B in the direction of B D is less than 1000, the resultant must necessarily be in a direction below the half-angle formed by two equal opposing forces: and, on the contrary, should the force

exerted on B in the direction BD be greater than 1000, the resultant must be in a direction above the half-angle.

Now as the resultant of two equal opposing forces is in a direction of exactly half the angle formed by the two forces, and the downward force of gravity is always vertical, it follows that to obtain a resultant in a horizontal direction or above the horizontal, the force exerted in the upward direction must exceed the downward pull of gravity. How much extra force will be required? The answer is obtained by calculating the parallelogram of forces; and it will be found that to obtain a resultant of 17.6 in a direction. of 5° above the horizontal (a convenient angle for practical flight) only an extra force of about 1.7 per 1000 of weight is required to be exerted in an upward direction 1° in advance of the vertical. The Constant Vertical Pull of Gravity being 1000.

The above table gives the various amounts of upward forces

required at different angles to obtain resultants desired in a

horizontal direction and at angles of 5° and 10° above the horizontal, taking 1000 as the constant vertical pull of gravity. From this table (which any mathematician can verify) it is easy to calculate the force of upward thrust required for a body of given weight to walk, run, or fly.

How, then, are we to obtain this upward thrust in the air? The air, unlike the ground, has no visible solidity upon which to obtain a fulcrum. It is easy enough to appreciate that the legs of animals have solid substance upon which to obtain resistance. We can see that substance. It is, however, more difficult for those who have not fully studied the air as an element, to appreciate how a bird is capable of finding with its wings as firm a resistance on the air as an animal on land does with its feet. Few think of the solidity of air when it is compressed and yet most people are fully aware of the strength and solidity of an air-cushion when the air cannot escape. The power of the air is enormous; we know the force of the wind when we try to walk against it, but we cannot tell whence it cometh or whither it goeth.' By study, however, we can find a way of harnessing the power contained in the air as a bird is able to do; and it is not a difficult matter to design machinery capable of harnessing the air upon the same principle as that employed by the birds. What, then, is the method of extracting and utilising the great power which the air pcssesses? Having explained the method of progression by utilising the force of gravity in opposition to an upward force, and knowing that gravity is a constant with which we are compelled to reckon, let us investigate how to deal with the air so as to obtain the opposing upward force required.

THE ENERGY OF THE AIR AND HOW TO UTILISE IT

You can have a drop of water or other liquid, but you cannot have a drop of air. Every particle of water tends to cling to every other particle, whereas every particle of air tends to get as far away from every other particle as the surrounding particles will permit.

The writer claims to have discovered many years ago the fundamental source of energy of which the bird is able to take advantage, viz. the expansive energy of the compressed air which exists all round the earth.

Every particle of air has weight and is itself attracted towards the earth by gravity. Owing to the weight of the air above, the lower air becomes proportionately compressed; at sea-level it is calculated to have a pressure of 15 lb. to the square inch under normal conditions.

When a properly shaped curved plane is projected through the

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air, an excess of pressure on the concave surface as compared with a reduction of pressure on the convex surface is produced, and the curved plane is forced to move out of the line of projection, the force giving effect more or less at right angles to the direction of projection. In the case of birds the direction of projection must therefore be more or less horizontal in order to obtain an approximately vertical upward thrust; which thrust, with the opposing vertical pull of gravity, creates the resultant force necessary to continue the projection.

An aeroplane is not supported in the air by simple action and reaction, i.e. by pushing the air downwards to obtain support. An aeroplane is supported mainly by the accumulation of compressed air underneath the faster it is projected through the air, the more is the air compressed and accumulated under it, and yet the movement impressed upon the air over which the curve is projected (produced by the compressed air endeavouring to escape downwards) decreases as the speed of projection increases, because this movement is distributed over a greater area. The disturbance of the air caused by present-day aeroplanes is due almost entirely to the rotation of the propeller.

Enormous power is wasted in causing a propeller to rotate in the air simply to obtain an approximate thrust of 200 lb., for it is this thrust of 200 lb. (varying, of course, with the efficiency of the propeller) that projects the aeroplane through the air, and it is this projection of a curved plane which thus obtains the support of the air. It is not the 40 or 60 h.p. that lifts the machine, but the 200-lb. thrust obtained by using that power to rotate the propeller and give projection to the aerocurve. Is it not more reasonable, therefore, to devote the power to the direct projection of aerocurves through the air and thus obtain the upward thrust? This can be done in a very simple manner by projecting the aerocurves round and round by direct engine-power instead of straight ahead by means of propellers.

If mathematicians and scientists would study the air on the basis of its expanding energy, instead of treating the air as water, much valuable information would soon be acquired. The active energy that is in the air is capable of exerting great force when properly dealt with. The passive resistance of water merely permits weight to float upon its surface.

How BIRDS SOAR AND HOW MACHINES ALSO MAY SOAR

Soaring is a question which has exercised the minds of a large number of keen observers, and given rise to much speculation. The writer ventures to assert that the theory put forward by him accounts for every description of soaring by birds of every variety.

Those who have observed soaring birds will admit that no bird soars straight from the ground. It must first obtain a certain initial air speed. Given, however, this air speed, which is maintained by keeping the upward thrust in advance of the vertical, it acquires this upward thrust owing to the difference of pressure on the concave under-surface of the wings as against the pressure on the convex upper-surface, caused by the projection of these curved wings through the air.

The soaring bird, by this difference of pressure, extracts from the existing expansive forces of the air sufficient energy to give an upward thrust so far in excess of the downward vertical pull of gravity that the resultant force necessary to maintain the initial air speed is in a direction above the horizontal, and this resultant force carries the bird forward and upwards.

This to many may sound like perpetual motion. It is, however, nothing of the sort. The great existing expansive power of the air is the source of the energy employed, and the birds are so formed as to be able to utilise that energy and know instinctively how to do it. Man may also by means of machinery take advantage of, and utilise, this great force which the air is capable of exerting. It has already been done by the aeroplane, but apparently without any definite knowledge of the principle.

What is known generally is that an aerocurve projected through the air supports a weight. Apparently the impression is that in order to rise the aeroplane must be inclined upwards in the direction of motion, and that the curve must be continually pushing the air down at a certain velocity.

This is undoubtedly the case with the greater number of the present-day aeroplanes, but there are some so formed that they will rise at a greater angle than the angle of projection. In fact, some aeroplanes do a considerable amount of soaring when they attain air speed proportionate to their weight and curve. Were an aeroplane to be built with the proper curve, and with the resistance of the wire stays, landing chassis, etc., as far as possible eliminated, as also the drag of the propeller, and could it thus be projected into the air at its correct air speed, it should be able (if properly balanced) to keep the angle of upward thrust so far in advance of the vertical as to maintain its air speed and yet rise in the air.

In order to rise, this air speed must be sufficient to create an upward thrust so far in excess of the downward pull of gravity that the resultant force is in a direction above the horizontal, and it would thus soar like a bird. It is believed that this has actually been accomplished by Mr. Weiss with his model bird, on one or two occasions, for considerable distances; but the variation of air currents is such that, of course, it is impracticable, for an entirely

automatic structure, to continue ad infinitum. There must be intelligence to provide for the regaining of speed or stability lost for the moment by the alteration of air currents. There is no reason, however, why man should not successfully construct a machine that will soar, provided it is of sufficient size to contain the intelligence necessary to combat irregular air currents. (Since writing this the Wright Brothers in America have practically accomplished soaring.)

At the same time it must not be forgotten that soaring can only be attained when sufficient initial air speed has been acquired. Thus any machine made by man must have means of attaining that initial air speed which the bird acquires by flapping or jumping off from a height.

It would not be advisable for a machine carrying a number of passengers to attempt that latter method of obtaining air speed.

It is true the Wright Brothers originally (in a most ingenious manner) obtained their initial air speed by being projected somewhat after this fashion, but it is not practical for commercial aerial locomotion. To obtain initial air speed a rotary motion, giving the same result as the flapping motion of the bird's wing, should be employed in other words, rotary wings. The rotary wings should be designed so as to offer as little resistance as possible to the forward motion of the machine, their duty being simply to give the necessary upward thrust.

Both the fixed and rotary wings should be so formed as to extract the greatest possible amount of expansive energy from the air in an upward direction.

The 'gyropter' (a word registered by the writer), meaning rotary wing, is not a propeller, nor can it be classed as a helicopter. It is not designed to screw itself through the air in the direction of its axis, or, by pushing the air downwards, to impart upward motion to the structure, as a screw propeller in water imparts a forward motion to a vessel by pushing the water backwards. The 'gyropter' is designed to obtain by a rotary motion the same upward thrust in opposition to the downward pull of gravity as the flapping wings, and the passive outspread wings of birds, obtain by the blades being projected through the air in such a manner as to extract and utilise the practically constant energy of the expansive force of the air.

It is admitted by those who have carefully observed birds in flight, that the motion of the wings in flapping flight is not downwards and backwards, as would be considered correct for forward propulsion, but that the flap is invariably downwards and forwards.

The general but erroneous impression seems to be that by some marvellous flex of the wing the bird is propelled in the