the method of differencing, or finding the fluxions of exponential quantities, and of summing up those differences, or finding their fluents.
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(a) Professor Busch published in 1792 a work entitled *A Theoretical and Practical Delineation of Commerce*. Exponential Curve, is that whose nature is defined or expressed by an exponential equation; as the curve denoted by $a^x = y$, or by $x^y = y$.
Exponential Equation, is one in which is contained an exponential quantity: as the equation $a^x = b$, or $x^y = ab$, &c.
Exponential Quantity, is that whose power is a variable quantity; as the expression $a^x$, or $x^x$. Exponential quantities are of several degrees and orders according to the number of exponents or powers, one over another.
Extra Constellatory Stars, such as are not properly included in any constellation.
Extra Mundane Space, is the infinite, empty, void space, which is by some supposed to be extended beyond the bounds of the universe, and consequently in which there is really nothing at all. The phrase extra mundane space has been so long in use among our best writers, that it is now impossible to banish it from the language; and yet it has been the source of some extravagant mistakes. Many philosophers consider space as something real, distinct both from body and mind; and no less a man than Dr Clarke considered it as an attribute of the Deity. Yet we think nothing more evident, than that if body had never existed, space would never have been thought of; and if this be so, extra mundane space, instead of denoting any real thing, or attribute infinitely extended, can mean nothing more than the possibility of enlarging the corporeal universe, however widely extended it may be. See Metaphysics Extremes (Encycl.), Part II. ch. iv.
Extrados, the outside of an arch of a bridge, vault, &c. See Arch in this Supplement.
Extremes Conjunct, and Extremes Disjunct, in spherical trigonometry, are, the former the two circular parts that lie next the assumed middle part; and the latter are the two that lie remote from the middle part. These were terms applied by Lord Napier in his universal theorem for resolving all right-angled and quadrantial spherical triangles, and published in his Logarithmorum Canonis Descriptio, an. 1614. In this theorem, Napier condenses into one rule, in two parts, the rules for all the cases of right angled spherical triangles, which had been separately demonstrated by Pitiscus, Lansbergius, Copernicus, Regiomontanus, and others. In this theorem, neglecting the right angle, Napier calls the other five parts circular parts, which are, the two legs about the right angle, and the complements of the other three, viz. of the hypotenuse, and the two oblique angles. Then taking any three of these five parts, one of them will be in the middle between the other two, and these two are the extremes conjunct when they are immediately adjacent to that middle part, or they are the extremes disjunct when they are each separated from the middle one by another part.
F.
Face or Façade, in architecture, is sometimes used for the front or outward part of a building, which immediately presents itself to the eye; or the side where the chief entrance is, or next the street, &c.
Falconry is a species of sport, about the antiquity of which there has been some dispute. Under the word Hawking (Encycl.) we have deduced what we thought sufficient evidence of its being practised among the Thracians, and likewise among the Britons before the invasion of this island by the Romans. Flavius Blondus, however, and Laurentius Valla, both writers of the 15th century, and the latter, one of the most learned men of his time, affirm that no nation or people were accustomed to catch either land or water fowls with any rapacious bird trained for the purpose.
We were pleased to see our own opinion, so different from this, completely established by the learned labours of Professor Beckmann. So early (says he) as the time of Ctesias (and he refers to the page and edition of his author) hares and foxes were hunted in India by means of rapacious birds. The account of Aristotle *, however, is still more to the purpose, and more worthy of notice. "In Thrace (says he) the men go out to catch birds with hawks. The men beat the reeds and bushes which grow in marshy places, in order to raise the small birds, which the hawks pursue and drive to the ground; where the fowlers kill them with poles." Falconry.
The same account is to be found in another book ascribed also to Aristotle; and which appears, at any rate, to be the work of an author not much younger. Respecting Thrace, which is situated above Amphipolis, a wonderful thing is told, which might appear incredible to those who had never heard it before. It is said that boys go out into the fields, and pursue birds by the assistance of hawks. When they have found a place convenient for their purpose, they call the hawks by their names, which immediately appear as soon as they hear their voices, and chase the birds into the bushes, where the boys knock them down with sticks and seize them. What is still more wonderful, when these hawks lay hold of any birds themselves, they throw them to the fowlers; but the boys, in return, give them some share of the prey. De mirabilibus auscultat. cap. 128.
In this passage, there are two additions which render the circumstance still more remarkable. The first is, that the falcons appeared when called by their names; and the second, that of their own accord they brought to the fowlers whatever they caught themselves. Nothing is here wanting but the spaniel employed to find out game, the hood which is put upon the head of the hawk while it stands on the hand, and the thong used for holding it, to form a short description of falconry. as still practised. Our falconers, when they have taken the bird from the hawk, give him, in return, a small share of it; and in the like manner the Thracian hawks received some part of their booty.
Other writers after Aristotle, such as Antigonus, Eluan, Pliny, and Phile, have also given an account of this method of fowling. Eluan, who seldom relates any thing without some alteration or addition, says, that in Thrace nets were used, into which the birds were driven by the hawks; and in this he is followed by the poet Phile. Eluan, also, in another place describes a manner of hunting with hawks in India, which, as we are told by several travellers, is still practised in Persia, where it is well understood, and by other eastern nations.
The Indians (says he) hunt hares and foxes in the following manner: They do not employ dogs, but eagles, crows, and, above all, kites, which they catch when young, and train for that purpose. They let loose a tame hare or fox, with a piece of flesh fastened to it, and suffer these birds to fly after it, in order to seize the flesh, which they are fond of; and which, on their return, they receive as the reward of their labour. When thus instructed to pursue their prey, they are sent after wild foxes and hares in the mountains; these they follow in hopes of obtaining their usual food, and soon catch them and bring them back to their masters, as we are informed by Ctesias. Instead of the flesh, however, which was fastened to the tame animals, they receive as food the entrails of the wild ones which they have caught.
It seems, therefore, that the Greeks received from India and Thrace the first information respecting the method of fowling with birds of prey; but it does not appear that this practice was introduced among them at a very early period. In Italy, however, it must have been very common, for Martial and Apuleius speak of it as a thing every where known; the former calls a hawk the fowler's servant.
The Professor traces the history of this art with great learning down to the present time. It was carried to the highest perfection at the principal courts of Europe (he says) in the 12th century, when the ladies kept hawks, which were as much fondled by those who wished to gain their favour, as lap-dogs are at present. Among the oldest writers on falconry, as an art he reckons Demetrius, who about the year 1270 was physician to the Emperor Michael Paleologus. His book, written in Greek, was first printed at Paris in 1612 with a Latin translation; but its precepts (says our author) would be thought of very little value at present. For an account of the modern art of falconry see Encyclopaedia.