Pivots, in horology, the portions of the arbors carrying the wheels that support them as they receive the rotating motion imparted by the motive force.

Motive force in horology is the power that drives clocks and watches. There are two kinds: weight and elasticity. The first is employed in the form of a weight fitted to large clocks; the second employing a spring instead of the weight, fitted to small clocks and all watches. See Impulse arc, where you will see how to measure motive force in clocks and watches.

Pivots must therefore be strong enough to withstand that force, in proportion to the effort they receive, so that they may not bend or break.

Since pivots are pressed by the force applied to them, as a consequence they undergo the same resistance that friction causes in all bodies pressed together to impart motion to them; with this difference, however, that friction can be decreased in pivots without decreasing the pressure. But since almost nothing positive is known about the nature of friction ( see Friction, Horology ), in this article we shall merely report the experiments we have made, not to determine a law of original friction, but only relatively: the relationship of friction from the same pressure on pivots of various diameters. ( See Machine, etc.)

These experiments show that the friction in pivots of different diameters is exactly proportional; for example, pivots double or triple in size have twice or three times the friction, etc.

Horology, [Section II], Plate [I] A [key f], Machine with several uses: 1) To experiment on pivot friction relative to diameter. 2) To test watches in all positions. 3) As a compass whose needle rests on two extremely fine pivots .

Figure 1. Top view of the machine; circle MI is a mirror secured by three screws, VVV. PPP are three studs that fit a holder, M, Figure 2, with three notches, EEE, that fit into the three studs, PPP, Figure 1. The holder is for a watch or repeater movement, and mirror MI affords a view of the going balance when underneath.

Figure 3 shows a compass that is familiar in every respect except its needle, which instead of a single pivot has two that are very fine; their diameter is only one thirty-sixth of a ligne . The advantage of suspension on two pivots lies in eliminating all motion not associated with the magnetic current that affects needles with a single pivot , for example oscillating vertically; with two pivots , the needle can only turn correctly, without oscillating.

Figure 1, ABCDEF, is the mechanism shown below, in which several balances can be substituted.

DD is an index plate.

EE is another index plate.

SS is a spiral spring.

See [Horology, Section II] Plate [II] A, [key g], Figure 1, showing the same mechanism in front view.

CC is a balance wheel concentric to index plate DD.

EE is another index plate, mounted on post A.

SR is an elastic strip whose end R acts on a very small lever perpendicular to the axis of the balance wheel.

PP is a thread that when pulled draws the elastic strip through an arc. When the thread is released, end R brushes past a small lever mounted for this purpose on the balance staff, and this contact imparts motion to the balance.

But since the balance has a spiral, SS, it follows that strip R imparts to the spiral spring an alternating motion of contraction and expansion, its elasticity imparting to the wheel a certain number of vibrations before it stops. The number and the scope of these vibrations are greater as the pivots of the balance staff are smaller and the tension of the small strip SR is greater. Index plates DD and EE were installed in order to measure these two things.

1, 2, 3, and 4 are various arbors with pivots of different diameters, which fit by friction into pipes swaged to the balance, for easy substitution when changing experiments.

x x are two spiral springs of different stiffness, which fit on all the staffs.

PP are studs that fit by friction into pivot-carrier F, which has a hole for the end of spiral spring SS, the other end being secured to the balance staff.

This illustration shows that the machine is supported by a pedestal, QQ, which has a ball joint at G to give any desired tilt; that sector LL is used to measure the degrees of inclination given to the base plate, HH; and that sector LL fits the foot of the pedestal by friction, allowing it to be rotated around base plate HH.

K is a collar to which sector LL is secured by means of screw M; screw N sets collar K on column OO, secured by nut Z under the crown of pedestal QQ.

Between the three feet is located compass B, seen from the side.

Horology, [Section II,] Plate [III] A, [key h]. The same machine in side view, instead of in front view as in the preceding plate.

Figure 2, solid balance wheel.

Figure 3, solid sphere.

Figure 4, socket piece for the pedestal ball joint.

SS, spiral spring

MM, FF, pivot carrier for the balance staff.

x , balance staff.

DD, CC, index plates.

AA, post holding the elastic strip.

PPP, studs for the movement holder.

LL, indexed sector plate.

[Horology] Plate IV A [key i], Figure 1, the same machine seen with the movement holder in place, holding a watch movement, the balance reflected in mirror MI. [1]

Figures 2 & 3, two balance wheels.

Horology, [Section II,] Plate V A (key k], the same machine seen from below.

Figure 2 is a pair of dividers for measuring pivots ; legs AB are to legs AP as 12 is to 1, so if opening BCB is one pouce , opening PCP will be one ligne .

KK is a screw for adjusting the dividers very gradually when the pivots are very small, for example the ones for the compass, which are the finest it is possible to make, just fitting in the small opening PCP. I measured the other opening on an inch divided into lignes and parts of a ligne , and I found the opening to be one-third of a ligne , which led me to conclude that my pivots were only one thirty-sixth of a ligne in diameter; I believe this is the limit for reducing the diameter of pivots .

Here are the chief experiments that enabled me to determine the friction of pivots as a function of their diameter.

Returning to [Section II,] Plate II A, [key g,] assume balance CC with its spiral spring SS is mounted; by hand I move the balance through a certain arc, but since the balance staff has a spiral spring with the inner end secured to the staff and the outer end secured to the pivot -carrier, it follows that the balance cannot be moved through an arc without contracting or expanding the spiral. If the balance is left to the contractions and expansions of the spiral, the reaction of its elasticity will cause a certain number of vibrations before running down, and the arcs will diminish continually until they stop.

I carefully counted the number of balance vibrations for every 10 degrees of tension in the spiral spring up to 360, and I found that the number of vibrations is essentially proportional to the amount of tension given the spiral spring: at 60 degrees the balance made 9 vibrations; at 70 degrees it made 10; at 80 it made 11; at 90, 12; at 100, 13; etc. However, I noticed that the number of vibrations increased in a slightly smaller proportion as 360 degrees of tension were being reached. I repeated these experiments with the balance staff horizontal, vertical, and at various angles.

I substituted various staffs whose pivots were of different diameters in a given ratio.

I also substituted various balances: a solid disk, a solid sphere, several wheels of different diameters, and finally a wheel whose mass is distant from the pivots ; all these bodies had exactly the same weight, so they always exerted the same pressure on the pivots , which I consider here to be the sole source of friction . I also used the elastic strip to set the balance in motion, making it strike the little lever on the balance staff, to see the difference in motion imparted by a shock and a uniform effort. Finally, in all those various cases, I always found the number of vibrations essentially proportional to the degrees of tension I gave the little strip.

From these first experiments it results that the force released by the different degrees of tension I give to the spiral spring must be considered an active force, which overcomes not only the inertia of the balance but also the resistance of the friction in the pivots to the motion of the balance. Having established that, I shall report the experiments that may finally determine the relationship of that resistance to different diameters of pivots , the inertia of the balance being exactly the same. The pivots of the arbors that I used in my experiments were carefully measured with the dividers in Plate V [A, key k], Figure 1.

1) The smallest is 1/15 ligne in diameter.

2) The medium is 5/15 [2] ligne in diameter.

3) The largest is 9/15 ligne in diameter; so that their relationship is 1 : 5 : 9.

First experiment with the large balance wheel, no. 1. Pivot , 1/15 ligne . The large balance is 41 lignes in diameter and weighs 56 grains ; with 360 degrees of tension on the spiral spring, it made one hundred vibrations and stopped after 220 seconds. The staff was horizontal; I shall not report all the experiments I made with the staff vertical [and] inclined. Suffice it to say that the greatest difference was between vertical and horizontal, the vertical staff making almost a quarter more vibrations than the horizontal, and this number of vibrations was essentially the same for all the degrees of inclination: 10, 20, 30, 40; only after 45 and 50 degrees did the number of vibrations increase, and did so until 90 degrees.

I did not think it necessary to report those experiments because my purpose was to see the number of vibrations for the true diameter of the pivots , whereas with the staff vertical, the diameter of the pivot that bears, and therefore rubs, is always less than the true diameter that rubs when the staff is horizontal. The reason must be understandable: it is impossible to finish the ends of pivots well enough that the true diameter bears fully.

Table of experiments made with various balances, all weighing 56 grains, with the same spiral spring, at the same 360 degrees of tension and the staff horizontal, substituting pivots of various diameters.

[Left of table, opposite the 6 lines]

• 1st Balance, 41 lignes in diameter
• 2nd Balance, 20 1/4 lignes in diameter
• 3rd Balance, 10 1/4 lignes in diameter
• 4th Balance, solid sphere 3 1/4 lignes in diameter
• 5th Balance, solid wheel 21 lignes in diameter
• 6th Balance, 20 lignes in diameter, mass distant from pivots

Note: In all the experiments, when the staff was vertical and supported by the pivot whose mass was below the bearing point, it made a greater number of vibrations; on the contrary, in the opposite position, it made fewer.

I repeated all these experiments with different degrees of tension in spiral springs of different strengths; in all positions, horizontal, vertical and inclined; and even at different temperatures. I always found the number of vibrations proportional to the degree of tension and the diameter of the pivots . Although the number of vibrations varied according to the circumstances, when the same it remained essentially proportional to the diameter of the pivots ; I say essentially because it was impossible for me to perform two precisely identical experiments, despite all my care. It could therefore be objected that since the number of vibrations I report in this example is not exactly proportional to the diameter of the pivots , I may be wrong to conclude.

I reply that besides the fact that the difference is very slight, in the large number of experiments I made, there were often ones that came closer to that proportion. But since my purpose was to report the best-performed experiment, without regard to whether it fits perfectly with the conclusion I draw from it, I had to prefer the one to which I gave all the precision of which I am capable, and the one which I am confident was the most successful; in all these experiments there are degrees of delicacy that are easier to feel than describe, that are not grasped at will. Finally, it must be observed that in a large number of vibrations, one more or fewer makes no difference, while in a small number, one more appears as an object, which distinction must be made in order to disregard it; because in all these cases, when the balance is about to stop, a trifling external cause may produce one vibration more or fewer, with no regard for the preceding one. It is the instant between repose and motion that must be grasped in order to evaluate the true resistance of friction in imparting or maintaining motion, but my goal was not to discover the law of friction in and of itself; that is too difficult, if not impossible [3], but only the relationship of friction to the diameter of the pivots affected by it.

I say therefore that the active force that imparts motion to the balance, determining a certain number of vibrations, encounters no other resistance than the inertia of the balance, plus the friction of its pivots . Now if the inertias are the same and the diameter of the pivots is varied, the number of vibrations will also vary, but in inverse proportion to the diameter of the pivots , as is easily seen in the table of experimental results. Therefore the friction of pivots is proportional to their diameter.

Article by M. Romilly, horologist.

1. The plate does not show a movement in the holder (translator's note).

2. The original gives "5/15" (translator's note).

3. Perhaps in the future I may discover something more specific about this topic, but since the subject matter is abundant and requires a great number of experiments, it is better to reflect further and more precisely before hastening on.