I am curious. Greater ease of positional adjustment? More isochronous? Something else? What justified the added effort?
Most visitors online was 1990 , on 7 Feb 2022
Frodsham’s spiel sounds like typical sales hype, but I suppose hyperbole is sometimes built on a kernel of truth.The Duo in Uno spring was first shown to the public on the Charles Frodsham stand at the Great Exhibition of 1862 in Kensington, London.
Vaudrey Mercer's book The Frodshams says the following of the spring:
This is praised on Page 22 [of the Exhibition catalogue], where he [Frodsham] says that it ensures "almost certainly correct performance in all the various positions with a perfectly poised balance".
This type of balance spring is said to have been invented by Mr Mairet, of Baker Street, and was shown by Charles and Mr McLennan in the 1862 Exhibition, but had been used by Arthur Paul Walsh since about 1860.
I have a copy of the appropriate section of the Exhibition catalogue, but it is out on oan right now. As soon as I get it back, I will post again and further reference to the duo-in-uno which it may contain.
Do you have a picture, Ethan?I have a free-sprung C. Frodsham (made by Daniel Buckney) with what was described as a double overcoil hairspring. I assume that's a different breed of hairspring from the duo-in-uno, but how so, and what were its perceived advantages?
A normal helical balance spring has 'overcoil' terminals at top and bottom.I have a free-sprung C. Frodsham (made by Daniel Buckney) with what was described as a double overcoil hairspring.
Ah, so just a nonstandard term for a helical hairspring, perhaps? Though wouldn't one of those terminals actually be an undercoil?Hi Ethan,
A normal helical balance spring has 'overcoil' terminals at top and bottom.
Regards,
Graham
I guess that depends on which way up you're standing . . ....Though wouldn't one of those terminals actually be an undercoil?
Yes, this was in the July and August issues in 2018, and I had some correspondence with David regarding this.There was a recent BHI article about them though, by David Boettcher, which may explain further.
Could you possibly summarize the main relevant point(s) of that article, for those of us who do not subscribe?Hi Seth,
Yes, this was in the July and August issues in 2018, and I had some correspondence with David regarding this.
Regards,
Graham
I'll dig out the article and see what I can do.Could you possibly summarize the main relevant point(s) of that article, for those of us who do not subscribe?
Lovely watch.Here are the best photos I could take of my double overcoil C. Frodsham's hairspring.
View attachment 525785 View attachment 525786 View attachment 525787 View attachment 525788 View attachment 525789 View attachment 525790
Thanks for posting these, they illustrate the structure nicely. It appears that the 'double' refers to the extra turn at the outer end before the stud, and the slight step in the cock table accommodates the resulting small increase in height.Here are the best photos I could take of my double overcoil C. Frodsham's hairspring.
David begins by stating that John Hammersley announced his invention of the tria-in-uno spring in the February 1860 edition of the HJ, with the stated objective of eliminating the problem of 'acceleration' in new chronometers, and that this has not been disputed. However the origins of the duo-in-uno spring were disputed with Hammersley by both McLennon and Walsh. Acceleration is the effect seen in chronometers with balance springs formed by hardening and tempering the helical portion and only afterwards forming the terminal curves at each end by bending. Such springs can take a long time in use to settle into a stable rate. Hammersley's invention allowed the spring to be completely formed into its final shape before hardening and tempering, without resorting to any manipulations afterwards. He includes diagrams of tria and duo from Rupert Gould's famous work on chonometers. David goes on to mention Hammersley's design for a 'double flat isometrical balance spring' which corresponds exactly with the example shown by Ethan in post #17, and which was contested by J.F. Cole who stated that he had made such springs 30 years earlier, which Hammersley had subsequently to accept.I'll dig out the article and see what I can do.
Thank you, Graham. That was very informative.Hi Clint,
David begins by stating that John Hammersley announced his invention of the tria-in-uno spring in the February 1860 edition of the HJ, with the stated objective of eliminating the problem of 'acceleration' in new chronometers, and that this has not been disputed. However the origins of the duo-in-uno spring were disputed with Hammersley by both McLennon and Walsh. Acceleration is the effect seen in chronometers with balance springs formed by hardening and tempering the helical portion and only afterwards forming the terminal curves at each end by bending. Such springs can take a long time in use to settle into a stable rate. Hammersley's invention allowed the spring to be completely formed into its final shape before hardening and tempering, without resorting to any manipulations afterwards. He includes diagrams of tria and duo from Rupert Gould's famous work on chonometers. David goes on to mention Hammersley's design for a 'double flat isometrical balance spring' which corresponds exactly with the example shown by Ethan in post #17, and which was contested by J.F. Cole who stated that he had made such springs 30 years earlier, which Hammersley had subsequently to accept.
In 1894 Hammersley wrote in the HJ that he accepted that McLennon had been the first to apply a duo-in-uno spring to a watch, although he had been making the claim earlier on his own watches for some time. Hammersley did however claim that the duo-in-uno was merely a tria-in-uno with one spiral cut short.
In a letter to the HJ of September 2018, David expanded on his article with an image of a US patent, (2,457,631 from Dec. 28 1948), concerning a complex demountable former for cylindrical balance springs, by W.O. Bennett Jr. for Hamilton's Model 21. He supposes that Hammersley must have used a similar former to avoid damage to the finished spring when the former was removed. He also clarified a point I had brought to his attention regarding the exact configuration of duo-in-uno springs.
Regards,
Graham
Despite the vagueness, Frodsham nevertheless is claiming that duo-in-uno hairsprings confer some kind of an advantage regarding positional adjusting. An interesting claim. Pocket chronometers were serious working watches, not just rich men's toys, so if duo-in-uno hairsprings were not actually perceived to provide some kind of a genuine advantage to justify their additional expense, you would think they would have been no more than a quickly passing fad.I now have a scan of the 1862 catalogue page containing i nformation on the Charles Frodsham stand. It says of the duo-in-uno harispring (at the bottom right of the page attached):
New "Duo in Uno" balance springs for perfecting the adjustments of high-class watches and chronometers in their various positions.
Not very specific or intelligible, I suspect, but Charles was "the greatest showman" I think.
Interesting. So Huriet's theory would imply that a simple volute hairspring would be the most theoretically isochronous, would it not? But conversely, it may also be the toughest to adjust to positions. So perhaps the duo-in-uno hairspring was envisioned to enable a superior trade-off between isochronism and positional adjustment?Theory was evolving then as now, but the primary theory was that of Huriet who showed that a balance spring is isochronous if and only if the force is exactly in the radial direction. This placed the focus on terminal curves. The thinking was that spiral was a kind of lower end terminal curve allowing a smaller collet and possibly a thinner watch than fully helical spring with Arnold type terminal curves.
Another possibility is due it being a longer spring than would be practical in a pocket timepiece so thicker wore could be used. A thicker spring is less affected by inclusions in the steel making it more likely to behave according to theory.
From the standpoint of a watchmaker adjusting beat it combines the worst of both worlds. You have to take the balance out to adjust it's beat position. Perhaps this difficulty was seen as a benefit too.
Ah, normal to the radius. That would be called "axial" in most situations. But you mean that the restoring force points along the line of the spring at the terminal points, right? But wouldn't a spring with a single turn need to be weaker, not stronger than a multi-turn spring, because the strain (dL/L) for a given angle of balance wheel rotation would be greater?No, the hairspring has to open and close such that the spring force at the stud and collet are normal (perpendicular) the the radius. This was and is the defining requirement for terminal curves. This condition is met when the spring opens and closes concentrically. Perhaps a single properly curved volute would work were the material strong enough that a single turn would could have the right frequency. Huriet advocated and used spherical springs.
Philip, the phenomenon you describe, which I do not doubt was a real phenomenon, might be explained by oxidation of the surface of the spring. If the oxidation process passivates, it will shut off after a while. There may be some other explanation for the phenomenon that has been reported. However, it is certain that hardening processes do not affect the elastic modulus of a material. Some crystallographic phase transformation might, however. Tempering is supposed to eliminate the hard martensite phase that develops upon rapid cooling.[QUOTE=".. I must beg to differ with you, however, only on one point, from my perspective as a materials physicist. ...Elasticity is the ability of a material to deform without losing its original shape when unloaded.
Hi Clint,
This discussion has been going on ever since Arnold started hardening (and tempering) his hairsprings.
The process was simple starting with a soft steel helical spring with alraedy formed terminal curves which was hardened, tempered, and installed in a chronometer.
And this is when the problem started - regardless of how well the chronometer was adjusted it started accelerating about one second per month - after the first month it was 1 sec fast, after the second month 2 seconds, etc.
In other words, new chronometers went faster day after day. To make sure that there is no room for ambiguity in the explanation; after the first month, the chronometer could be re-adjusted perfectly, and a month later it would gain a second again, then re-adjusted again, and again would run one second fast the next month and so on for at least twelve months.
Eventually, between the twelfth and 24th month the acceleration stopped.
It was a serious problem for chronometer makers. Old springs that were already settled, were in high demand. Some chronometer makers installed a light balance and ran the chronometer for six months to make the setting faster.
If a hairspring was changed for an old, already settled one, the acceleration did not occur. This proved the anomaly was restricted to the hairspring only. Clearly, the hardened and tempered spring was getting stronger day by day, the coefficient of elasticity was continuously changing.
Evidently, there must have been changes in the molecular structure of the spring.
Already in 1923 Commander Gould, stated “It is now fairly certain that this acceleration is due to the molecular change which the outer surface of the spring undergoes during the process of hardening”.
To me it was clear that this anomaly proved that Hooke’s law quantifying the elasticity of small deformations, is pretty good, but not perfect. I do not think in other fields but horology, such minuscule anomalies have ever been noticed. In what other field would an experiment be made by bending and re-bending a spring over 126 million times? But this is a question for a materials physicist, not a historian.
Now, let’s go back to the duo- and tria-in-uno springs.
In practice, even if a hairspring is already hardened and tempered with formed terminal curves, the curves need a final adjustment. It was found that manipulation of the tempered curves can make the acceleration even more rapid. This is what Hammersley had on mind in his explanation from February 1, 1860.
Tria-in-uno springs do not need that final curve adjustment, the curvature of their terminals is small. Therefore their acceleration is smaller than helical springs which gives them advantage over the former. The same is true, although obviously to a lesser degree, with duo-in-uno springs.
Duo-in-uno and tria-in-uno springs were installed in pocket watches to save on the thickness (and to a lesser degree on the acceleration) and in marine chronometers to limit the acceleration.
Philip Poniz
Marty, to paraphrase a famous quote: All theories are "wrong," some theories are useful. My point is that science is progressive. Einstein did not toss Newton's work into the dustbin, he built on it. He showed that Newtonian mechanics was a special case of a more general theory, and an extremely accurate approximation for treating objects moving at speeds less than a substantial fraction of the speed of light. At 10% of the speed of light, which is 30,000 kilometers per second, faster than just about any macroscopic object moves in our part of the Milky Way, nearly all the predictions of Newtonian mechanics are still accurate to within half a percent. At common terrestrial speeds the errors incurred by the Newtonian formulation are typically too small to measure. Someday most physicists expect that General Relativity will be quantized, and then Einstein's theories will likewise be shown to be a special case of an even more general theory - Quantum Relativity.So Hooke's Law, like Newton's Law of Gravity (and his Laws of Motion) before it, has now to be consigned to the dustbin of history.
Is nothing sacrosanct?![]()
Unlikely Clint, oxidation would have the reverse effect - it would weaken the spring, not make it stronger.Philip, the phenomenon you describe ... might be explained by oxidation ...
But the restoring force, in this case, would be continuously increasing.The restoring force associated with that potential is then: F = -(d/dx)V(x) = -2c(x - xo).
Philip, I don't have a definite answer for the empirical fact you state that hairsprings in watches tend to get "stronger" over time. But I can tell you that it is a very well-established fact of 21st century material science that elastic properties are not affected by hardening. Hardening means that the yield stress of the material has increased. Elasticity is what happens before the yield stress is reached. Citing 18th and 19th century sources who speculated on the subject before x-ray crystallography, transmission electron microscopes, or a real understanding of the nature of atomic bonds existed is only of historical interest.Unlikely Clint, oxidation would have the reverse effect - it would weaken the spring, not make it stronger.
The fact that hardened and tempered balance springs become stronger in time is the most remarkable aspect of the anomaly.
Maybe the molecular friction during the bending hardens the spring? Interestingly, molecular friction in hairsprings was already realized by Breguet before 1820, although he did not elaborate on it.
But the restoring force, in this case, would be continuously increasing.
Horological metallurgy is probably the least understood subject of horology. Even the model of basic bimetallic balance, as far as I know, is just made with many assumptions and simplifications (Yvon Villarceau, 1862, the Grossmanns, 1905, Mrugalski, 1972). I have tried to find a math model describing behavior of bimetallic laminae but could find only the basics (associated with bimetallic thermostats).
Nice discussion Clint!
Philip
Philip,Unlikely Clint, oxidation would have the reverse effect - it would weaken the spring, not make it stronger.
The fact that hardened and tempered balance springs become stronger in time is the most remarkable aspect of the anomaly.
Maybe the molecular friction during the bending hardens the spring? Interestingly, molecular friction in hairsprings was already realized by Breguet before 1820, although he did not elaborate on it.
But the restoring force, in this case, would be continuously increasing.
Horological metallurgy is probably the least understood subject of horology. Even the model of basic bimetallic balance, as far as I know, is just made with many assumptions and simplifications (Yvon Villarceau, 1862, the Grossmanns, 1905, Mrugalski, 1972). I have tried to find a math model describing behavior of bimetallic laminae but could find only the basics (associated with bimetallic thermostats).
Nice discussion Clint!
Philip