I shows the slips corresponding to the numbers 2, o, 8, 5 placed side by side in contact with one another, and next to them is placed another slip containing, in squares without **diagonals**, the first nine digits.

The octahedral formula discussed by Julius Thomsen (Ber., 1886, 19, p. 2 944) consists of the six carbon atoms placed at the corners of a regular octahedron, and connected together by the full lines as shown in (I); a plane projection gives a hexagon with **diagonals** (II).

Arrangements connected with Claus' formula are obtained by placing six tetrahedra on the six triangles formed by the **diagonals** of a plane hexagon.

The C.P. of water lines passing through a fixed point lies on a straight line, the antipolar of the point; and thus the core of a triangle is a similar triangle of one quarter the size, and the core of a parallelogram is another parallelogram, the **diagonals** of which are the middle third of the median lines.

In bottom booms and **diagonals**, 6 o tons in top booms, 5.

9), which, on transverse section, have the form of a cross constituting the two **diagonals** of the rhombic or squarish pattern of the mineral.

The anthelion (a) may be explained as caused by two internal reflections of the solar rays by a hexagonal lamellar crystal, having its axis horizontal and one of the **diagonals** of its base vertical.

Consider, for example, a frame whose sides form the six sides of a hexagon ABCDEF and the three **diagonals** AD, BE, CF; and suppose that it is required to find the stress in CF due to a given system of extraneous forces in equilibrium, acting on the joints.

For the condition of equilibrium of forces not parallel is that they shall be represented in direction and magnitude by the sides and **diagonals** of certain parallelograms, and of parallel forces that they shall divide certain straight lines in certain ratios; and the parallel projection of a parallelogram is a parallelogram, and that of a straight line divided in a given ratio is a straight line divided in the same ratio.

One form consists of adjustable **diagonals**, rods or bars, properly fastened to the columns in the building; these **diagonals** may run through one floor and be attached to the columns at the floor above.