~27. Work~ is the result of force acting through s.p.a.ce. When force produces motion, the result is work. _Work is measured by the product of the resistance into the s.p.a.ce through which it is overcome._

~28. Energy~, which is defined[6] as the capacity for doing work, is either _actual_ or _potential_. _Actual_ or _kinetic energy_ is the energy of an actually moving body, and is measured by the work which it is capable of performing while being brought to rest under the action of a r.e.t.a.r.ding force.

_Potential Energy_ is the capacity for doing work possessed by a body in virtue of its position, of its condition, or of its intrinsic properties. A bent bow or a coiled spring has potential energy, which becomes actual in the impulsion of the arrow or is expended in the work of the mechanism driven by the machine. A clock weight, condensed air and gunpowder are examples.

This form of energy appears in every moving part of every machine and its variations often seriously affect the working of machinery. (84.)

FOOTNOTES:

[5] This and some of the definitions that follow are adapted from "Elements of Physics" by A. P. Gage.

[6] Thurston. "Friction and Lost Work in Machinery," from which excellent work much of the next chapter is adapted.

CHAPTER III.

FRICTION--ITS NATURE AND THEORY.

~29. Friction.~ The relative motion of one particle or body in forced contact with another is always r.e.t.a.r.ded, or prevented, by a resisting force called friction.

Friction manifests itself in three ways: Between solids it is called _sliding_ and _rolling friction_; between the particles of liquids, or of ga.s.ses, when they move in contact with each other, or with other bodies, it is called _fluid friction_. Quite different laws govern these three kinds of friction, as they are quite different in character.

Friction can never of itself produce or accelerate motion, being always a resisting force, acting at the surfaces of contact of the two particles, or ma.s.ses, between which it occurs, and in the direction of their common tangent, resisting relative motion in whichever direction it may be attempted to produce it. The greatest loss of energy in a timepiece in which all the parts are rigid enough to prevent permanent distortion, is that occurring through friction. Another source of loss of energy is the reduction in elasticity of springs caused by a rise of temperature.

~30. The Cause of Sliding Friction~ is the interlocking of the asperities of one surface with those of another; and only by the riding of one set over the other, or by a rubbing down or tearing off of projecting parts, can motion take place. It follows, then, that roughness is conducive to friction; and that the smoother the surface the less the friction will be.

~31. The Cause of Rolling Friction~ is the irregularity and lack of symmetry of the surfaces between which it occurs. It acts as a resisting, or r.e.t.a.r.ding, force when a smoothly curved surface rolls upon another surface, plane or curved.

Motion is prevented, or r.e.t.a.r.ded, by the irregular variation of the distance between the center of gravity and the line of motion in the common tangent of the two bodies at the point of contact, caused by the irregularity of form, or of surface, in the one or the other body.

Rolling friction is small where hard, smooth, symmetrical surfaces are in contact, and increases as the surfaces are soft, rough or irregular.

In a knife edge support, seen in some forms of pendulums, is exhibited a form of rolling friction.

~32. Solid Friction~, either sliding or rolling, could be overcome if it were possible to produce _absolutely_ smooth surfaces. It is evident, then, that the character of the material, as well as the form of their surfaces, determines the amount of friction.

In all time-keeping mechanism both sliding and rolling friction manifest themselves; the former princ.i.p.ally between the surfaces of pivots and bearings and in the escapements, the latter mainly between the surfaces of the teeth of wheels, and to some extent in some of the pivots, and sometimes in parts of escapements. It is not the intention of the author to treat of the proper shape of the teeth of wheels, leaves of pinions, or the proportions of the escapements, the nature and scope of this work not permitting of it; but he will confine his remarks princ.i.p.ally to the parts that involve lubrication.

~33. The Laws of Sliding Friction~, as given by Thurston,[7] with solid, unlubricated surfaces, are, up to the point of abrasion, as follows:

1. The direction of frictional resisting forces is in the common tangent plane of the two surfaces, and directly opposed to their relative motion.

2. The point, or surface, of application of this resistance is the point, or the surface, on which contact occurs.

3. The greatest magnitude of this resisting force is dependent on the character of the surfaces, and is directly proportional to the force with which two surfaces are pressed together.

4. The maximum frictional resistance is independent of the area of contact, the velocity of rubbing, or any other conditions than intensity of pressure and condition of surfaces.

5. The friction of rest or quiescence, "statical friction," is greater than that of motion, or "kinetic friction."

He further states that these "laws" are not absolutely exact, as here stated, so far as they affect the magnitude of frictional resistance. It is found that some evidence exists indicating the continuous nature of the friction of rest and of motion.

When the pressure exceeds a certain amount, fixed for each pair of surfaces, abrasion of the softer surface or other change of form takes place, the resistance becomes greater and is no longer wholly frictional.

When the pressure falls below a certain other and lower limit the resistance may be princ.i.p.ally due to adhesion, an entirely different force, which may enter into the total resistance at all pressures, but which does not always appreciably modify the law at high pressures.

This limitation is seldom observable with solid, unlubricated surfaces, but may often be observed with lubricated surfaces, the friction of which, as will presently be seen (41), follows different laws. The upper limit should never be approached in machinery.

The coefficient of friction is that quant.i.ty which, being multiplied by the total pressure acting normally to the surfaces in contact, will give the measure of the maximum frictional resistance to motion.

~34. Sliding Friction is Proportional to Pressure~ according to the third law quoted above. This is easily demonstrated by ascertaining what force is necessary to produce, or continue, motion in a body lying on a plane surface; double the weight of the body and the force required to produce, or continue, motion, will have to be doubled. The converse is also true (36).

~35. Sliding Friction is Independent of the Area Of Contact~, the pressure remaining the same (law 4, 33).

This is accounted for by the fact that if, for example, the area of contact be doubled, though twice the number of asperities will present themselves, each individual r.e.t.a.r.ding force is only half of what it was previously, and the general effect is the same (36).

~36. The Intensity of Sliding Friction is Independent of Velocity.~ (Law 4, 33.) This is explained by the fact that the interlocking of the asperities on each surface has a shorter time to take place in increased speed, and consequently cannot be so effective as with slow speed. But with high speed more asperities are presented than in low speed, so the effect is the same in both cases.

_The above (33-36) are not exact, being the statement of experimental laws, and admit of considerable modification when applied in horological science, as will be shown (41-42.)_

[Ill.u.s.tration: Fig. 12.]

~37. The Effect of a Loose Bearing~ is an increase of friction, and consequently a loss of energy, resulting in the wear of _one_ or _both_ surfaces in contact, according to conditions. In Fig. 12, A is a loose bearing, B a journal at rest and C the point of contact. If the journal be now turned in the direction of the arrow by the motive force, it will have a tendency to roll over a short arc of the bearing to a new point of contact, as at D, when it begins to slide; so long as the coefficient of friction is unchanged it retains this position; but 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_ s.p.a.ce; 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 quant.i.ties 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.