Some idea of the nature of these forces and why they give rise to precession may be understood by reference to the diagram, Figure 77. Here we have a disk with a heavy rim turning on the axis X, X′. At _A_, _B_, _C_ and _D_ are four particles whose flights we are going to consider. Suppose the wheel to be at rest; then if _X, X′_ is tilted in the direction of the arrows _x_ _x′_, the wheel will turn about the line _Y Y′_; _D_ will move forward toward _D′_, and _B_ backward toward _B′_, but _A_ and _C_ will remain where they are. Now, suppose, the wheel to be revolving clockwise, or in the direction _A_, _B_, _C_, _D_, then the particle _A_ will pursue a spiral course that will bring it to _B′_, and _C_ will pursue a spiral course that will bring it to _D′_. However, particle _D_ will have an irregular course, as indicated by the dotted line, starting first to move forward and then curving back toward _A_. The same will be true of _B_, except in the reverse direction. The course of particles _D_ and _B_ is, therefore, materially different from that of _A_ and _C_. Now, the particle _D_ will resist being deflected from its course and will develop an opposing force represented by the arrow _d_. A moment later this is reversed as the particle bends back toward the axis _Y Y′_, and we may represent the new force by the arrow _d′_. It may be proved that the force _d′_ is more powerful than that of _d_. The particle _A_ in the meantime exerts a force opposing its deflection, which is represented by the arrow _a_. On the other half of the wheel there are similar but opposite forces, _b_, _b′_ and _c_. The sum of these forces gives the wheel a tendency to turn about the axis _Z Z′_. To avoid complicating our diagram with too many arrows, we had better refer to a new diagram (Figure 78) which shows only the resultant of the forces developed. The application of the forces _x_ _x′_, which would have turned the wheel on the axis _Y Y′_, had it been stationary, have resulted in the development of forces _z_ _z′_ at right angles to _x_ _x′_, tending to turn the wheel about the axis _Z Z′_. Now, if we go through the same processes of reasoning as before, it will be evident that the forces _z_ _z′_ will result in a third set of forces _y_ _y′_ at right angles to _z_ _z′_ tending to turn the wheel about the axis _Y Y′_. The forces _y_ _y′_ exactly balance the forces _x_ _x′_, and hence the wheel does not turn about the axis _Y Y′_ in response to the original forces, but starts instead to revolve slowly about the axis _Z Z_. Because the forces _x_ _x′_ and _y_ _y′_ balance each other, there is no fourth couple developed and hence no opposition to the forces _z_ _z′_. [Illustration: FIG. 78.--DIAGRAM EXPLAINING PRECESSIONAL MOVEMENT OF A GYROSCOPE]