator for the North Magnetic Pole. He assumed that the prolongation of the axes of the declination-needles at various points on the Earth's surface would intersect at the magnetic pole. Thus observations of the declination at two points on the Earth would suffice for determining the pole's position. Therefore, assuming that the direction of the compass-needle followed a great circle, he utilized the two stations at his disposal, namely, the Dutch island of Walcheren (9° east) and Danzig (14° east) and found the desired position at longitude 168° west and latitude 79° north--the degrees of longitude being counted from the meridian of the Azores. This point would lie somewhat to the northwest of Bering Strait and in no wise corresponds to the accepted position of the North Magnetic Pole.

GERHARD _MERCATOR OF RUPELMONDE TO ANTONIUS PERRENOTUS, MOST VENERABLE BISHOP OF ARRAS, A. D. 1546

Thenever I examined nautical charts, most reverend Bishop, I had to wonder, how it could be that ship-courses, when the distances of the places were exactly measured, at times show their difference of latitude greater than it really is, and at other times on the contrary, smaller, and again frequently hit upon a correct difference of latitude ior the places in question. Since this matter caused me anxiety for a long time, because I saw that all nautical charts, by which I was hoping especially to correct geographical errors, would not serve the purpose, I began to investigate carefully the cause of their errors, and found them chiefly to rest on an ignorance of the nature of the magnet.

For the magnet-needle does not always point towards the same point everywhere as shipmasters believe, and Hydrographers pretend, but changes its direction with change of latitude or longitude, for which reason it happens that a given course, for example, which runs east and west now gradually turns more and more towards the south, and so makes the shore-lines appreciably more to the north than they should be, as may be seen along the coast of Africa from the Strait of Gibraltar as far as Carthage, now deviates towards the north and shifts the shore-line . by that much more towards the south as is observed by those sailing in the opposite direction from Carthage to Cadiz.

Hydrographers, therefore, should pay more attention to the laws of nautical science, when they delineate coast-lines on the basis of data of ships' courses, otherwise they will not in any way give satisfaction either to themselves or to geographers. In what place, therefore, that point lies, which the magnet so greatly seeks, I shall explain, in general, as far as is now possible, to your Reverence. In the first place, it has been found by experience that at one and the same place, the magnetic needle declines from the true north by the same amount. The point, therefore, can certainly not be in the heavens, because, since every point in the heavens, except the poles, is subject to a rotational motion, the needle, owing to the diurnal rotation of such a point in the heavens, would necessarily wander now this way now that, and hence decline al­ternately to the east and to the west, which is contrary to experience. On the Earth, therefore, which remains fixed, this point is to be sought. Although the exact difference in longitude between the Zeeland Island of Walcheren and Danzig is known and the intervening coasts have been very accurately depicted from information supplied by mariners, I find Danzig to be indicated further to the north by almost 1° than its true position whence I conclude that the magnetic declination at Danzig is 5° greater from the true north than in Walcheren. At places near Walcheren, I learned that the needle declines 9° to the east from the true north. Hence the magnetic declination is 14° at Danzig. If now, through both places, greatest circles are drawn making an angle with the meridian equal to the observed declination, then it will be found that the point of intersection of these circles will be at about 168° longitude and 79° latitude, and that at this place the magnetic pole must be. Now when­ ever the needle is in this meridian it will point due north, but if (in the region of Europe) one continues to sail from it toward the east, it will decline more and more towards the east from the true north, the more the higher latitude, until a quadrant of longitude has been traversed. From that point the declination will diminish in equal degree until the meridian of 168° longitude is attained, whence the needle begins to turn in the opposite direction towards the west until another quadrant of longitude has been passed over. The remaining longitude brings the different directions of the meridian and needle into agreement. However, that this concept of mine corresponds nearly with reality is attested by the map of Canada which I showed your Reverence, for thereon the Hydrographer, whoever he was, had depicted Canada on the basis of voyages made thither, laying out degrees of latitude near Europe, as they really are, and found it necessary to use another latitude-scale for Canada because the declina- tion of the needle from north to west made, on the basis of experience, the latitudes of the places greater; hence he was obliged to displace the numbers of the latitude-degrees farther to the north. Somewhere, there- fore, between Canada and Europe, there must exist a meridian common to the world pole and the magnetic pole. And that this (meridian) and the magnetic pole must lie approximately where I said, I could show, considering the longitude of Canada, from the difference of the latitudes attributed to Canada and Europe, if a period of time commensurate with the importance of the matter were at my disposal.

But since there are many other and indeed difficult points to be dis- cussed for the improvement of navigation and of marine charts, it will be enough, I hope, for your Reverence, that I have indicated the funda- mentals of that investigation of the magnetic pole. But if at some future time, I shall be free from pressing matters, I have decided to pursue this subject in a suitable manner and solve it. In the meantime, I desire to commend myself to your Reverence and to express my wish for good health and happiness.

Louvain, February 23, 1546.

Always most devoted to your Reverence.