approaches or retreats from the point C, as the coefficient of friction diminishes or increases, continually finding new conditions of equilibrium. The arc of contact is thus too small to withstand the pressure without abrasion of one or both surfaces.

It will thus be seen that the journal, or pivot, should fit its bearing closely; but it should be borne in mind that no tendency to "bind" should be produced, the fitting being such that the wheel will turn readily with a minimum pressure.

The film of oil which must be interposed between the bearing surfaces of the journal, or pivot, and its bearing, will also occupy some space; and this must be remembered, particularly in the case of pivots in the escapement.

38. The Laws of Rolling Friction are not as yet definitely established, because of the uncertainty of the results of experiments, as to the amount of friction due to (1) roughness of surface, (2) irregularity of form, (3) distortion under pressure.

The first and second of these quantities vary inversely as the radius; and the third depends upon the character of the material composing the two surfaces in contact.

It follows, then, that in such minute mechanical contrivances as are used in horology, as the motive force is in some cases very light, the horologist should endeavor to produce, where rolling friction takes place, the maximum—smoothness of surface—regularity of form—adaptation of surfaces (31.)

There are many other points on which the writer would like to dwell, as engaging and disengaging friction, internal friction, etc., etc., but the scope of this paper will not permit.

39. The Friction Of Fluids in horology is of grave importance. It is subject to quite different laws from those met with in the motion of solids in contact. When a fluid moves in contact with a solid the resistance to motion experienced is due to relative motion of layers of fluid moving in contact with each other. At surfaces of contact with a solid the fluid lies against the solid without appreciable relative motion; as the distance from the surface is increased by layer upon layer of the fluid, the relative velocity of the solid and the fluid becomes greater. Fluid friction is, therefore, the friction of adjacent bodies of fluid in relative motion.

While fluid friction acts as a retarding force in mechanism it converts the mechanical energy required to produce it into its heat equivalent, thus raising the temperature of the mass in a greater or lesser degree.

The resisting property which thus effects this conversion, and which is the cause of fluid friction, is called viceosity.

It is thus apparent that a variation of the viceosity of the oil used on a watch would cause a variation of fluid friction and consequently a variation of the effort (11), and would seriously interfere with the rate of the watch. This will be discussed (84) more thoroughly in another paragraph.

40. The Laws of Fluid Friction are:

1. Fluid friction is independent of the pressure between the masses in contact.

2. Fluid friction is directly proportional to the surfaces between which it occurs.

3. This resistance is proportional to the square of the relative velocity at moderate and high speeds, and to the velocity nearly at very low speeds.

4. It is independent of the nature of the surfaces of the solid against which the stream may flow, but it is dependent to some extent upon the degree of roughness of those surfaces.

5. It is proportional to the density of the fluid and is related in some way to its viscosity.

41. The Compound Friction of Lubricated Surfaces, as Thurston terms it, or friction due to the action of surfaces of solids partly separated by a fluid, is observed in all cases in which the rubbing surfaces are lubricated. The solids, in such instances, though partly supported by the layer of lubricant which is retained in place by adhesion (21) and cohesion (20), usually rub on each other more or less, as they are usually not completely separated by the liquid film interposed between them.

Wear is produced by the rubbing together of the two solids; and the rate at which the lubricant becomes discolored and charged with abraded metal indicates the amount of wear.

The journal and bearing are forced into close contact in the case of heavy pressures and slow speeds, as is shown by their worn condition; while the journal floats on the film of fluid which is continually interposed between it and the bearing, in the case of very light pressures, and high velocities; in the latter instance the friction occurs between two fluid layers, one moving with each surface.

With heavy machinery, as the hardness and degree of polish of the surfaces cannot be increased in proportion to their weight, the solid friction is so great that while the interposition of a lubricant between the surfaces adds fluid friction, it also reduces the solid friction; and as the fluid friction is so insignificant as compared to the solid friction, the former is almost completely masked by the latter. In this case the laws of solid friction are more nearly applicable.

But in a delicate machine like a watch, especially in the escapement, where the power is so light, and where the rubbing surfaces are so hard, smooth and regular, the solid friction is so minute as compared to the fluid friction, that the former is relatively very slight, as compared with the latter. The laws of fluid friction are more nearly applicable in this instance.

There are thus, evidently, two limiting cases between which all examples of satisfactorily lubricated surfaces fall; the one limit is that of purely solid friction, which limit being passed, and sometimes before, abrasion ensues; the other limit is that at which the resistance is entirely due to the friction of the film of fluid which separates the surfaces of the solids completely.

42. The Laws of Friction of Lubricated Surfaces are evidently neither those of solid friction nor those of fluid friction, but will resemble more nearly the one or the other, as the limits described in the previous paragraph are approached. The value of the coefficient of friction varies with every change of velocity, of pressure, and of temperature, as well as with the change of character of the surfaces in contact.

For perfectly lubricated surfaces, were such attainable, assuming it practicable with complete separation of the surfaces, the laws of friction, according to Thurston, would become:

1. The coefficient is inversely as the intensity of the pressure, and the resistance is independent of the pressure.

2. The friction coefficient varies as the square of the speed.

3. The friction varies directly as the area of the journal bearing.

4. The friction varies as the temperature rises, and as the viscosity of the lubricant is thus decreased (80).

43. The Methods of Reducing Waste of Energy Caused by Friction in time keeping mechanisms are based upon a few simple principles. It is evident that to make the work and power so lost a minimum, it is necessary to adopt the following precautions:

1. Proper choice of materials for rubbing surfaces (29-32).

2. Smooth finish and symmetrical shape of surfaces in contact (29-32 and 38).

3. The use of a lubricant the viscosity of which is adapted to the pressure between the bearing surfaces (80).

4. The best methods for retaining the lubricant at the places required, and for providing for a continual supply of the lubricant.

5. The bearing surfaces of such proportions that the lubricant will not be expelled at normal pressure.

6. The reducing of the diameters of all journals, shoulders