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
