# Early Methods of Correcting Middle Temperature Error

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
I think this chronometer is pretty interesting. I am very interested in correction of middle temperature error.

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
For the general audience, middle temperature refers to the phenomenon where a timepiece that has been designed with a bimetallic balance to run with the same rate in heat and cold (typically 32 deg. and 92 deg.) will lose time when running at the middle temperature ( 62 deg.). I am not sure who first addressed the problem, and it may have been LeRoy with his original temperature compensated mercury balance.

In any case J. R. Arnold investigated it along with his business associate, E. J. Dent and they came up with a number of approaches. Essentially all of the 19th century approaches involved some additional temperature sensitive part on the balance that would cause the balance to gain time as the temperature moved toward the mid point and then lose that time as the temperature moved toward the other temperature extreme.

This example is a form of Frodsham's Micrometric balance. This balance has the normal bimetallic rim that moves in with heat and out with cold. In addition it has two arms that are flat and attached (actually formed) in the cross arm and carry a weight at the extreme end. These arms are bimetallic and designed to be flat and in the same plane as the cross arm at the middle temperature. As the temperature goes up, they curve upward and carry their weight toward the center, which makes the rate increase. However, when they cool, they also curve downward toward the center and make the rate increase.

In Mercer's book on The Frodsham's, this type of balance is discussed and the examples shown have the two middle temperature arms parallel to the balance arm. In this examples they are at an angle which allowed a simpler construction with very slightly less length to the arms.

I do not know how many of these were actually fitted to chronometers. I am sure there are much more erudite descriptions of it elsewhere, but this is a new toy and I wanted to share.

I also have a chronometer with the Lund Corrector and one with E. J. Dent's variant on this theme, his staple balance as well as the very common Poole's auxiliary that simply limits the change in the balance in one direction to cause the curve of radius with temperature to be discontinuous.

Perhaps other readers of this forum who collect these interesting artifacts can show and describe some of theirs.

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
J. R. Arnold's middle temperature corrector is incomplete in that it only compensates half of the temperature defect. In that respect it is similar to the Poole auxiliary, but has a wider range of correctness. By shifting the mean temperature point of the balance, it (and the Poole) are made more effective but still do not completely correct.

This chronometer has Arnold's type of compensation with a bimetallic arm laid atop the cross arm with a pair of weights on uprights that are thrown inward with the change.

This chronometer also shows that treasure can be found in strange packages. It is a very small Frodsham marine chronometer with serial number 2274, quite a bit earlier than the micrometric above. The box is an ordinary pine box that some enterprising soul made to hold his chronometer.

#### gmorse

NAWCC Member
Hi Tom,

If these extra parts are integral with the main crossing and are bimetallic, is the whole crossing bimetallic and how does that affect the whole crossing? Or are the brass lamina applied to just the underside of those arms? It's hard to tell from the pictures but I can't see any brass in their edges.

Regards,

Graham

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
I have not torn them down and cannot see well under the arm. I believe the design as described in Mercer has the central arm steel and the arms carrying the weights steel on top and brass below. The movement is not large, but the effect of the upward curve in cold and the downward curve in heat was a subject of correspondence between Frodsham and Airy.

On the Arnold form with the stalks, the vertical displacement of the weight is adjustable and the movement is amplified by length of the arm.

Airy thought Arnold's form inferior, but with the ability to set the middle temperature with the weight on the main arm, I think it does not matter much. I will try generating some curves from the equation for the moment of inertia vs temperature for the various forms. The calculus was over 100 years old when they were chasing this problem, but I do not see much use of it in the discussions.

My friend John Huber has a strong interest in these balances also and a few years ago he did a demonstration disassembly and reassembly at our regional meeting in Florida. It occurs to me that we might be able to have a really good discussion on the topic at our National Meeting in Springfield this June. I suspect we can put together a study of at least 5 o 6 different designs and possibly 10 and maybe more if others how up with examples.

Last edited:

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
This is the Parkinson & Frodsham that shared the lot with the Frodsham Arnold. It has a slightly enhanced form of Poole’s auxiliary acting in heat. You may be able to see the fixture with 3 available positions to hold the constraint screw.

Last edited:

#### Paul Regan

NAWCC Member
Looks like Lot 18 landed in the right hands Tom. Congrats on getting the pair.
Paul

#### Jerry Freedman

NAWCC Star Fellow
NAWCC Member
I know I have shown this before, but here is Kullberg's balance with his attempt to correct the
middle temperature error.

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
Jerry, in the recent auction, this balance in a chronometer signed for Johnson Walker & Tolhurst was described as having Kullberg's "flat rim" balance. I do not have a description of its operation. I tried, unsuccessfully, to buy it.

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
This chronometer from the same sale is signed M. F. Dent. It is an 8 day in a beautiful box with a balance that looks to my eye the same as @Jerry Freedman's example.

#### gmorse

NAWCC Member
Hi Tom,

Kullberg's flat rim design is described in Gould.

By the way, I was interested to see the Walsh pocket chronometers 311, 312 and 186(4); there didn't appear to be any frame makers' marks on them but the frames look identical to one I serviced recently, made by Joseph Preston, and finished by John Hammersley, (with a duo in uno balance spring), for M.F Dent.

It also had the steel detent stop which wrapped around the balance lower jewel with the adjustment by a screw through the extension, (slightly bent as received).

Regards,

Graham

#### Jerry Freedman

NAWCC Star Fellow
NAWCC Member
Tom: Page 90 of Whitney's has a good drawing of Kullberg's balance. My addition of Gould's book has a drawing of Kullberg's flat rim
balance.

#### Tom McIntyre

Staff member
NAWCC Star Fellow
NAWCC Ruby Member
I dug out my copy of the second edition of Gould and have been reading the section on middle temperature error.

I think he does a good job explaining why the discontinuous balances of the Arnold type function as well as they do and also why the Poole was so popular in comparison to the more complex forms.

The discussion in Mercer that revolves around the correspondence between Charles Frodsham and Airy on "true" middle temperature correction with a mass moving inward in both heat and cold is a little clearer than the similar discussion in Gould. Gould does capture it well in his description of the action of Lund's Corrector (which is renamed from the erroneous Barraud's Corrector in the first edition).

He also give a nice clear discussion of Loseby's balance which is conceptually much simpler than the others since it only requires you to make a cycloidal curved thermometer to match the hairsping's linear change with temperature. (Which no one except Loseby and Robert Gardner were ever able to do. )

I will try to read Whitney later this evening.

The diagram is a simple illustration of the middle temperature problem that I drew for my presentation on the Evolution of the Marine Chronometer some years ago.

#### gmorse

NAWCC Member
Hi Tom,

In the October 2018 edition of the Horological Journal there's part 2 of a series of articles on balance springs by David Boettcher. In it he goes into some detail on the source of middle temperature error, including the conclusion that 'Dent's anomaly' was based on an erroneous supposition, namely that the turning force of the balance spring varies linearly with temperature and makes little or no contribution to the observed error, all the blame being placed on the moment of inertia of the balance varying with the square of the radius of gyration. Later investigations, (by E.T. Loseby, Dr. Guillaume and Philip Woodward amongst others), revealed that the balance spring's thermoelastic response is not linear but actually quadratic, and constitutes the major component of middle temperature error. Well worth reading!

Regards,

Graham

#### DeweyC

NAWCC Member
This is a very interesting topic.

For those interested, there is an article in the February 1991 Bulletin containing pictures, descriptions and an analysis of the approaches to reduce middle temperature error. I included Poole, Hartnup, Kullburg, Guillaume to name a few. If you are a member you can access the article via this link:

http://docs.nawcc.org/Bulletins/1990/articles/1991/270/270_41.pdf

Since selling those instruments, I did come across a staple balance and I will post a photo of it later today. It and the Hartnup balance follow a similar conceptual approach but are different executions. Of course, Guillaume was awarded the Nobel prize for his work to produce the "perfect" mechanical oscillator in 1922. This whole area shows human beings at their best.

RULES & GUIDELINES