the length of the pendulum, and consequently, by pendulum law, the oscillations must be much quicker and shorter and will at once damp out. It is curious that this point seems to have escaped the designers. It is well known that all pendulum motion tends to damp out, and the shorter the pendulum the quicker it comes to rest. Hitherto the idea has been to shorten it vertically, but the same effect exactly is obtained by shortening it horizontally, and the low centre of gravity remains to give stability. It was stated by some sapient objector to the low centre of gravity, that the pendulum motion once set up, increased till it turned the machine over. A pendulum which increased its swing at every stroke would be something new in the scientific world.

Fig. 4.

Fig. 5.

Another development of the pendulum difficulty is the probable fore and aft sway, but this may be overcome by increasing the supporting surface of the tail. Many machines do not lift with the tail at all, and those that do employ lifting tails, have them with very small surface. Consequently, the centre of gravity comes nearly under the centre of the main plane, and the whole machine, turning on its centre of gravity in all directions as on a pivot, is liable to swing fore and aft. If the supporting surface of the tail be increased and the centre of gravity carried further aft, this pendulum motion is also rendered impossible, and the machine is stable both ways.

A few illustrations may serve to make the advantages of the low centre of gravity more clear, and to avoid complications we will suppose the planes to be still and in still air. Let Fig. 6 represent an ordinary flat plane having its centre of gravity coincident with its centre of pressure, the centre of pressure of each half or wing being at A A. The plane is in equilibrium. Now allow it to tilt (Fig. 7), and it will be seen that it is still in equilibrium, since the weight is in the centre and the wing tips equidistant from it. Let it tilt still more till it is vertical (Fig. 8), and the balance is still the same. It is evident, therefore, that such a plane would travel equally well in any of the positions shown, and that it can only be kept in position (Fig. 6) by the skilful manipulation of the pilot.

Fig. 6., Fig. 7., and Fig. 8.

In the same way, the machine having no lifting tail is longitudinally unstable, for, being balanced on its centre of pressure which would be coincident with its centre of gravity and probably about 2 feet from the trailing edge of the plane—it may assume any position (Figs. 9, 10, 11 and 12), and still be in equilibrium, when it is evident that the proper position (Fig. 9) is only maintained by the constant control of the tail elevator.

Fig. 9., Fig. 10., Fig. 11., Fig. 12., and Fig. 13.

Now take the case of a machine having a low centre of gravity. Its natural position is shown at Fig. 13, and it is at once evident that any other position such as Figs. 14 and 15 could not be maintained for a moment, since the weight being at an angle, must inevitably drag the machine back to its natural position (Fig. 13). In the same way with regard to longitudinal balance, a machine with two lifting surfaces such as Fig. 13, is in its natural position with the centre of gravity perpendicularly under the centre of pressure, any other position, such as Fig. 17, A, is impossible, as the gravity pull must drag the machine along the dotted line till it resumes its proper and natural position (B).

Fig. 14., Fig. 15., and Fig. 16.

The next difficulty is in the banking or tilting caused by the turning of the machine in going round a curve. In a very interesting discussion carried on in the “Aero,” it was stated that a low centre of gravity machine could not bank up, as the pull of gravity acting on the low weight would prevent it. It was also stated by another writer that the machine would bank up too much and slide down sideways, because the greatest weight having the greatest momentum would swing out too much. There is evidently some confusion here. Let us consider the question.

In turning there are three forces to take into consideration:

(1) The centrifugal force, which tends to make the machine fly off at a tangent to the curve at which it is turning.

(2) The action of gravitation.

(3) The extra lift given by the wing on the outside of the curve, owing to the fact that it travels faster through the air.

Fig. 17.

The centrifugal force acts strictly in proportion to the mass it acts on, but, at the same time it must be remembered that the greater force acting on the greater mass has the greater mass to move. That is to say, that if the top part of the machine was very light and the bottom part very heavy, the force acting on the light part would be sufficient to send that part swinging out when rounding a curve, and the greater force acting on the greater mass at the bottom would be sufficient to send that out to exactly the same degree. Consequently, if only centrifugal force is considered, the whole machine would swing out without any tilting at all, retaining its upright position. But here we must take another factor into consideration, the resistance of the air. This resistance would be greater on the greater surface of the light top part than on the heavy bottom part, and consequently the bottom part would, automatically, swing out most, giving the banking effect. This would be increased by the extra lift given to the outer wing by reason of its greater speed. If we then take the force of gravitation into the problem we shall see that we have two factors—unequal speed and unequal air resistance—tending to bank up the machine, and one force—gravity—tending to pull it straight again. At a certain angle due to the amount of force exerted by each of these, the two opposing factors would balance, and the machine would be in equilibrium.

It would appear that most of the difficulties connected with the low centre of gravity machine are the result of hazy thinking and slip-shod reasoning, and that they do not exist in fact. And let it be remembered that the low centre of gravity machine with short span has not yet been tried except by the writer, who has succeeded in making a paper model on this plan turn in its own length without in any way losing its stability, swaying, banking too much, turning over, sliding sideways, or doing any of the frightful things which some people declare it must do. What it does do is to recover its balance though started from the most impossible positions and always land on