(see Encycl.) are, by some, distinguished into various orders. The asymptote is said to be of the first order, when it coincides with the base of the curvilinear figure; of the second order, when it is a right line parallel to the base; of the third order, when it is a right line oblique to the base; of the fourth order, when it is the common parabola, having its axis... axis perpendicular to the base; and, in general, of the \( n + 2 \) order, when it is a parabola whose ordinate is always as the \( n \) power of the base. The asymptote is oblique to the base, when the ratio of the first fluxion of the ordinate to the fluxion of the base approaches to an assignable ratio, as its limit; but it is parallel to the base, or coincides with it, when this limit is not assignable.

**ATTAR OF ROSES.** See Roses, Otter of, both in the Encyclopedia and in this Supplement.

**AVANT-FOSS,** or Ditch of the Counterfarp, in fortification, is a wet ditch surrounding the counterfarp on the outer side, next to the country, at the foot of the glacis. It would not be proper to have such a ditch if it could be laid dry, as it would then serve as a lodgment for the enemy.

**AUBIGNE.** See Stuart in this Supplement.

**AUMIL,** in Bengal, a native collector or manager of a district on the part of government.

**AUTENIQUA,** a large and beautiful country in Africa, lying to the east of the Cape of Good Hope, and inhabited, part of it, by Dutch colonists. The word Auteniqua signifies, in the Hottentot language, "a man loaded with honey;" a name which is not improperly given to the country, since, as you enter it from the Cape, you cannot proceed a step without seeing a thousand swarms of bees. The flowers on which they feed spring up in myriads; and your attention is engaged, and your course suspended, by the mixed colours which exhale from them, by their colours and variety, and by the pure cool air which you breathe. Nature has made these enchanting regions like fairy land. The calyxes of all the flowers abound with excellent juices, from which the bees extract the honey that they everywhere deposit in hollow rocks and trees.

This country was visited in 1782 by M. Vaillant, who calls it the most delightful region in the universe; and says, that, as he approached it, he beheld, from the top of a very high mountain, an immense valley, adorned with agreeable hills, variegated in an infinite number of shapes, and extending in an undulating manner as far as the sea; while enamelled meads, and the most beautiful pastures, fill added to the magnificent scene. It abounds with small rivulets, which, flowing down from the mountains, run into the sea through a hundred different channels. The water of these rivulets has the colour of Madeira wine, and a ferruginous taste; but our traveller did not examine whether this taste and colour proceed from their flowing through some mine in their passage, or from the roots and leaves of trees which they carry along with them.

The whole of Auteniqua, from the chain of mountains which divides it from the country of that race of Hottentots called Gonaquas to the sea, is inhabited by several planters, who rear a number of cattle, make butter, cut down timber, and collect honey; all of which they transport to the Cape; but it appears that they make not the most of their situation. "Can it be believed (says M. Vaillant), that the directors of the Company, for their own use, should order ships to be sent every year from Amsterdam, loaded with planks and boards of every kind, whilst in this country there are immense forests, and the most beautiful trees in the world? This absurdity, however, is not at all astonishing. The Company gratuitously furnishes the governor and all the officers with whatever wood they have Auteniqua occasion for; and it is delivered to them at their houses without any expense. The governor therefore has no personal interest to extend his views to this part of the administration, and to abolish an abuse so prejudicial to the colony."

But the colonists themselves must be a very indolent and stupid kind of people; since, if our traveller deserves credit, they neglect advantages with which the personal interest of the governor cannot possibly interfere. "I was filled with indignation (says M. Vaillant) to see people, who have wood within their reach, employ it in commerce, and not have the courage to build for themselves habitable houses. They live in wretched hovels, constructed of wicker-work, daubed over with clay; the skin of a buffalo, fixed at the four corners to as many stakes, serves them for a bed; and the door, which is at the same time a window, is shut by a mat; while two or three mutilated chairs, a few pieces of plank, a kind of table, and a pitiful box of two feet square, form all the furniture of these colonial habitations. Thus is the picture of the most profound misery contrasted with the charms of this terrestrial paradise; for the beauties of these regions extend even beyond Auteniqua. The people, however, though their hovels be bad, live well. They have game and salt water fish in abundance; and enjoy exclusively, over all the other cantons of these colonies, the advantage of having, for the whole year without interruption, vegetables of every kind in their gardens. For this they are indebted to the excellence of the soil, and to its being naturally watered by small streams, which cross each other in a thousand different directions, and, as one may say, lay the four seasons under contribution to fertilize Auteniqua. These streams, which frequently overflow their banks, but never dry up, proceed from a cause well known; the high mountains towards the east, which are covered with forests, stop the clouds and the fogs carried from the sea, and this occasions very abundant rains."

In these mountainous regions, which, as well as the plain, our author comprehends under the denomination of Auteniqua, there are multitudes of elephants, buffaloes, panthers, hyenas, and antelopes of every species and all these animals are hunted and killed by the natives, as well for food as for the protection of their flocks and herds from such as are beasts of prey. Our author has eaten the flesh of every one of them except the hyena; and declares, that the foot of an elephant, baked after the Hottentot manner, is one of the most delicious morsels that he ever tasted. He gives directions for hunting them all; but warns his readers from attacking elephants when he finds them in droves, for then, he says, they are invincible. He even thinks it exceedingly dangerous for one man, however well armed, to attack a single elephant in the plain. The buffalo he describes, contrary to most other travellers, as a timid animal, which never retails till his situation becomes desperate; and he thinks that there would be no difficulty in training him, if caught when a calf, to the yoke like the bullocks of Europe.

The kites and vultures of this country, our traveller represents as in the highest degree voracious and fierce, in such a manner that it is hardly possible to frighten them from their prey. He had on one occasion killed two buffaloes, which which he ordered to be cut into very small pieces, that they might be more easily salted, and exposed afterwards to the air and the sun. His waggon, as well as the bullocks and trees which surrounded him and his people, were loaded with the bloody fragments of these two animals, and they had begun their operation of salting; but on a sudden, while they were not expecting it, they found themselves attacked by flights of kites and vultures, which, without exhibiting the least symptoms of fear, perched in the midst of them. The kites were above all the most impudent. They seized upon the morsels of flesh, and even contended furiously with his people. "When they had each carried away (says he) a pretty large piece, they retired to some branch, at the distance of ten paces from us, and devoured it before our eyes. Though we fired our fusées they were not frightened, but returned incessantly to the charge; so that finding our powder wasted in vain, we resolved to keep them off with large poles until our provisions should be quite dry. This manoeuvre, which for a long time harassed my people, did not prevent us from being plundered without mercy; but had we not employed it, nothing would have remained to us of our two buffaloes."

This battle with the kites took place on the confines of the Dutch settlements; but when M. Vaillant had with difficulty passed over the mountains which bound them, the prospects became more magnificent, the soil seemed to be more fruitful and rich, nature appeared to be more majestic and grand, and the lofty mountains presented on all sides more charming and delightful points of view than any that he had ever before met with. These scenes, contrasted with the dry and parched fields of the Cape, made him exclaim, he says, in ecstacy, "What! shall these superb regions be eternally inhabited by tygers and lions? What speculator, with the fordid view only of establishing a kind of centre for commerce, could have preferred the flamy Table Bay to the numberless roads and commodious harbours which are to be found on the eastern coasts of Africa? Thus (continues he) was I reflecting within myself, whilst I was climbing the mountain, and forming vain wishes for the conquest of this beautiful country, which the indolent policy of the European nations will perhaps never gratify."

If his description of its beauties and fertility be not greatly exaggerated, it is indeed wonderful that either the Dutch or some other maritime power of Europe has not long ago taken possession of it. After he had passed the mountain, one could not, he says, choose a more agreeable or advantageous spot than that upon which he then was for establishing a thriving colony. The sea advances through an opening of about a thousand paces in breadth, and penetrates into the country to the distance of more than two leagues and a half. The basin which it forms is more than a league in extent (he does not say whether in breadth or in circumference); and the whole coast, both on the right and the left, is bordered with rocks, which intercept all communication with it. The land is watered by limpid and refreshing streams, which flow down on all sides from the eastern mountains; and these mountains, crowned with majestic woods, extending as far as the basin, and winding round it with a number of sinuosities, exhibit a hundred groves, which are naturally variegated, and each Auteniqua more agreeable than another.

The author proceeding forwards about two days journey, arrived at a bay known to navigators by the name of the Bay of Agua, but called by the colonists Blettenberg's Bay, from its having been visited some time before by a Governor Blettenberg, who ordered his name, together with the year and day of his arrival, to be engraven on a stone column. This bay is a little beyond the limits of the country called Auteniqua; but it is not foreign from the purpose of this article to insert in this place our traveller's account of it, and of the country around it.

The bay itself, he says, is very spacious, and has a sufficient depth of water for the largest vessels. The anchoring ground is fine, and boats can sail to a beautiful part of the shore, which is not confined by the rocks, as they are all there detached from one another. By advancing a league along the coast, the crews would arrive at the mouth of a considerable river called the Quem-Boom, where they would find water. Refreshments might be procured from the inhabitants of the environs; and the bay would supply them with excellent fish, with which it abounds.

This bay is one of those places where government might establish warehouses and repositories for timber; and it is for this reason that we have introduced it to notice in this article. The forests around it, says M. Vaillant, are everywhere magnificent, and the trees could be more easily cut down than anywhere else; for it is not so steep mountain that one must go for wood, as at Auteniqua; it is here ready at hand; and during the fine monsoon might be transported to the Cape with little trouble and no risk. The inexhaustible and fertile lands in the neighbourhood of the bay, if once cultivated, would produce abundant crops, and draw together a great number of intelligent planters, on account of the ready communication which they would have with the Cape. In a word, the Company, continues he, have nothing to do so much for their own interest as to form here a proper establishment. To the general profits of such an institution, would be added those of individuals, which could not fail to be of great importance. They might, for example, cut down a certain tree called flanking wood, and export it to Europe, where it would undoubtedly be soon preferred to mahogany and every other kind of wood employed by cabinet makers.

The Hottentots, who in scattered kraals inhabit this delightful country, our author describes as a faithful, gentle, and rather timid race. He affirms, that they have no religious impressions whatever, nor any notion of superior powers who govern the world. But this, if not a wilful falsehood dictated by the philosophy of France, is probably a mistake arising from his scanty knowledge of their language, and total ignorance of the meaning of their religious ceremonies. His great matter, as well as the matter of his sect, Lucretia, might have taught him, that fear, if not a better principle, will generate the notion of superior beings in the minds of savages; and from fear, by his own account, the inhabitants of Auteniqua are far from being free. He likewise affirms, and seems to consider it as much to their credit, that this race of gentle beings, so far from being a prey to the passion of jealousy (as other travelers have represented the Hottentots in general), are so obliging, as to lend their wives to travellers who visit them, and that they actually accommodated his Hottentots in this way. Auteniqua, as laid down in M. Vaillant's map, lies between $33^\circ 30'$ and $34^\circ 50'$ of south latitude, and between $20^\circ$ and $23^\circ 45'$ of east longitude; and his rout through the country was from south-west to north-east, or nearly so.