Chapter XLVIII: Section 6: , quoted above, gave rise to an immense amount of (7)

AEOLUS, in Greek mythology, according to Homer the son of Hippotes, god and father of the winds, and ruler of the island of Aeolia. In the Odyssey (x. I) he entertains Odysseus, gives him a favourable wind to help him on his journey, and a bag in which the unfavourable winds have been confined. Out of curiosity. or with the idea that it contains valuable treasures, Odysseus' companions open the bag; the winds escape and drive them back to the island, whence Aeolus dismisses them with bitter reproaches. According to Virgil, Aeolus dwells on one of the Aeolian islands to the north of Sicily, Lipara or Strongyle (Stromboll), where he keeps the winds imprisoned in a vast cavern (Virgil, Aen. i. 52). Another genealogy makes him the son of Poseidon and Arne, granddaughter of Hippotes, and a descendant of Aeolus, king of Magnesia in Thessaly, the mythical ancestor of the tribe of the Aeolians (Diodorus iv. 67).

AEON, a term often used in Greek (aion) to denote an indefinite or infinite duration of time; and hence, by metonymy, a being that exists for ever. In the latter sense it was chiefly used by the Gnostic sects to denote those eternal beings or manifestations which emanated from the one incomprehensible and ineffable God. (See GNOSTICISM.)

AEPINUS, FRANZ ULRICH THEODOR (1724-1802), German natural philosopher, was born at Rostock in Saxony on the 13th of December 1724. He was descended from John Aepinus (1499-1553), the first to adopt the Greek form (aipernos) of the family name Hugk or Huck, and a leading theologian and controversialist at the time of the Reformation. After studying medicine for a time, Franz Aepinus devoted himself to the physical and mathematical sciences, in which he soon gained such distinction that he was admitted a member of the Berlin academy of sciences. In 1757 he settled in St Petersburg as member of the imperial academy of sciences and professor of physics, and remained there till his retirement in 1798. The rest of his life was spent at Dorpat, where he died on the 10th of August 1802. He enjoyed the special favour of the empress Catherine II., who appointed him tutor to her son Paul, and endeavoured, without success, to establish normal schools throughout the empire under his direction. Aepinus is best known by his researches, theoretical and experimental, in electricity and magnetism, and his principal work, Tentamen Theoriae Electricitatis et Magnetismi, published at St Petersburg in 1759, was the first systematic and successful attempt to apply mathematical reasoning to these subjects. He also published a treatise, in 176I, De distributione caloris per tellurem, and he was the author of memoirs on different subjects in astronomy, mechanics, optics and pure mathematics, contained in the journals of the learned societies of St Petersburg and Berlin. His discussion of the effects of parallax in the transit of a planet over the sun's disc excited great interest, having appeared (in 1764) between the dates of the two transits of Venus that took place in the 18th century.

AEQUI, an ancient people of Italy, whose name occurs constantly in Livy,s first decade as hostile to Rome in the first three Centuries of the city's existence. They occupied the upper reaches of the valleys of the Anio, Tolenus and Himella; the last two being mountain streams runing northward to join the Nar. Their chief centre is said to have been taken by the Romans about 484 B.C. (Diodorus xi. 40) and again about ninety years later (id. xiv. 106), but they were not finally subdued Until the end of the second Samnite war (Livy ix. 45,; x. 1; Diod. xx. 101), when they seem to have received a limited form of franchise (Cic. Off. i. II, 35). All we know of their subsequent political condition is that after the Social war the folk of Cliternia and Nersae appear united in a res Publica Aequiculorum, which was a municipium of the ordinary type (C.I.L. ix. p. 388). The Latin colonies of Alba Fucens (304 B.C.) and Carsioll (298 B.C.) must have spread the use of Latin (or what passed as such) all over the district; through it by the chief (and for some time the only) route (Pia Valeria) to Luceria and the south. Of the language spoken by the Aequi before the Roman conquest we have no record; but since the Marsi (q.v.), who lived farther east, spoke in the 3rd century B.C. a dialect closely akin to Latin, and since the Hernici (q.v.), their neighbours to the south-west, did the same, we have no ground for separating any of these tribes from the Latian group (see LATINI). If we could be certain of the origin of the a in their name and of the relation between its shorter and its longer form (note that the i in Aequicidus is long--Virgil, Aen. vii. 74----which seems to connect it with the locative of aequum ``a plain,'' so that it would mean ``dwellers in the plain''; but in the historical period they certainly lived mainly in the hills), we should know whether they were to be grouped with the q or the p dialects, that is to say, with Latin on the one hand, which preserved an original q, or with the dialect of Velitrae, commonly called Volscian (and the Volsci were the constant allies of the Aequi), on the other hand, in which, as in the Iguvine and Samnite dialects, an original q is changed into p. There is no decisive evidence to show whether the q in Latin aequus represents an Indo-European q as in Latin quis, Umbro-Volsc. pis, or an Indo-European k+u as in equus, Umb. ekvo-. The derivative adjective Aequicus might be taken to range them with the Volsci rather than the Sabini, but it is not clear that this adjective was ever used as a real ethnicon; the name of the tribe is always Aeqai, or Aequicoli. At the end of the Republican period the Aequi appear, under the name Aequiculi or Aequicoh, organized as a municipium, the territory of which seems to have comprised the upper part of the valley of the Salto, still known as Cicolano. It is probable, however, that they continued to live in their villages as before. Of these Nersae (mod. Nesce) was the most considerable. The polygonal terrace walls, which exist in considerable numbers in the district, are shortly described in Romische Mitteilungen (1903), 147 seq., but require further study. See further the articles MARSI, VOLSCI, LATINI, and the references there given; the place-names and other scanty records of the dialect are collected by R. S. Conway. The Italic Dialects, pp. 300 ff. (R. S. C.)

AERARII (from Lat. aes, in its subsidiary sense of ``polltax''), originally a class of Roman citizens not included in the thirty tribes of Servius Tullius, and subject to a poll-tax arbitrarily fixed by the censor. They were (1) the inhabitants of conquered towns which had been deprived of local self-government, who possessed the jus eonubii and ius commercii, but no political rights; Caere is said to have been the first example of this (353 B.C.); hence the expression ``in tabulas Caeritum referre'' came to mean ``to degrade to the status of an aerarius'': (2) full citizens subjected to civil degradation (infamia) as the result of following certain professions (e.g. acting), of dishonourable acts in private life (e.g. bigamy) or of conviction for certain crimes; (3) persons branded by the censor. Those who were thus excluded from the tribes and centuries had no vote, were incapable of filling Roman magistracies and could not serve in the army. According to Mommsen, the aerarii were originally the non-assidui (non-holders of land), excluded from the tribes, the comitia and the army. By a reform of the censor Appius Claudius in 312 B.C. these non-assidui were admitted into the tribes, and the aerarii as such disappeared. But in 304, Fabius Rullianus limited them to the four city tribes, and from that time the term meant a man degraded from a higher (country) to a lower (city) tribe, but not deprived of the right of voting or of serving in the army. The expressions ``tribu movere'' and ``aerarium facere,': regarded by Mommsen as identical in meaning (``to degrade from a higher tribe to a lower,'), are explained by A. H. J. Greenidge---the first as relegation from a higher to a lower tribe or total exclusion from the tribes, the second as exclusion from the centuries. Other views of the original aerarii are that they were--artisans and freedmen (Niebuhr); inhabitants of towns united with Rome by a hospitium publicum, who had become domiciled on Roman territory (Lange); only a class of degraded citizens, including neither the cives sine suffragio nor the artisans (Madvig); identical with the capite censi of the Servian constitution (Belot, Greenidge). See A. H. J. Greenidge, Infamia in Roman Law (1894), where Mommsen's theory is criticized; E. Belot, Histoire des chevaliers romains, i. p. 200 (Paris, 1866); L. Pardon, De Aerariis (Berlin, 1853); P. Willems, Le Droit public romain (1883); A. S. Wilkins in Smith's Dict. of Greek and Roman Antiquities (3rd ed., 189I); and the usual handbooks of antiquities.

AERARIUM (from Lat. aes, in its derived sense of ``money'') the name (in full, aerarium stabulum, treasure-house) given in ancient Rome to the public treasury, and in a secondary sense to the public finances. The treasury contained the moneys and accounts of the state, and also the standards of the legions; the public laws engraved on brass, the decrees of the senate and other papers and registers of importance. These public treasures were deposited in the temple of Saturn, on the eastern slope of the Capitoline hill, and, during the republic, were in charge of the urban quaeators (see QUAESTOR), under the superintendence and control of the senate. This arrangement continued (except for the year 45 B.C., when no quaestors were chosen) until 28 B.C., when Augustus transferred the aerarium to two praojecti aerarii, chosen annually by the senate from ex-praetors; in 23 these were replaced by two praetors (praetores aerarii or ad aerarium), selected by lot during their term of office; Claudius in A.D. 44 restored the quaestors, but nominated by the emperor for three years, for whom Nero in 56 substituted two ex-praetors, under the same conditions. In addition to the common treasury, supported by the general taxes and charged with the ordinary expenditure, there was a special reserve fund, also in the temple of Saturn, the aerarium sanctum (or sanctius), probably originally consisting of the spoils of war, afterwards maintained chiefly by a 5% tax on the value of all manumitted slaves, this source of revenue being established by a lex Manlia in 357. This fund was not to be touched except in cases of extreme necessity (Livy vii. 16, xxvii. 10). Under the emperors the senate continued to have at least the nominal management of the aerarium, while the emperor had a separate exchequer, called fiseus. But after a time, as the power of the emperors increased and their jurisdiction extended till the senate existed only in form and name, this distinction virtually ceased. Besides creating the fiscus, Augustus also established in A.D. 6 a military treasury (aerarium militare), containing all moneys raised for and appropriated to the maintenance of the army, including a pension fund for disabled soldiers. It.was largely endowed by the emperor himself (see Monumentum Ancyranum, iii. 35) and supported by the proceeds of the tax on public sales and the succession duty. Its administration was in the hands of three praefecti aerarii militaris, at first appointed by lot, but afterwards by the emperor, from senators of praetorian rank, for three years. The later emperors had a separate aerarium privatum, containing the moneys allotted for their own use, distinct from the fiscus, which they administered in the interests of the empire.

The tribuni aerarii have been the subject of much discussion. They are supposed by some to be identical with the curatores tribuum, and to have been the officials who, under the Servian organization, levied the war-tax (tributum) in the tribes and the poil-tax on the aerarii (q.v.). They also acted as paymasters of the equites and of the soldiers on service in each tribe. By the lex Aurella (70 B.C.) the list of judices was composed, in addition to senators and equites, of tribuni aerarii. Whether these were the successors of the above, or a new order closely connected with the equites, or even the same as the latter, is uncertain. According to Mommsen, they were persons who possessed the equestrian census, but no public horse. They were removed from the list of judices by Caesar, but replaced by Augustus. According to Madvig, the original tribuni aerarii were not officials at all, but private individuals of considerable means, quite distinct from the curatores tribuuin, who undertook certain financial work connected with their own tribes. Then, as in the case of the equites, the term was subsequently extended to include all those who possessed the property qualification that would have entitled them to serve as tribuni aerarii. See Tacitus, Annals, xiii. 29, with Furneaux's notes; O. Hirschfeld, ``Das Aerarium militare in der romischen Kaiserzeit,'' in Fleckeisen's Jahrbuch, vol. xcvii. (1868); S. Herrlich, De Aerario et Fisco Romanorum (Berlin, 1872); and the usual handbooks and dictionaries of antiquities. On the tribuni aerarii see E. Belot, Hist. des chevaliers romains, ii. p. 276; J. N. Madvig, Opuscula Academica, ii. p. 242; J. B. Mispoulet, Les Institutions politiques des Romains (1883), ii. p. 208; Mommsen, Romisches Staatsrecht, iii. p. 189; A. S. Wilkins in Smith's Dictionary of Greek and Roman Antiquities (3rd ed., 1890).

AERATED WATERS. Waters charged with a larger proportion of carbon dioxide than they will dissolve at ordinary atmospheric pressure occur in springs in various parts of the world (see MINERAL WATERS). Such waters, which also generally hold in solution a considerable percentage of saline constituents, early acquired a reputation as medicinal agents, and when carbon dioxide (``fixed air'') became familiar to chemists the possibility was recognized, as by Joseph Priestley (Directions for impregnating water with fixed air . . . to communicate the peculiar Spirit and Virtues of Pyrmont water, 1772), of imitating them artificially. Many of the ordinary aerated waters of commerce, however, do not pretend to reproduce any known natural water; they are merely beverages owing their popularity to their effervescing properties and the flavour imparted by a small quantity of some salt such as sodium bicarbonate or a little fruit syrup. Their manufacture on a considerable scale was begun at Geneva so far back as 1790 by Nicholas Paul, and the excellence of the soda water prepared in London by J. Schweppe, who had been a partner of Paul's, is referred to by Tiberius Cavallo in his Essay on the Medicinal Properties of Factitious Airs, published in 1798. Many forms of apparatus are employed for charging the water with the gas. A simple machine for domestic use, called a gasogene or seltzogene, consists of two strong glass globes connected one above the other by a wide glass tube which rises nearly to the top of the upper and smaller globe. Surmounting the small globe there is a spring valve, fitted to a narrow tube that passes through the wide tube to the bottom of the large globe. To use the machine, the lower vessel is filled with water, and in the upper one, round the base of the wide tube, is placed a mixture, commonly of sodium bicarbonate and tartaric acid, which with water yields carbon dioxide. The valve head is then fastened on, and by tilting the apparatus some water is made to flow through the wide tube from the lower to the upper vessel. The water in the lower globe takes up the gas thus produced, and when required for use is withdrawn by the valve, being forced up the narrow tube by the pressure of the gas. In another arrangement the gas is supplied compressed in little steel capsules, and is liberated into a bottle containing the water which has to be aerated. On a large scale, use is made of continuously acting machinery which is essentially of the type devised by Joseph Bramah. The gas is prepared in a separate generator by the action of sulphuric acid on sodium bicarbonate or whiting, and after being washed is collected in a gas-holder, whence it is forced with water under pressure into a receiver or saturator in which an agitator is kept moving. Some manufacturers buy their gas compressed in steel cylinders. The water thus aerated or carbonated passes from the receiver, in which the pressure may be 100-200 lb. on the square inch, to bottling machines which fill and close the bottles; if beverages like lemonade are being made the requisite quantity of fruit syrup is also injected into the bottles, though sometimes the fruit syrup mixture is aerated in bulk. For soda water sodium bicarbonate should be added to the water before aeration, in varying proportions up to about 15 grains per pint, but the simple carbonated water often does duty instead. Potash water, lithia water and many others are similarly prepared, the various salts being used in such amounts as are dictated by the experience and taste of the manufacturer. Aerated waters are sent out from the factories either in siphons (q.v.) or in bottles; the latter may be closed by corks, or by screw-stoppers or by internal stoppers consisting of a valve, such as a glass ball, held up against an indiarubber ring in the neck by the pressure of the gas. For use in ``soda-fountains'' the waters are sent out in large cylinders.

See W. Kirkby, Evolution of artificial Mineral Waters (Manchester, 1902).

AERONAUTICS, the art of ``navigating'' the ``air.'' It is divisible into two main branches--aerostation, dealing properly with machines which like balloons are lighter than the air, and aviation, dealing with the problem of artificial flight by means of flying machines which, like birds, are heavier than the air, and also with attempts to fly made by human beings by the aid of artificial wings fitted to their limbs.

Historically, aviation is the older of the two, and in the legends of gods or myths of men or animals which are supposed to have travelled through the air, such as Pegasus, Medea's dragons and Daedalus, as well as in Egyptian bas-reliefs, wings appear as the means by which aerial locomotion is effected. In later times there are many stories of men who have attempted to fly in the same way. John Wilkins (1614-1672), one of the founders of the Royal Society and bishop of Chester, who in 1640 discussed the possibility of reaching the moon by volitation, says in his Mathematical Magick (1648) that it was related that ``a certain English monk called Elmerus, about the Confessor's time,'' flew from a town in Spain for a distance of more than a furlong; and that other persons had flown from St Mark's, Venice, and at Nuremberg. Giovanni Battista Dante, of Perugia, is said to have flown several times across Lake Trasimene. At the beginning of the 16th century an Italian alchemist who was collated to the abbacy of Tungland, in Galloway, Scotland, by James IV., undertook to fly from the walls of Stirling Castle through the air to France. He actually attempted the feat, but soon came to the ground and broke his thigh-bone in the fall--an accident which he explained by asserting that the wings he employed contained some fowls' feathers, which had an ``affinity'' for the dung-hill, whereas if they had been composed solely of eagles' feathers they would have been attracted to the air. This anecdote furnished Dunbar, the Scottish poet, with the subject of one of his rude satires. Leonardo da Vinci about the same time approached the problem in a more scientific spirit, and his notebooks contain several sketches of wings to be fitted to the arms and legs. In the following century a lecture on flying delivered in 1617 by Fleyder, rector of the grammar school at Tubingen, and published eleven years later, incited a poor monk to attempt to put the theory into practice, but his machinery broke down and he was killed.

In Francis Bacon's Natural History there are two passages which refer to flying, though they scarcely bear out the assertion made by some writers that he first published the true principles of aeronautics.

The first is styled Experiment Solitary, touching Flying in the Air --``Certainly many birds of good wing (as kites and the like) would bear up a good weight as they fly; and spreading leathers thin and close, and in great breadth, will likewise bear up a great weight, being even laid, without tilting up on the sides. The further extension of this experiment might be thought upon.'' The second passage is more diffuse, but less intelligible; it is styled Experiment Solitary, touching unequal weight (as of wool and lead or bone and lead); if you throw it from you with the light end forward, it will turn, and the weightier end will recover to be forwards, unless the body be over long. The cause is, for that the more dense body hath a more violent pressure of the parts from the first impulsion, which is the cause (though heretofore not found out, as hath been often said) of all violent motions; and when the hinder part moveth swifter (for that it less endureth pressure of parts) that the forward part can make way for it, it must needs be that the body turn over; for (turned) it can more easily draw forward the lighter part.'' The fact here alluded to is the resistance that bodies experience in moving through the air, which, depending on the quantity of surface merely. must exert a proportionally greater effect on rare substances. The passage itself, however, after making every allowance for the period in which it was written, must be deemed confused, obscure and unphilosophical. In his posthumous work, De Motu Animalium, published at Rome in 1680-1681, G.A.Borelli gave calculations of the enormous strength of the pectoral muscles in birds; and his proposition cciv. (vol. i. pp. 322-326), entitled Est impossibile ut homines pro priis viribus artificiose volare possint, points out the impossibility of man being able by his muscular strength to give motion to wings of sufficient extent to keep him suspended in the air. But during his lifetime two Frenchmen, Allard in 1660 and Besnier about 1678, are said to have succeeded in making short flights. An account of some of the modern attempts to construct flying machines will be found in the article FLIGHT AND FLYING; here we append a brief consideration of the mechanical aspects of the problem.

The very first essential for success is safety, which will probably only be attained with automatic stability. The underlying principle is that the centre of gravity shall at all times be on the same vertical line as the centre of pressure. The latter varies with the angle of incidence. For square planes it moves approximately as expressed by Joessel's formula, C + (0.2 + 0.3 sin a) L, in which C is the distance from the front edge, L the length fore and aft, and a the angle of incidence. The movement is different on concave surfaces. The term aeroplane is understood to apply to flat sustaining surfaces, but experiment indicates that arched surfaces are more efficient. S. P. Langley proposed the word aerodrome, which seems the preferable term for apparatus with wing-line surfaces. This is the type to which results point as the proper one for further experiments. With this it seems probable that, with well-designed apparatus, 40 to 50 lb. can be sustained per indicated h.p., or about twice that quantity per resistance or ``thrust'' h.p., and that some 30 or 40 k of the weight can be devoted to the machinery, thus requiring motors, with their propellers, shafting, supplies, &c., weighing less than 20 lb. per h.p. It is evident that the apparatus must be designed to be as light as possible, and also to reduce to a minimum all resistances to propulsion. This being kept in view, the strength and consequent section required for each member may be calculated by the methods employed in proportioning bridges, with the difference that the support (from air pressure) will be considered as uniformly distributed, and the load as concentrated at one or more points. Smaller factors of safety may also have to be used. Knowing the sections required and unit weights of the materials to be employed, the weight of each part can be computed. If a model has been made to absolutely exact scale, the weight of the full-sized apparatus may approximately be ascertained by the formula

$$W' = W\sqrt{\left({S'\over S}\right)}^3,$$

in which W is the weight of the model, S its surface, and W' and S' the weight and surface of the intended apparatus. Thus if the model has been made one-quarter size in its homologous dimensions, the supporting surfaces will be sixteen times, and the total weight sixty-four times those of the model. The weight and the surface being determined, the three most important things to know are the angle of incidence, the ``lift,'' and the required speed. The fundamental formula for rectangular air pressure is well known: P=KV2S, in which P is the rectangular normal pressure, in pounds or kilograms, K a coefficient (0.0049 for British, and 0.11 for metric measures), V the velocity in miles per hour or in metres per second, and S the surface in square feet or in square metres. The normal on oblique surfaces, at various angles of incidence, is given by the formula P = KV2Se, which latter factor is given both for planes and for arched surfaces in the subjoined table:--.

PERCENTAGES OE AIR PRESSURE AT VARIOUS ANGLES OF INCIDENCE

PLANES (DUCHEMIN FORMULA, VERIFIED BY LANGLEY). WINGS (LILIENTHAL). N = P(2sina/(1+sin2a)). Concavity 1 in 12

Angle. Normal. Lift. Drift. Normal. Lift. Drift. Tangential a e ecosa esina e ecosa esina force a -9 deg. 0.0 0.0 0.0 +0.070 -8 deg. 0.040 0.0396 -0.0055 +0.067 -7 deg. 0.080 0.0741 -0.0097 +0.064 -6 deg. 0.120 0.1193 -0.0125 +0.060 -5 deg. 0.160 0.1594 -0.0139 +0.055 -4 deg. 0.200 0.1995 -0.0139 +0.049 -3 deg. 0.242 0.2416 -0.0126 +0.043 -2 deg. 0.286 0.2858 -0.0100 +0.037 -1 deg. 0.332 0.3318 -0.0058 +0.031 0 deg. 0.0 0.0 0.0 0.381 0.3810 -0.0 +0.024 +1 deg. 0.035 0.035 0.000611 0.434 0.434 +0.0075 +0.016 +2 deg. 0.070 0.070 0.00244 0.489 0.489 +0.0170 +0.008 +3 deg. 0.104 0.104 0.00543 0.546 0.545 +0.0285 0.0 +4 deg. 0.139 0.139 0.0097 0.600 0.597 +0.0418 -0.007 +5 deg. 0.174 0.173 0.0152 0.650 0.647 +0.0566 -0.014 +6 deg. 0.207 0.206 0.0217 0.696 0.692 +0.0727 -0.021 +7 deg. 0.240 0.238 0.0293 0.737 0.731 +0.0898 -0.028 +8 deg. 0.273 0.270 0.0381 0.771 0.763 +0.1072 -0.035 +9 deg. 0.305 0.300 0.0477 0.800 0.790 +0.1251 -0.042 10 deg. 0.337 0.332 0.0585 0.825 0.812 +0.1432 -0.050 11 deg. 0.369 0.362 0.0702 0.846 0.830 +0.1614 -0.058 12 deg. 0.398 0.390 0.0828 0.864 0.845 +0.1803 -0.064 13 deg. 0.431 0.419 0.0971 0.879 0.856 +0.1976 -0.070 14 deg. 0.457 0.443 0.1155 0.891 0.864 +0.2156 -0.074 15 deg. 0.486 0.468 0.1240 0.901 0.870 +0.2332 -0.076

The sustaining power, or ``lift'' which in horizontal flight must be equal to the weight, can be calculated by the formula L=KV2Secosa, or the factor may be taken direct from the table, in which the ``lift'' and the ``drift'' have been obtained by multiplying the normal e by the cosine and sine of the angle. The last column shows the tangential pressure on concave surfaces which O. Lilienthal found to possess a propelling component between 3 deg. and 32 deg. and therefore to be negative to the relative wind. Former modes of computation indicated angles of 10 to 15 as necessary for support with planes. These mere prohibitory in consequence of the great ``drift''; but the present data indicate that, with concave surfaces, angles of 2 deg. to 5 will produce adequate ``lift.'' To compute the latter the angle at which the wings are to be set must first be assumed, and that of @ will generally be found preferable. Then the required velocity is next to be computed by the formula

$$V = \sqrt{L\over KS\eta\cos\alpha};$$

or for concave wings at +3 deg. :

$$V = \sqrt{W\over 0.545KS}.$$

Having thus determined the weight, the surface, the angle of incidence and the required seed for horizontal support, the next step is to calculate the power required. This is best accomplished by first obtaining the total resistances, which consist of the ``drift'' and of the head resistances due to the hull and framing. The latter are arrived at preferably by making a tabular statement showing all the spars and parts offering head resistance, and applying to each, the coefficient appropriate to its ``master section,'' as ascertained by experiment. Thus is obtained an ``equivalent area'' of resistance, which is to be multiplied by the wind pressure due to the speed. Care must be taken to resolve all the resistances at their proper angle of application, and to subtract or add the tangential force, which consists in the surface S, multiplied by the wind pressure, and by the factor in the table, which is, however, 0 for 3 and 32, but positive or negative at other angles. When the aggregate resistances are known, the ``thrust h.p.'' required is obtained by multiplying the resistance by the speed, and then allowing for mechanical losses in the motor and propeller, which losses will generally be 50% of indicated h.p. Close approximations are obtained by the above method when applied to full sized apparatus. The following example will make the process clearer. The weight to he carried by an apparatus was 189 lb. on concave wings of 143.5 sq. ft. area, set at a positive angle of 3 deg. There were in addition rear wings of 29.5 sq. ft., set at a negative angle of 3 deg. ; hence, L= 189=.o.oo5XV2X143.5X0.545. Whence

$$V = \sqrt{189\over 0.005\times 143.5\times 0.545 = 22\hbox{ miles per hour},$$

at which the air pressure would be 2.42 lb. per sq. ft. The area of spars and man was 17.86 sq. ft., reduced by various coefficients to an ``equivalent surface'' of 11.70 sq. ft., so that the resistances were:-- Drift front wings, 143.5X0.0285X2.42 . . . .= 9.90 lb. Drift rear wings, 29.5X(o.o43-0.242X0.05235)X2.42 = 2.17 lb. Tangential force at 3 deg. . . . . . . . . = 0.00 lb. Head resistance, 11.70X2.43 . . . . . = 28.31

Total resistance . . . . . . . .= 40.38

Speed 22 miles per hour. Power = (40.38X22)/375 = 2.36 h.p. for the ``thrust'' or 4.72 h.p. for the motor. The weight being 189 lb., and the resistance 40.38 lb., the gliding angle of descent was 40.38/189 = tangent of 12 deg. , which was verified by many experiments.

The following expressions will be found useful in computing such projects, with the aid of the table above given:

1. Wind force, F = KV2. 8. Drift, D = KSV2esina 2. Pressure, P = KV2S. 9. Head area E, get an equivalent 3. Velocity, V = sqrt. (W/(KSecosa)) 10. Head resistance, H = EF. 4. Surface S varies as 1/V2. 11. Tangential force, T = Pa 5. Normal, N = KSV2e. 12. Resistance, R = D + H (+ or -) T. 6. Lift, L = KSV2ecsoa. 13. Ft. lb., M = RV. 7. Weight, W = L = Ncosa. 14. Thrust, h.p., = RV/factor.

AEROSTATION.---Possibly the flying dove of Archytas of Tarentum is the earliest suggestion of true aerostation. According to Aulus Genius (Noctes Atticae) it was a ``model of a dove or pigeon formed in wood and so contrived as by a certain mechanical art and power to fly: so nicely was it balanced by weights and put in motion by hidden and enclosed air.'' This ``hidden and enclosed air'' may conceivably represent an anticipation of the hot-air balloon, but it is at least as probable that the apparent flight of the dove was a mere mechanical trick depending on the use of fine wires or strings invisible to the spectators. In the middle ages vague ideas appear of some ethereal substance so light that vessels containing it would remain suspended in the air. Roger Bacon (1214-1294) conceived of a large hollow globe made of very thin metal and filled with ethereal air or liquid fire, which would float on the atmosphere like a ship on water. Albert of Saxony, who was bishop of Halberstadt from 1366 to 1390, had a similar notion, and considered that a small portion of the principle of fire enclosed in a light sphere would raise it and keep it suspended. The same speculation was advanced by Francis Mendoza, a Portuguese Jesuit, who died in 1626 at the age of forty-six, and by Gaspar Schott (1608-1666), also a Jesuit and professor of mathematics at Wurzburg, though for fire he substituted the thin ethereal fluid which he believed to float above the atmosphere. So late as 1755 Joseph Galien (1699-1782), a Dominican friar and professor of philosophy and theology in the papal university of Avignon, proposed to collect the diffuse air of the upper regions and to enclose it in a huge vessel extending more than a mile every way, and intended to carry fifty-four times as much weight as did Noah's ark. A somewhat different but equally fantastic method of making heavy bodies rise is quoted by Schott from Lauretus Laurus, according to whom swans' eggs or leather balls filled with nitre, sulphur or mercury ascend when exposed to the sun. Laurus also stated that hens' eggs filled with dew will ascend in the same circumstances, because dew is shed by the stars and drawn up again to heaven by the sun's heat during the day. The same notion is utilized by Cyrano de Bergerac (1619-1655) in his romances describing journeys to the moon and sun, for his French traveller fastens round his body a multitude of very thin flasks filled with the morning's dew, whereby through the attractive power of the sun's heat on the dew he is raised to the middle regions of the atmosphere, to sink again, however, on the breaking of some of the flasks.

A distinct advance on Schott is marked by the scheme for aerial navigation proposed by the Jesuit, Francis Lana (1631-1687), in his book, published at Brescia in 1670, Prodromo ovvero Saggio di alcune invenzioni nuove promesso all' Arte Maestra. His idea, though useless and unpractical in so far that it could never be carried out, is yet deserving of notice, as the principles involved are sound; and this can be said of no earlier attempt. His project was to procure four copper balls of very large dimensions (fig. 1), yet so extremely thin that after the air was exhausted from them they would be lighter than the air they displaced and so would rise; and to those four balls he proposed to attach a boat, with sails, &c., which would carry up a man. He submitted the whole matter to calculation, and proposed that the globes should be about 25 ft. in diameter and 1/225th of an inch in thickness; this would give from all four balls a total ascensional force of about 1200 lb., which would be quite enough to raise the boat, sails, passengers, &c. But the obvious objection to the whole scheme is, that it would be quite impossible to construct a globe of so large a size and of such small thickness which would even support its own weight without collapsing if placed on the ground, much less bear the external atmospheric pressure when the internal air was removed. Lana himself noticed this objection, but he thought that the spherical form of the copper shell would, notwithstanding its extreme thinness, enable it, after the exhaustion was effected, to sustain the enormous pressure, which, acting equally on every point of the surface, would tend to consolidate rather than to break the metal. His proposal to exhaust the air from the globes by attaching to each a tube 36 ft. long, fitted with a stopcock, and so producing a Torricellian vacuum, suggests that he was ignorant of the invention of the air-pump by Otto von Guericke about 1650.

We now come to the invention of the balloon, which was due to Joseph Michel Montgolfier (1740-1810) and Jacques Etienne Montgolfier (1745-1799), sons of Pierre Montgolfier, a large and celebrated papermaker at Annonay, a town about 40 m. from Lyons. The brothers had observed the suspension of clouds in the atmosphere, and it occurred to them that if they could enclose any vapour of the nature of a cloud in a large and very light bag, it might rise and carry the bag with it into the air. Towards the end of 1782 they inflated bags with smoke from a fire placed underneath, and found that either the smoke or some vapour emitted from the fire did ascend and carry the bag with it. Being thus assured of the correctness of their views, they determined to have a public ascent of a balloon on a large scale. They accordingly invited the States of Vivarais, then assembled at Annonay, to witness their aerostatic experiment; and on the 5th of June 1783, in the presence of a considerable concourse of spectators, a linen globe of 105 ft. in circumference was inflated over a fire fed with small bundles of chopped straw. When released it rapidly rose to a great height, and descended, at the expiration of ten minutes, at the distance of about 1 1/2m. This was the discovery of the balloon. The brothers Montgolfier imagined that the bag rose because of the levity of the smoke or other vapour given forth by the burning straw; and it was not till some time later that it was recognized that the ascending power was due merely to the lightness of heated air compared to an equal volume of air at a lower temperature. In this balloon, no source of heat was taken up, so that the air inside rapidly Cooled, and the balloon soon descended.

The news of the experiment at Annonay attracted so much attention at Paris that Barthelemi Faujas de Saint-Fond (1741-1819), afterwards professor of geology at the Musee d'Histoire Naturelle, set on foot a subscription for paying the expense of repeating the experiment. The balloon was constructed by two brothers of the name of Robert, under the superintendence of the physicist, J. A. C. Charles. The first suggestion was to copy the process of Montgolfier, but Charles proposed the application of hydrogen gas, which was adopted. The filling of the balloon, which was made of thin silk varnished with a solution of elastic gum, and was about 13 ft. in diameter, was begun on the 23rd of August 1783, in the Place des Victoires. The hydrogen gas was obtained by the action of dilute sulphuric acid upon iron filings, and was introduced through leaden pipes; but as the gas was not passed through cold water, great difficulty. was experienced in filling the balloon completely; and altogether about 300 lb. of sulphuric acid and twice that amount of iron filings were used (fig. 2). Bulletins were issued daily of the progress of the inflation; and the crowd was so great that on the 26th the balloon was moved secretly by night to the Champ de Mars, a distance of 2 m. On the next day an immense concourse of people covered the Champ de Mars, and every spot from which a view could be ob obtained was crowded. About five o'clock a cannon was discharged as the signal for the ascent, and the balloon when liberated rose to the height of about 3000 ft. with great rapidity. A shower of rain which began to fall directly after it had left the earth in no way checked its progress; and the excitement was so great, that thousands of well-dressed spectators, many of them ladies, stood exposed, watching it intently the whole time it was in sight and were drenched to the skin, The balloon, after remaining in the air for about three-quarters of an hour, fell in a field near Gonesse, about 15 m. off, and terrified the peasantry so much that it was torn into shreds by them. Hydrogen gas was at this time known by the name of inflammable air; and balloons inflated with gas have ever since been called by the people air-balloons, the kind invented by the Montgolfiers being designated fire-balloons. French Writers have also very frequently styled them after their inventors, Charlieres and Montgolfieres. On the 19th of September 1783 Joseph Montgolfier repeated the Annonay experiment at Versailles, in the presence of the king, the queen, the court and an immense number of spectators. The inflation was begun at one o'clock, and completed in eleven minutes, when the balloon rose to the height of about 1500 ft., and descended after eight minutes, at a distance of about 2 m., in the wood of Vaucresson. Suspended below the balloon: in a cage, had been placed a sheep, a cock and a duck, which were thus the first aerial travellers. They were quite uninjured, except the cock, which had its right wing hurt in consequence of a kick it had received from the sheep; but this took place before the ascent. The balloon, which was painted with ornaments in oil colours, had a very showy appearance (fig. 3). Francois Pilatre de Rozier (1756-1785), a native of Metz, who was appointed superintendent of the natural history collections of Louis XVIII. On the 15th of October 1783, and following days, he made several ascents (generally alone, but once with a companion, Girond de Villette) in a captive balloon (i.e. one attached by ropes to the ground), and demonstrated that there was no difficulty in taking up fuel and feeding the fire, which was kindled in a brazier suspended under the balloon, when in the air. The way being thus prepared for aerial navigation, on the 21st of November 1783, Pilatre de Rozier and the marquis d'Arlandes first trusted themselves to a free fire-balloon. The experiment was made from the Jardin du Chateau de la Muette, in the Bois de Boulogne. A large fire-balloon was inflated at about two o'clock, rose to a height of about 500 ft., and passing over the Invalides and the Ecole Mililaire, descended beyond the Boulevards, about 9000 yds. from the place of ascent, having been between twenty and twenty-five minutes in the air. Only ten days later, viz. on the 1st of December 1783, Charles ascended from Paris in a balloon inflated with hydrogen gas. The balloon, as in the case of the small one of the same kind previously launched from the Champ de Mars, was constructed by the brothers Robert, one of whom took part in the ascent. It was 27 ft. in diameter, and the car was suspended from a hoop surrounding the middle of the balloon, and fastened to a net, which covered the upper hemisphere. The balloon ascended very gently from the Tuileries at a quarter to two o'clock, and after remaining for some time at an elevation of about 2000 ft., it descended in about two hours at Nesle, a small town about 27 m. from Paris, when Robert left the car, and Charles made a, second ascent by himself. He had intended to have replaced the weight of his companion by a nearly equivalent quantity of ballast; but not having any suitable means of obtaining such at the place of descent, and it being just upon sunset, he gave the word to let go, and the balloon being thus so greatly lightened, ascended very rapidly to a height of about 2 m. After staying in the air about half an hour, he descended 3 m. from the place of ascent, although he believed the distance traversed, owing to different currents, to have been about 9 m. In this second journey he experienced a violent pain in his right ear and jaw, no doubt produced by the rapidity of the ascent. He also witnessed the phenomenon of a double sunset on the same day; for when he ascended, the sun had set in the valleys, and as he mounted he saw it rise again, and set a second time as he descended.

All the features of the modern balloon as now used are more or less due to Charles, who invented the valve at the top, suspended the car from a hoop, which was itself attached to the balloon by netting, &c. With regard to his use of hydrogen gas, there are anticipations that must be noticed. As early as 1766 Henry Cavendish showed that this gas was at least seven times lighter than ordinary air, and it immediately occurred to Dr Joseph Black, of Edinburgh, that a thin bag filled with hydrogen gas would rise to the ceiling of a room. He provided, accordingly, the allantois of a calf, with the view of showing at a public lecture such a curious experiment; but for some reason it seems to have failed, and Black did not repeat it, thus allowing a great discovery, almost within his reach, to escape him. Several years afterwards a similar idea occurred to Tiberius Cavallo, who found that bladders, even when carefully scraped, are too heavy, and that China paper is permeable to the gas. But in 1782, the year before the invention of the Montgolfiers, he succeeded in elevating soap-bubbles by inflating them with hydrogen gas. Researches on the use of gas for inflating balloons seem to have been carried on at Philadelphia nearly simultaneously with the experiments of the Montgolfiers; and when the news of the latter reached America, D. Rittenhouse and F. Hopkinson, members of the Philosophical Society at Philadelphia; constructed a machine consisting of forty-seven small hydrogen gas-balloons attached to a car or cage. After several preliminary experiments, in which animals were let up to a certain height by a rope, a carpenter, one James Wilcox, was induced to enter the car for a small sum of money; the ropes were cut, and he remained in the air about ten minutes, and only then effected his descent by making incisions in a number of the balloons, through fear of falling into the river, which he was approaching.

First Ascents in Great Britain.

Although the news of the Annonay and subsequent experiments in France rapidly spread all over Europe, and formed a topic of general discussion, still it was not till five months after the Montgolfiers had first publicly sent a balloon into the air that any aerostatic experiment was made in England. In November 1783 Count Francesco Zambeccari (1756-1812), an Italian who happened to be in London, made a balloon of oil-silk, 10 ft. in diameter, and weighing 11 lb. It was publicly shown for several days, and on the 25th it was three-quarters filled with hydrogen gas and launched from the Artillery ground at one o'clock. It descended after two hours and a half near Petworth, in Sussex, 48 m. from London. This was the first balloon that ascended from English ground. On the 22nd of February 1784 a hydrogen gas balloon, 5 ft. in diameter, was let up from Sandwich, in Kent, and descended at Warneton, in French Flanders, 75 m. distant. This was the first balloon that crossed the Channel. The first person who rose into the air from British ground appears to have been J. Tytler1, who ascended from the Comely Gardens, Edinburgh, on the 27th of August 1784, in a fire-balloon of his own construction. He descended on the road to Restalrig, about half a mile from the place where he rose.

But it was Vincent Lunardi who practically introduced aerostation into Great Britain. Although Tytler had the precedence by a few days still his attempts and partial success were all but unknown; whereas Lunardi's experiments excited an enormous amount of enthusiasm in London. He was secretary to Prince Caramanico, the Neapolitan ambassador, and his published letters to his guardian, the chevalier Compagni, written while he was carrying out his project, and detailing all the difficulties, &c., he met with as they occurred, give an interesting and vivid account of the whole matter. His balloon was 33 ft. in circumference (fig.4), and was exposed to the public view at the Lyceum in the Strand, where it was visited by upwards of 20,000 people. He originally intended to ascend from Chelsea Hospital, but the conduct of a crowd at a garden at Chelsea, which destroyed the fire-balloon of a Frenchman named de Moret, who announced an ascent on the 11th of August, but was unable to keep his word, led to the withdrawal of the leave that had been granted. Ultimately he was permitted to ascend from the Artillery ground, and on the 15th of September 1784 the inflation with hydrogen gas took place. It was intended that an English gentleman named Biggin should accompany Lunardi; but the crowd becoming impatient, the latter judged it prudent to ascend with the balloon only partially full rather than risk a longer delay, and accordingly Mr Biggin was obliged to leave the car. Lunardi therefore ascended alone, in presence of the prince of Wales and an enormous crowd of spectators. He took up with him a pigeon, a dog and a cat, and the balloon was provided with oars, by means of which he hoped to raise or lower it at pleasure. Shortly after starting the pigeon escaped, and one of the oars became broken and fell to the ground. In about an hour and a half he descended at South Mimms, in Hertfordshire, and landed the cat, which had suffered from the cold: he then ascended again, and descended, after the lapse of about three-quarters of an hour, at Standon, near Ware, where he had great difficulty in inducing the peasants to come to his assistance; but at length a young woman, taking hold of one of the cords, urged the men to follow her example, which they then did. The excitement caused by this ascent was immense, and Lunardi at once became the star of the hour. He was presented to the king, and was courted and flattered on all sides. To show the enthusiasm displayed by the people during his ascent, he tells himself, in his sixth letter, how a lady, mistaking the oar which fell for himself, was so affected by his supposed destruction that she died in a few days; but, on the other hand, he says he was told by the judges ``that he had certainly saved the life of a young man who might possibly be reformed, and be to the public a compensation for the death of the lady''; for the jury were deliberating on the fate of a criminal, whom they must ultimately have condemned, when the balloon appeared, and to save time they gave a verdict of acquittal, and the whole court came out to view the balloon. The king also was in conference with his ministers; but on hearing that the balloon was passing, he broke up the discussion, and with them watched the balloon through telescopes. The balloon was afterwards exhibited in the Pantheon. In the latter part of the following year (1785) Lunardi made several successful ascents from Kelso, Edinburgh and Glasgow (in one of which he traversed a distance of 110 m.); these he described in a second series of letters. The first ascent from Ireland was made on the 19th of January 1785 by a Mr Crosbie, who on the following 19th of July attempted to cross St George's Channel to England but fell into the sea. The second person who ascended from Ireland was Richard Maguire. Mr Crosbie had inflated his balloon on the 12th of May 1785, but it was unable to take him up. Maguire in these circumstances offered himself as a substitute, and his offer being accepted he made the ascent. For this he was knighted by the Lord-Lieutenant. Another attempt to cross St George's Channel was made by James Sadler on the 1st of October 1812, and he had nearly succeeded when in consequence of a change of wind he was forced to descend into the sea off Liverpool, whence he was rescued by a fishing-boat. But on the 22nd of July 1817 his second son, Windham Sadler, succeeded in crossing from Dublin to Holyhead.