conclusion that air density must formerly have been very much greater, judging from the pterodactyl with wing span over thirty feet, equal to a Bleriot machine, and fossil dragon-flies of the carboniferous era, over three feet between the tip of the wings.

The winged figures of Assyrian art may prove an inherited reminiscence of the time of the pterodactyl, in an atmosphere of perhaps two-fold density.

The figures have come down to us through the Greek Mythology to the representation by the modern artist of the winged angel, described by Milton in "Paradise Lost," and painted in the cathedral altar-piece.

But while the poet and artist invites us to consider his human figure, Isis, Nike, Michael, as life size with wings proportioned to suit the æsthetic sense, mechanical science of similitude requires our imagination to reduce the scale to the size of the present dragon-fly, if flight is to be maintained on unassisted one-man power, in the tenuity of our present atmosphere.

Pope, however, has grasped the principle of Mechanical Similitude in his "Rape of the Lock," where he arms his Gnome and Ariel Sprite with a bodkin spear:

"Know, then, unnumbered Gnomes around thee fly,
The light Militia of the lower sky."

A thought echoed by Tennyson's "Airy navies of the blue."
In all the recent rapid progress there is one difficulty still
unsolved; a name has not been discovered for the flying machine
of universal acceptance; and here the poverty comes out of the
English language in the formation of a new compound word.

The German calls it a dragon, as in the car of Demeter; and Demoiselle (dragon-fly) is the name given by Santos Dumont to his mount.

The lady of the "Rape of the Lock," reminded by

"Think what an Equipage thou hast in Air,

And view with scorn two Pages and a Chair."

might say then, "Bring the dragon-fly round to the door," or dragon instead of the brougham.

Santos Dumont takes the dragon-fly as his mechanical model; but the two inches of length of the insect becomes twenty-four feet in the Demoiselle, a linear scale of 144 to 1, and the speed must be raised twelve-fold, to over sixty miles an hour, from five or six in the dragon-fly.

Size and weight mount up, then, 144 times 144 times 144 times, three million-fold, and a few grains in the fly become nearly half a ton in the Demoiselle. And the power required is another twelve times more, so we have to multiply by twelve seven times over, thirty-six million times, to go from the horse power of the fly to the dragon.

This is the simple calculation which the mathematician has brought to the attention of the mechanical enthusiast, and SO the mathematician, as Clifford or Herbert Spencer,

is accused of proving that Human Flight was an impossibility.

And so it was, as a retrospect of the last few years will show. It was impossible till the motor was available, strong and light enough to lift itself and three- or four-fold weight, including a man pilot. For the development of the motor we have to thank the Associated Motor Car industry, but for which we should still be waiting.

Such a mechanical genius as Maxim, working about fifteen years ago, and with unlimited resources, was not able to achieve a flight, and so we may be sure no one else could. A few poor aeronautical enthusiasts might still be working, and for a hundred years more, without arriving at a result presented to them now ready made.

All such experimenters, however, were doing valuable work in preparing the way for success, Langley for instance, subsidised by the American Government, so that the moment the motor was available, man could fly.

But not with one man power, as in the artist's picture. The pilot likes to ride on 50 horse-power at least, and the power is mounting up to 100 horse-power and more, before he will secure the speed to become the real mechanical enlargement of the model dragon-fly.

Roger Bacon has described the direction he would like to

follow in his inventions, impossible to carry out in his own day from lack of mechanical skill.

Beginning with the Motor Car, he would follow on with the Flying Machine, and then the Diving Dress, and the Suspension Bridge perhaps. But Bacon is as cautious as Herodotus in distinguishing between what he has heard only, and seen himself, as we read in these extracts

De secretis operibus artis et naturæ, Caput IV.
De instrumentis artificiosis mirabilibus.

Currus etiam possent fieri ut sine animali moveantur cum impetu in æstimabili, ut existimantur currus falcati fuisse quibus antiquitus pugnabatur.

Possunt etiam fieri instrumenta volandi, et homo sedens in medio instrumenti revolvens aliquod ingenium, per quod alæ artificialiter compositæ aerem verberent, ad modum avis volantis.

Possunt etiam fieri instrumenta ambulandi in mari et in fluviis ad fundum sine periculo corporali. Nam Alexander magnus his usus est, ut secreta maris videret, secundum quod Ethicus narrat astronomus.

Hæc autem facta sunt antiquitus, et nostris temporibus.

Et certum est, præter instrumentum volandi quod non vidi nec hominem qui vidisset cognovi, sed sapientem qui hoc artificium excogitavit explicité cognosco.

LECTURE I

GENERAL PRINCIPLES OF FLIGHT, LIGHT AND DRIFT

A SIMPLE preliminary calculation will show the requirements indispensable for a flight in the air of an aeroplane machine.

Take an aeroplane, AA', rectangular, moving horizontally at a slope a in still air with velocity Q f/s (feet per second) (Figs. 1, 2, 4).

This is the velocity as observed by a spectator standing on the ground.

But the pilot on his seat. looking ahead, is unconscious of his own motion, and feels the air blowing past with velocity Q f/s; and the dynamical problem is the same from each point of view of the pilot who thinks himself stationary, as a Wright glider, and the air blowing past, or of the spectator standing in still air, and watching the pilot flying past with velocity Q f/s.

But when the spectator is standing in a wind blowing over the ground with velocity W f/s, he will notice a difference in the speed of the machine, QF W f/s, according as it is flying up the wind or down.

The pilot, however, will not be aware of a difference any more than a bird in a gale, as his machine cleaves the air with the same speed as before.

Suppose a bird then, or an aviator is to make a flight in a wind; he will start for preference against the wind, so as to increase his relative velocity, and so rise quicker. It is easier then, to rise against the wind than with the wind behind; and to alight also, provided the pilot does not descend into a region of relative calm.

The aeroplane AA' is now supposed up in the air, with the wind blowing past it at Q f/s; and a pressure difference arises in consequence, which gives a resultant thrust, T lb, on the under side of the plane.

The vertical component, T cos a, is called the Lift, as it is required to lift the weight, W lb; and T sin a, the horizontal

component, is called the Drift, and this drift has to be overcome by the thrust of the screw, working at

(1)

T sin a

Q

effective horse power (E.H.P.)

550'

reckoning 1 H.P. at 550 ft-lb/sec, that is, 33,000 ft-lb/min on Watt's estimate.

The ratio then of

if the slope of the aeroplane is reckoned at 1 in n; but it is prudent to double the E.H.P. to arrive at an estimate of the I.H.P. (indicated horse power), reckoning engine and propeller efficiency at 50 per cent.