An Attempt to determine the mean height of Continents.

By Baron Von Humboldt.

At the meeting of the Berlin Academy of Sciences, on 18th July 1842, a memoir by M. de Humboldt was read, of which we think it necessary to give a somewhat lengthened account.

It is entitled "An attempt at determining the mean height of Continents."

"Among the numerical elements on which the progress of physical geography appears more particularly to depend, there is one which no attempt has been hitherto made to determine.

The notion which seemed to prevail, that it was impossible to come to such a determination, has perhaps been the principal cause of the subject being neglected.

However, the extension of our orographical knowledge, as well as the greater accuracy of the maps which represent large portions of country, determined me, says M. de Humboldt, to undertake, some years ago, a work of great labour, and in appearance barren in results, the object of which is the knowledge of the mean height of continents, and the determination of the mean height of the centre of gravity of their volume.

In such a case as this, as with many others, such as the dimensions of the globe, the probable distance of the fixed stars, the mean temperature of the poles of the earth, the thickness of the atmospheric stratum above the level of the sea, or the enumeration of the general population of the globe, we arrive at limited numbers, between which the results must fall.

In like manner, it is by the perfect knowledge of the geometrical and hypsometrical surface of a country, of France, for example, that we may thus be led, by analogy, to extend the conclusions to a great part of Europe and America, and are enabled to establish numerical data, which have recently been completed in a very satisfactory manner in regard to central and western Asia.

"It was likewise necessary to collect, with the greatest care, astronomical determinations of the height of places, in order to establish, to about 300 or 400 metres of absolute height, the limits between the acclivities of the mountains and the edges of the valleys.

I long since demonstrated the possibility of such a determination of limits, and, from the comparison which depends on it, I have deduced the extent of the surface of the plains, and the horizontal and flat portions of mountains, in my geognostical researches on South America; a portion of the globe in regard to which the length of the immense wall which forms the Cordillera of the Andes, and of the elevated masses of Parima and Brazil, was so incorrectly limited and circumscribed on all maps.

In fact, there is a general tendency in all graphic representations to give the mountains a greater degree of breadth than they really possess, and even in the flat portions to confound plateaux of various kinds with each other."

M. de Humboldt published, in 1825, two memoirs inserted in the Memoires de l'Academie des Sciences of Paris, on the mean height of continents, and an estimate of the volume of the elevated ridges of mountains, compared with the extent of the surface of the lower regions.

An assertion of Laplace in the Mecanique Celeste (vol. v., book xi. chap. i. page 13), gave rise to these researches.

This great geometer had established in principle, that the agreement observed between the results of experiments made with the pendulum and the compression of the earth, deduced as well from the trigonometrical measurement of the degrees of the meridian as from the inequality of the moon, furnished a proof "that the surface of the terrestrial spheroid would be nearly that of equilibrium, if that surface became fluid.

Hence, and from the consideration that the sea leaves vast continents uncovered, we conclude that it cannot be of great depth, and that its mean depth is of the same order as the mean height of the continents and islands above its level, a height which does not exceed 1000 metres" (or 3073 Parisian feet, that is to say, only 463 feet less than the summit of the Brocken, according to M. Gauss, or a little more than the most elevated mountains of Thuringia).

Laplace further adds, "This height is, then, a small fraction of the excess of the radius of the equator over that of the pole, an excess which exceeds 20,000 metres. Just as high mountains cover some parts of continents, so there may be great cavities in the bed of the sea; but it is natural to suppose that their depth is less than the elevation of high mountains, as the deposits from the waves, and the remains of marine animals, must have tended, in the lapse of time, to fill up these great cavities."

Considering the profound and extensive knowledge which the author of the Mecanique Celeste possessed in the highest degree, an assertion of this nature was the more striking, as he could not be ignorant that the most elevated plateau of France, that from which the extinct volcanoes of Auvergne have risen, does not rise, according to Ramond, to more than 1044 feet, and that the great Iberian plateau is not, according to my own measurements, more than 2100 feet above the level of the sea.

Laplace has therefore fixed the upper limit at 1000 metres, merely because he has considered the extent and the mass of the elevations of mountains to be much greater than they really are, inasmuch as he has confounded the height of the insulated peaks or culminating points with the mean height of the mountain ridges; he has admitted much too low a number for the depth of seas, because, in his time, data could not be found on the subject, and he has thence inferred the proportion of the extent of the surface (in square miles) in regard to all continents, to the extent of the projection of the surfaces covered by mountains.

A very exact calculation has shewn that the mass of the chain of the Andes, in South America, from where it leaves the whole portion of the eastern plains of the pampas and forests, regions whose surface is one-third larger than that of Europe, does not rise above 486 feet. M. de Humboldt hence concludes, "That the mean height of continental lands depends much less on those chains or longitudinal ridges of little breadth which traverse continents, and on their culminating points or domes, which attract common observation, than on the general configuration of the different orders of plateaux and their ascending series, and on those gently undulating plains with alternating slopes, which have an influence, by their mass and extent, on the position of a mean surface, that is to say, on the height of a plain placed in such a manner that the sum of its positive ordinates shall be equal to the sum of its negative ordinates."

The comparison which Laplace has instituted in the passage quoted from the Mecanique Celeste between the depth of the sea and the height of continents, recalls a passage of Plutarch, in the 15th chapter of his Life of AEmilius Paulus (ed. Reiskii, vol. ii. page 276),--a passage the more remarkable, as it makes us acquainted with an opinion which generally prevailed among the philosophers of the Alexandrian school.

After quoting an inscription found on Mount Olympus, and giving the result of the measurement of its height by Xenagoras, Plutarch adds, "But geometricians (probably those of Alexandria) believe that there is no mountain higher, and no sea deeper, than ten stadia."

We can entertain no doubt about the exactness of the measurement made by Xenagoras; but it is striking to observe, that the philosophers of this school established in the structure of the earth a perfect equality between the heights or positive and negative ordinates.

Here the maximum of the heights and depths is alone taken into account, and not the mean height,--a consideration which rarely presented itself to the mind of the ancient philosophers, and which, for variable magnitudes, was applied in a useful manner to astronomy by the Arabs.

Even in the Metereologius of Cleomedes (i. 10), we meet with an assertion similar to that of Plutarch; while in the Meteorologicis of the philosopher of Stagira (Arist. Met. ii. 2), the only point considered is the influence of the inclination of the bottom of the sea, from east to west, on its currents.

When we try to determine the mean height of the elevation of continents above the present level of the seas, it means that the object is to find the centre of gravity of the volume of these continents above that level,--an investigation very different from that which consists in searching for the centre of gravity of the volume of the continental mass, or the centre of gravity of the masses, seeing that the portion which rises above the sea, in the crust of the globe, is by no means of the same density, as has been demonstrated both by geognosy and experiments with the pendulum.

The mode of simple calculation is as follows:--Each chain of mountains is considered as a triangular prism placed horizontally.

The mean height of the defiles or passes, which determine the mean height of the crest of the mountains, is the height of the ridge of the prism vertically above the surface, which constitutes the base of the chain.

The plateaux are calculated as straight prisms, in order to establish their solidity.

For the purpose of giving an example, taken from Europe, of this kind of calculation, M. de Humboldt states, that the surface of France contains 10,087 square geographical miles.

According to M. Charpentier, the Pyrenees cover 430 of these square miles; and, although the mean height of the summits of the Pyrenees rises to 7500 feet, M. de Humboldt makes a reduction upon it, on account of the erosions produced on the prism supposed to be lying horizontally, and which have tended specially to diminish the size of the deep transverse valleys.

The effect of the Pyrenees on the whole of France is not more than 35 metres or 108 feet; that is to say, it is to that extent that the normal surface of the entire plain of France would be increased, and the elevation of that surface by the comparison of a great number of very accurate measurements at places towards the centre (such as Bourges, Chartres, Nevers, Tours, &c.) has been found to be 480 feet.

This calculation, which M. de Humboldt has made along with M. Elie de Beaumont, furnishes the following general result, in measures thus given by the author:--

Toises.

1. Effect of the Pyrenees, 18 2. The French Alps, the Jura, and the Vosges, a few toises more than the Pyrenees; common effect, 20 3. The plateaux of Limousin, Auvergne, the Cevennes, Aveyron, Forez, Morvant, Cote d'Or; common effect, nearly equal to that of the Pyrenees, 18 Now, as the normal height of the plain of France is at its maximum about 80 It follows that the mean height of France does not exceed 136 toises, or 816 feet.

The Baltic, Sarmatian, and Russian plains are separated from those of the north of Asia only by the meridian chain of the Oural.

It is for this reason that Herodotus, who was acquainted with the connection of the southern extremity of the Oural in the country of the Issidones, called the whole of Europe to the north of the Altai Mountains, Asia.

In the neighbouring region of the Baltic plains, near the shores of the Baltic Sea, there are partial elevated masses which deserve particular attention.

To the west of Dantzic, between that town and Butow, at the point where the shore of the sea advances much to the north, there are many villages situated at a height of 400 feet; the Thurmberg, moreover, the measurement of which has given rise to many hypsometrical controversies, rises, according to the trigonometrical observations of Major Baeyer, to 1024 feet, which is perhaps the greatest elevation to be found between the Harz and Oural.

It is surprising that, according to the measurements made by M.

Struve of the culminating point of Livonia, the Munamaggi, this mountain rises only 4 toises higher than the Thurmberg of Pomerania; while, on the other hand, according to Captain Albrecht's chart, the greatest depth of the Baltic Sea, between Gothland and Windau, is not more than 167 toises, a measurement almost identical with that of the Thurmberg.

The flat countries exclusively European, the normal height of which cannot be estimated at more than 60 toises, occupy, according to exact measurements, a surface nine times that of France.

The extraordinary extent of this low region is the cause of the mean continental height of all Europe, over an extent of 17,000 square geographical miles, being 30 toises below the result we have found for France.

As to the rest, not to occupy more time with numbers, M. de Humboldt adds, that an important consideration in the study of the general phenomena of geology is, that the elevated masses, over extensive countries, in the form of plateaux, produce an entirely different effect on the elevation of the centre of gravity of the volume from that of chains of mountains, when they have the same importance in breadth and in height.

While the Pyrenees produce scarcely the effect of a single toise on the whole of Europe, the system of the Alps, which cover a surface almost quadruple that of the Pyrenees, has the effect of 3 [Formel] toises; the Iberian peninsula, with its compact massive plateau of 300 toises, produces the effect of 12 toises.

The plateau just named, therefore, has an effect on the whole of Europe four times more considerable than the system of the Alps.

This result of calculations is the more satisfactory as it appears to be deduced without reference to any previous hypothesis.

We have recently acquired many new ideas respecting the configuration of Asia.

The effect of the elevated colossal masses of the southern portion is found to be weakened, since one-third of the whole continent of Asia, a portion of Siberia, which alone exceeds by a third the entire surface of Europe, does not reach a normal height of 40 toises.

This is, likewise, the height of Orenbourg, on the northern shore of the Caspian Sea.

Tobolsk does not attain the half of this height, and Casan, which is five times more distant from the shore of the Icy Sea than Berlin is from the Baltic, is scarcely half the height of the last mentioned city.

In Upper Irtysch, between Buktormensy and Lake Saysan, at a point nearer the Indian than the Icy Ocean, M. de Humboldt has found that the plains only reached a height of about 800 feet; this, however, has been called the plateau of Central Asia, and is not half the height of the streets of the city of Munich above the sea-level.

The celebrated plateau between Lake Baikal and the Wall of China (the stony desert of Gobi and Cha-mo), which the Russian academicians, MM.

Bunge and Fuss, have measured with the barometer, has a mean height of only 660 toises, which is nearly the same as that of the Müggelsberg at the summit of the Brocken.

There is, moreover, in the centre of this plateau, at the point where Ergi is situated (lat. 45°31') a cauldron-shaped depression, the bottom of which descends to 400 toises, that is to say, the height of Madrid.

"This depression," says M. Bunge, in a memoir not yet published, is covered with Halophytes and species of the genus Arundo, and, according to the tradition of the Mongolians who accompanied us, it was formerly a great inland sea."

The two extremities of this ancient inland sea are bounded by steep rocks, just like an ordinary sea, in the neighbourhood of Olonbaischan and Zukeldakan.

The surface of Gobi, in its masses of uniform elevation, and from the south-west to north-west, is twice as large as that of all Germany, and will raise the centre of gravity of Asia 20 toises; while the Himalaya and the Houen-lun, which is a prolongation of the Hindoo-Kho, with the plateaux of Thibet, which connect the Himalaya with the Kouen-lun, will only produce an effect of 56 toises.

In the examination of the considerable relief between the plains of the Indus and the depressed plateau of Tarim, which, on leaving Kaschgar, inclines to the east towards Lake Lop, it is necessary to examine with more care the point near the meridian of Kaylasa, and the two sacred lakes of Manasa and Ravana-Brada, on leaving which the Himalaya no longer runs from east to west parallel with the Kouen-lun, but takes the direction from south-east to north-west, and reunites at the projecting ridges of Tsun-ling.

The altitudes of the numerous passes of Bamian, as far as the meridian of Tschamalari (24,400 feet), by which Turner reached the Thibetian plateau of H'Lassa, are likewise known for an extent of 21° of longitude.

The greater part of them present a very uniform height of 14,000 English feet, or 2200 toises, a height which is not of rare occurrence in the passes of the chain of the Andes.

The great route which M. de Humboldt followed from Quito, on his way to Cuenca, was, for example, at Assuay (Ladera de Cadlud), and without snow, of the height of 2428 toises, that is to say, 1400 feet higher than this pass of the Himalaya.

The passes, as has been stated, give the mean height of mountains.

In a memoir on the relations between elevated summits or culminating points, and the height of mountain chains, M. de Humboldt has demonstrated that the chain of the Pyrenees, calculated from twenty-three passes, was 50 toises higher than the mean chain of the Alps, although the culminating points of the Pyrenees and the Alps were in the proportion of 1 to 1 [Formel] .

As the insulated passes of the Himalaya, for example, the Niti-Gate, by which we penetrate into the plain of the Cashmere goats, rise to the height of 2629 toises, M. de Humboldt has not admitted for the height of the Himalayan chain 14,000 English feet, but he proposes to fix it, although perhaps the elevation may be still too considerable, at 15,500 feet, or 2432 toises.

The plateau of the three Thibets of Iscardo, Ladak, and H'Lassa, is a prominence between two chains which unite with each other (the Himalaya and the Kouen-Lun).

Mr Vigne's travels in Baltistan, which have just appeared, the journal of the brothers Gerard, published by Lloyd, as well as the recent investigations undertaken in India respecting the relative height of perpetual snow on the Indian and Thibetian declivities of the Himalaya, have demonstrated that the mean height of the Thibetian plateaux has hitherto been greatly exaggerated.

In his work entitled "Central Asia," of which only a few pages of the third volume have been yet printed, and which will be accompanied by a hypsometrical map of Asia from the Phasis, as far as the gulf of Petcheli, and from the common embouchures of the Ob and the Irtysch to the parallel of Delhi, M. de Humboldt thinks that he has demonstrated, by bringing together a multitude of facts, that the prominence between the Himalaya and the Kouen-Lun (chains which form the southern and northern limits of Thibet), does not rise above the mean height of 1800 toises, and that it is, consequently, 200 toises lower than the plateau of Lake Titicaca.

The hypsometrical configuration of the Asiatic continent is perhaps still more remarkable for its plains and depressions, than for its colossal heights.

This continent is distinguished by two principal characteristic features; 1st, by the long series of meridian chains, which, with parallel axes, but alternating with each other (having perhaps been projected comme des filons) extend from Lake Comorin, opposite Ceylon, to the shores of the Icy Sea, in a uniform direction from south-south-east to north-north-west, under the name of Ghates, the Soliman chain, Paralasa, Bolor, and Oural.

This alternating situation of auriferous meridian chains (Vigne has recently visited, on the eastern declivity of Bolos, in the valley of Basha, in Baltistan, the auriferous sands mined, according to the Thibetians, by marmots, and, according to Herodotus, by large ants) reveals to us this law, that none of the meridian chains just named, between 64° and 75° of longitude, extend themselves upon the adjoining ones, either towards the east or the west, and that each of these longitudinal elevations does not begin to shew its extent, until a point is reached where the preceding has completely disappeared.

2d, Another characteristic trait in the configuration of Asia, and which has not been sufficiently observed, is the continuity of a considerable elevation, east and west, between 35° and 36 [Formel] ° of latitude, from Takhialoudag, in ancient Lycia, as far as the Chinese province of Houpih, an elevation thrice intersected by meridian chains (Zagros, in Western Persia, Bolos, in Affghanistan, and the chain of Assam, in the valley of Dzangho) from the west to the east of this chain, from the parallel of Dicearchus, which is at the same time that of Rhodes, Taurus, Elbrouz, Hindou- Kho, and Kouen-Lun or A-Neoutha.

In the third book of the geography of Eratosthenes, we find the first germ of the notion of a chain of mountains (Strabo, xv. p. 689, Cas.) running in a continuous manner, and dividing Asia into two parts.

Dicearchus perceived the connection between the Taurus of Asia Minor and the snow-covered mountains of Asia, which had acquired so much celebrity among the Greeks by the false accounts of those who had accompanied the Macedonians.

Importance was assigned to the parallel of Rhodes, and to the direction of this endless chain of mountains.

The chlamyde of Asia ought to be found further on under this parallel (Strabo, xi. p. 519), and perhaps, says Strabo, a little more to the east there may be another continent.

The Taurus and the plateaux of Asia Minor disclosed for the first time to the Greek philosophers the influence of height on temperature.

"Even in the southern latitudes," says the great geographer of Amasis, (Strabo, ii. p. 73) when the climate of the northern coasts of Cappadocia is compared with that of the plains of Argaios, situated 3000 stadia further south, the mountains and all the elevated lands are cold, even when these lands consist of plains."

Strabo is the only one among Greek authors who has made use of the word oropedia or mountain plain.

According to the final result of the whole of M. de Humboldt's investigations, the maximum assigned by Laplace for the mean height of continents is too considerable by two-thirds.

He found the following numerical elements for the three quarters of the world which have been the object of his calculations (Africa not yet presenting a sufficient number of data to be included).

Europe, 105 toises (205 metres).

North America, 117 ... (228 ...).

South America, 177 ... (345 ...).

Asia, 180 ... (351 ...).

For the whole of the new continent we have 146 toises (285 metres), and for the height of the centre of gravity of the volume of all the continental masses (Africa excepted) above the level of the present seas, 157.8 toises or 307 metres.

Von Hoff, who has measured with extreme accuracy 1076 different points, the greater part of them in the mountainous portion of Thuringia, over an extent of 224 square geographical miles, estimates that there are about five heights for each square mile, but that these heights are unequally scattered. M. de Humboldt has asked Von Hoff, always for the purpose of verifying Laplace's hypothesis respecting the mass of continents, to calculate the mean height of the hypsometrical measurements which he has made.

This philosopher has found it to be 166 toises, that is to say, 8 toises more than the result at which M. de Humboldt had arrived.

We ought thence to conclude, that, since a very mountainous country of Thuringia was measured, the number, 157 toises, or 942 feet, is a limit rather too high than too low.

In the certainty in which we now are respecting the progressive and partial rising of Sweden (one of the most important facts in physical geography, for a knowledge of which we are indebted to M. de Buch), we may suppose that the centre of gravity will not always continue the same.

At the same time, considering the smallness of the masses which are raised and the weakness of the subterranean forces in action, it may be presumed, regarding such variations, that they will in a great measure compensate each other, and that the position of the centre of gravity above the ocean will not be much changed; but a new circumstance, which appears to result from the numerical calculations of this hypsometrical labour, is, that the smallest heights in our hemisphere belong to the continental masses of the north.

Thus Europe has furnished 105 toises, North America 117 toises.

The prominent character of Asia between 28° and 40° of latitude compensates the subtractive effect of the lower portions of Siberia.

Asia and South America give 180 and 177 toises.

We thus read, so to speak, in these numbers, in what portions of the surface of our globe vulcanism, that is to say, the reaction of the interior on the exterior, has been felt with greatest intensity in the ancient soulevements. (L'Institut, 5th Jan. 1843 p. 4.)