If two such W2 0 - - **hyperboloids** E, F, equal or E T unequal, be placed in the closest possible contact, as in fig.

The motion of two such **hyperboloids**, turning in contact with each other, has hitherto been classed amongst cases of rolling ~ contact; but that classification is not strictly correct, for, although the corn ponent velocities of a pair of points of G contact in a direction at right angles --- to the line of contact are equal, still, - F as the axes are parallel neither to each - other nor to the line of contact, the velocities of a pair of points of contact FIG have components along the line of contact which are unequal, and their difference constitutes a lateral sliding.

The directions and positions of the axes being given, and the required angular velocity ratio, the following construction serves to determine the line of contact, by whose rotation round the two axes respectively the **hyperboloids** are generated: In fig.

~ A pair of thin frusta of a pair of **hyperboloids** are used in practice to communicate motion between a pair of axes neither parallel nor intersect- FIG.

II the velocity ratio to be communicated were variable, the point D would alter its position, and the line DT its direction, at different periods of the motion, and the wheels would be **hyperboloids** of an eccentric or irregular cross-section; but forms of this kind are not used in practice.