A similar movement from the British Museum, but with detent escapement, is illustrated by Vaudrey Mercer in The Frodshams, 1981, p. 412, pl.26.

Charles Frodsham (1810-1871) He was the most celebrated of the Frodsham family, with its numerous watchmakers, and was a prominent maker of very high grade chronometers and watches. For the 1851 exhibition, they introduced a three-quarter plate caliber which they marked “AD.FMSZ”, which continued subsequently to be put on all their highest grade work. In 1868 he devised a form of electrical contact for taking signals for chronometers. The company he founded continued after his death. From 1779 to 1850, a partnership existed between William James Frodsham (1779-1850) and William Parkinson (d. circa 1842) The firm, under the name of “Parkinson & Frodsham”, was established at 4 Change Alley and specialized in pocket and marine chronometers, for which a strong demand was beginning to be felt. Parkinson & Frodsham were quick to see the commercial advantage to be derived from supplying instruments for voyages of exploration, and in 1832, Frodsham published a summary of their performance in, “A Brief Account of the Chronometer, with Remarks on those furnished by Parkinson
& Frodsham to the Expeditions of Captains Ross, Parry, Sabine, King, Lyon, Foster, and Other Distinguished Navigators. With the Rate of those tried at the Royal Observatory, Greenwich in the Years 1828, 29, 30, 31”. Around 1847, William James Frodsham passed ownership of the buisness to his two sons, George and William. “AD Fmsz” does not indicate a year of manufacture, but the year 1850 when Frodsham?s firm introduced a new series of high-quality watches. The code is in his name: F=1, r=2, o=3, etc. z=0. His highest quality pieces were so marked. During the early 20th century, the firm was closely connected with Nicole Nielsen who made most of the movements, including some of the most perfect tourbillons ever made, and which still perform with almost unrivaled accuracy. At some time before the mid-20th century, the company began making lever escapement and chronometer escapement watches of the very highest quality and continued to do so until the outbreak of war in 1939. Frodsham watches are almost always elegant and well proportioned. Even as late as 1914, some of them, with engine-turned silver dials, were worthy of Breguet. The firm was appointed watchmaker to the King, The Prince of Wales, and to Queen Alexandra. They were responsible for maintenance and winding of all the clocks at Buckingham Palace, where they had a workshop. Frodsham´s best cases were made by his son, Harrison Mill Frodsham (1849-1922), who took over the firm after his father death and proved to be an expert horologist.
The ‘duo-in-uno’ and ‘trio-in-uno’ balance-springs
The ‘duo-in-uno’ balance-spring allows the height of a helical spring to be lowered, thus saving space in the height of a pocket chronometer movement.
The ‘duo-in-uno’ was first presented to the public at Charles Frodsham’s stand at the 1862 Great Exhibition in Kensington, London. Frodsham states that it provides “almost certainly correct performance in all the various positions with a perfectly poised balance” (Exhibition catalogue, p. 22).
This type of balance-spring is said to have been invented by Mr. Mairet of Baker Street and exhibited by Charles Frodsham and Mr. McLennan at the 1862 exhibition, but it had been in use by Arthur Paul Walsh since about 1860.

John Hammersley (1819-1901) – an excellent watch and chronometer maker who made movements for Dent, and deck watches for the Admiralty – is also credited with the invention of the ‘trio-in-uno’ balance-spring, in which a spiral form is made on both ends, forming a closed cage. They are even more difficult to manufacture than the ‘duo-in-uno’ and therefore extremely rare.

A ‘duo-in-uno’ has several coils shaped like a helical spring and of constant diameter the same as the outer diameter of the flat spiral part of the spring. Some (most?) did then also have an Arnold-style terminal curve towards the pinning point on the balance cock. A double overcoil would be a flat spring, pinned at the centre as usual but with, instead of a single turn (or 3/4ish turn) of overcoil, a gradually rising overcoil that makes getting on for two whole turns as it rises and then curves in towards the pinning point.

The existence of the terminal curve on the ‘duo-in-uno’ springs does away with the supposed intended advantage that Graham mentions of the quicker settling down of rate due to the stresses introduce in making the usual overcoil/ curve.

John Hammersley (1819-1901) – an excellent watch and chronometer maker who made movements for Dent, and deck watches for the Admiralty – is also credited with the invention of the ‘trio-in-uno’ balance-spring, in which a spiral form is made on both ends, forming a closed cage. They are even more difficult to manufacture than the ‘duo-in-uno’ and therefore extremely rare.