A viewer sent in a question that was so good it deserved its own blog post as it references two hundred years of adjusting theory. Here it is in his own words.
“I’ve always wondered about the line of eccentricity, the eccentric linear direction of breathing, on a flat hairspring as it corresponds with the line of centers, the line between center of oscillation and center of suspension. Kleinlein talks about this in Rules and Practice for Adjusting Watches, sections 32 to 36. I notice they never line up on any modern post-quartz-crisis watch. They’re always 5 to 10 degrees off. Is this done on purpose? I’d think orienting the hairspring so those two lines match would reduce some vertical timing errors by forcing the hairspring’s natural weight error to fall on a known axis, or at least make the positional errors more predictable rather than scattered diagonally across all of them.”
Good question, and I think the instinct behind it is the right instinct. It’s just aimed at a target watchmakers already hit, two centuries ago, by a different route. By the end of this article. you’ll see why the offset is built into the spring rather than chosen, why closing it would make your watch harder to adjust instead of easier, and why the 5 to 10 degrees you keep measuring is perhaps partly an artifact of where you’re measuring from.
The short version
Yes, it’s deliberate. No, lining the two up wouldn’t tighten your vertical positions. It would do the opposite, and on a modern watch you’re probably measuring the offset against the wrong point.
A flat spring can’t breathe evenly
A flat spiral doesn’t expand the same on every side. It develops harder on one side than the other, and you can’t poise that out of it. The Theory of Horology states the reason flatly in section 7.5.3: “In the case of a normal flat spring whose outer end is fixed to the balance cock by a stud concentric development is impossible.” Section 7.10.4 gives the mechanism. A spring can’t unwind concentrically because it’s pinned at both ends, so its centre of gravity can’t stay on the staff axis, and that eccentricity throws an extra couple on top of the spring’s normal torque. The “extra couple” is that stray rotational nudge riding on top of the good torque. It’s small, but it changes with the watch’s position and with amplitude, and that variation is what shows up as positional error.
That’s the key thing to notice. The offset isn’t something an adjuster sets and could choose to set to zero. It’s a property of any spiral pinned at two points. Kleinlein says the same from the bench in section 34: the natural error exists “because it is impossible to perfectly poise a spiral spring,” and he measures it at twelve to fifteen seconds even in a finely made watch. The error is going to exist. The only question an watchmaker gets to answer is where it lands. On the spring, the offset is the distance between the staff axis, where the pivots hold the balance and push back, and the line the off-center spring force actually acts along. The spring pulls slightly to one side of the axis, the pivots react on the axis, and the little gap between those two lines is the lever arm that produces the stray turning moment.
What you’re actually reaching for
When you talk about forcing the weight onto a known axis, you’re describing a real fix. The French mathematician Edouard Phillips worked out the theory of it in 1861, building on the overcoil that Arnold and Breguet had made by hand a century earlier. The Theory of Horology gives Phillips’ condition in 7.5.3: “The centre of gravity of the spring, at rest and in movement, should be at its centre, i.e. on the balance staff. When this is the case, the pivots do not apply any pressure on the balance jewels.”
That’s the genuine article. The spring’s weight taken out of the equation, no side load on the pivots, no scatter across the vertical positions. The catch, in the same section, is that a plain flat spring can’t get there. The Breguet overcoil and the Phillips terminal curve are the ones that do, and they’re why a good overcoil watch holds its positions the way it does. Most modern movements traded that away for a flat spring because a flat spring is cheaper to make and fit. So orienting a flat spring to put the weight on an axis is chasing a result the overcoil already delivers, on a spring that isn’t built to deliver the same results.
Where the error goes is the whole game
What the watchmaker or manufacture controls instead is the pinning point at the collet. Move it and you move the spring’s heavy point, which moves the error from one position to another. Kleinlein lays out four places to pin. Two sit on the horizontal line through the collet. Pin there and the spring develops upward as it leaves the collet, the watch runs fast pendant up against pendant down, and pendant right and left compare closely. Pin opposite and you get the slow point with everything reversed. The other two sit on the vertical line through the collet, and that’s the orientation where the breathing direction comes closest to lying on the staff-to-stud axis. Your aligned case.
Here’s why nobody uses it. Kleinlein, section 33: “The vertical points of attachment are seldom used, for the reason that the variation between the pendant right and left positions would be very difficult to control, due to the existence of the natural error.” Pin on the vertical and pendant up and down do come together, which looks like progress. But the error you couldn’t poise out doesn’t disappear. It moves into pendant right and left, the two positions a wristwatch spends most of its life in. Aligning the lines doesn’t park the weight on a tidy axis. It dumps it into the worst place on the dial.
The standard setting does the reverse on purpose. Develop upward, take the fast pendant-up rate, keep right and left close, and put the unavoidable error in pendant down, where Kleinlein says it does the least harm. The Theory of Horology states the aim of the whole exercise in 7.10.4: “The watchmaker will attempt to create a gain at low amplitudes in order to compensate for the loss caused by the escapement and the curb pins.” The few degrees of offset you see aren’t a miss. They’re the watchmaker placing the heavy point and buying that low-amplitude gain, trimming an eighth above or below the horizontal line at a time, which is what I think Kleinlein is saying in section 35.
The physics says ninety degrees, not zero
The elastic side thrust from the eccentric breathing is the Caspari effect, and it acts in every position. The Theory of Horology, 7.10.4, notes that in movements under 30 mm this elastic effect is larger than the Grossmann gravity effect, and cites Robert finding it about three times stronger in a 23 mm movement. So on a modern wristwatch the eccentric breathing dominates the weight error you’re focused on, not the other way around.
The same section gives the Caspari rule outright: the inner pinning point should sit at 90 or 270 degrees to the outer pinning point for the balance to run isochronously. Ninety degrees off the line, not on it. Put the two lines colinear and you sit at the extreme of that effect, gaining hard at low amplitude on one side and losing hard on the other. That’s the disturbance you were trying to remove, turned up to maximum.
You’re probably measuring to the wrong point
Now the 5 to 10 degrees. You’re defining your line of centers as staff to stud. On a wristwatch the spring isn’t referenced to the stud. The Theory of Horology, 7.10.4: “In a wristwatch, the outer setting does not generally affect the stud. In fact the curb pins already play a role. The effective setting point will be approximately one third of the way between the index and the stud.” And the pinning point that gives the most low-amplitude gain sits “on a radius which passes between the pins and the stud, but closer to the pins, or at the real counting point.”
So the spring is built around the staff-to-counting-point radius, and the counting point lives about a third of the way from the curb pins toward the stud. The gap between that point and the stud is a very plausible source of the steady few degrees you read against the stud. You’re measuring to the stud on a watch that was laid out to the counting point. Measure to the counting point and the offset would look different, and probably smaller.
These sources aren’t all describing the same watch
It’s worth keeping in mind when you put Kleinlein next to the rest. His book is copyright 1920, and he’s writing about American pocket watches, hunting models and the like, almost all of them running an overcoil. His whole pinning-point geometry comes out of that world.
The flat spring you’re actually asking about is a later problem. The Theory of Horology says so in 7.10.4: the classical work from Grossmann, Caspari and the others was done on helical springs, and “in the middle of the 20th century many adjusters adapted their theories to the wristwatch and to flat springs.” Jendritzki is one of the adjusters who did that adapting, and The Theory of Horology is a modern text built around the wristwatch as the normal case. So Kleinlein gives you the principle, the natural error and where you choose to put it, but his reference points were laid out for a pocket watch with an overcoil. The closer you get to a modern flat-spring caliber, the more the wristwatch sources earn their place, and the counting point from the last section is exactly the kind of thing Kleinlein had no reason to write about in 1920.
One last thing
“Line of eccentricity” and “line of centers” aren’t Kleinlein’s terms. He works off a vertical and a horizontal line through the collet, so when you go back to sections 32 through 36, read for the idea and not the phrasing. The Theory of Horology speaks in pinning point, point of attachment, centre of gravity, and counting point, and that vocabulary maps onto a modern movement cleanly. The next time a flat-spring watch comes across your bench with the breathing direction sitting a few degrees off, the question isn’t whether to close that gap. It’s where the adjuster decided to put the twelve seconds nobody can get rid of.
Sources
Walter J. Kleinlein, Rules and Practice for Adjusting Watches (copyright 1920).
- Section 32, “How to Find the Correct Collet Pinning Point for Any Watch” — locating the point of attachment, the spring developing right, left, or upward from the collet.
- Section 33, “Results in Vertical Position Rates Due to Changing the Pinning Point” — the fast and slow points, the vertical points of attachment and why they are seldom used, placing the error in pendant down.
- Section 34, “The Natural Position Error and Why it Cannot be Eliminated” — the impossibility of poising a spiral spring, the twelve-to-fifteen-second figure.
- Section 35, “Principle of Pinning Point Alterations” — trimming the pinning point an eighth above or below the horizontal line to adjust the rate.
The Theory of Horology, Chapter 7 (Regulating Organs).
- Section 7.5.3, “The flat balance spring and the Breguet overcoil” — concentric development being impossible for a flat spring, and Phillips’ 1861 condition that the centre of gravity sit on the balance staff.
- Section 7.10.4, “Disturbances caused by the pinning point” — the eccentric couple, the goal of creating gain at low amplitude, the Grossmann and Caspari effects, the elastic effect outweighing gravity under 30 mm, the Caspari 90/270 rule, the move to wristwatch flat springs in the mid-20th century, and the effective counting point about one third of the way from the curb pins to the stud.
Hans Jendritzki, Watch Adjustment (mid-20th century). Background on the Caspari and Grossmann effects as adapted to the wristwatch flat spring.