over this like the three legs of a tripod stand. The matches then form the skeleton of a regular tetrahedron. (See figure 11.)

A framework formed upon this model of six equal rods fastened together at the ends constitutes a tetrahedral cell possessing the qualities of strength and lightness in an extraordinary degree.

It is not simply braced in two directions in space like a triangle, but in three directions like a solid. If I may coin a word, it possesses "three-dimensional" strength; not "two-dimensional" strength like a triangle, or "one-dimensional" strength like a rod. It is the skeleton of a solid, not of a surface or a line.

FIG. 12-FOUR-CELLED TETRAHEDRAL FRAME

rods end to end so as to form four equilateral triangles.

Most of us no doubt are familiar with the common puzzle-how to make four triangles with six matches. Give six matches to a friend and ask him to arrange them so as to form four complete equilateral triangles. The difficulty lies in the unconcious assumption of the experimenter that the four triangles should all be in the same plane. The moment he realizes that they need not be in the same plane the solution of the problem becomes easy. Place three matches on the table so as to form a triangle, and stand the other three up

FIG. 13-SIXTEEN-CELLED TETRAHEDRAL

FRAME

It is astonishing how solid such a framework appears even when composed of very light and fragile material; and compound structures formed by fastening these tetrahedral frames together at the corners so as to form the skeleton of a regular tetrahedron on a larger scale possess equal solidity.

Figure 12 shows a structure composed of four frames like figure 11, and figure 13 a structure of four frames like figure

12.

When a tetrahedral frame is provided with aero-surfaces of silk or other material suitably arranged, it becomes a tetra

hedral kite, or kite having the form of a tetrahedron.

The kite shown in figure 14 is composed of four winged cells of the regular tetrahedron variety (see Fig. 10), connected together at the corners. Four kites like figure 14 are combined in figure 15, and four kites like figure 15 in figure 16 (at D).

Upon this mode of construction an empty space of octahedral form is left in the middle of the kite, which seems to have the same function as the space between the two cells of the Hargrave box kite. The tetrahedral kites that have the largest central spaces preserve their equilibrium best in the air.

reason why this principle of combination should not be applied indefinitely so as to form still greater combinations.

The weight relatively to the wingsurface remains the same, however large the compound kite may be.

The four-celled kite B, for example, weighs four times as much as one cell and has four times as much wing-surface, the 16-celled kite C has sixteen times as much weight and sixteen times as much-wing surface, and the 64-celled kite D has sixty-four times as much weight and sixty-four times as much wing-surface. The ratio of weight to

FIG. 14-FOUR-CELLED TETRAHEDRAL KITE

The most convenient place for the attachment of the flying cord is the extreme point of the bow. If the cord is attached to points successively further back on the keel, the flying cord makes a greater and greater angle with the horizon, and the kite flies more nearly overhead; but it is not advisable to carry the point of attachment as far back as the middle of the keel. A good place for high flights is a point half-way between the bow and the middle of the keel.

In the tetrahedral kites shown in the plate (Fig. 16) the compound structure has itself in each case the form of the regular tetrahedron, and there is no

FIG. 15-SIXTEEN-CELLED TETRAHEDRAL

KITE

surface, therefore, is the same for the larger kites as for the smaller.

This, at first sight, appears to be somewhat inconsistent with certain mathematical conclusions announced by Prof. Simon Newcomb in an article entitled "Is the Air-ship Coming," published in McClure's Magazine for September, 1901-conclusions which led him to believe that "the construction of an aerial vehicle which could carry even a single man from place to place at pleasure requires the discovery of some new metal or some new force.

The process of reasoning by which Professor Newcomb arrived at this re

markable result is undoubtedly correct. His conclusion, however, is open to question, because he has drawn a general conclusion from restricted premises. He says:

"Let us make two flying-machines exactly alike, only make one on double the scale of the other in all its dimensions. We all know that

the volume, and therefore the weight, of two similar bodies are proportional to the cubes of their dimensions. The cube of two is eight: hence the large machine will have eight times the weight of the other. But surfaces are as the squares of the dimensions. The square of two is four. The heavier machine will therefore expose only four times the wing surface to the air, and so will have a distinct disadvantage in the ratio of efficiency to weight."

a giant kite that should lift a manupon the model of the Hargrave box kite. When the kite was constructed with two cells, each about the size of a small room, it was found that it would take a hurricane to raise it into the air. The kite proved to be not only incompetent to carry a load equivalent to the weight of a man, but it could not even raise itself in an ordinary breeze in which smaller kites upon the same model flew perfectly well. I have no doubt that other investigators also have fallen into the error of supposing that large structures would necessarily be capable of flight, because exact models of them,