The physics of <PERSON>'s marine chronometers
I have read some of the history of <PERSON> marine chronometers and have found it fascinating. I would like to deepen my understanding of <PERSON>'s amazing inventions by learning more about how they actually worked, but I have had trouble finding sufficiently detailed descriptions, let alone analyses of why they work.
To give some idea of what I'm looking for, let's consider the design now known as H1. As I understand it, the crucial component consisted of two dumbbell-shaped rods, each pivoting about its own center and connected to each other by two springs. I believe that the main point—and here is where I'm speculating because I haven't actually done the calculations—is that the period of oscillation of this mechanism is relatively robust to impulses. More precisely, some things that I have read seem to suggest that the mechanism is particularly robust to impulses that lie in the plane of the two dumbbells, but that its main weakness is that it is not as robust to impulses in the direction perpendicular to this plane. Assuming that this is roughly correct, what I would ideally like to see is a series of exercises (of the type one might see in a course in advanced classical mechanics) that walk you through the relevant calculations and let you quantify the effect of various impulses.
In the case of H1, I might be able to flesh out the preceding paragraph myself, but for the other designs, particularly the famous H4 design, I have not been able to find sufficiently detailed descriptions of the mechanism to even begin to understand them at the level that I would like. Note: I recognize that some of <PERSON>'s innovations concerned robustness to temperature variations, by the use of things like bimetallic strips. 617
Personally, I'm less interested in that kind of thing (even though they are obviously extremely important in practice) than in the rigid-body mechanics of balance wheels, escapements, etc., and in particular the analysis of why they are (or are not) robust to the conditions on a moving ship.
Is there any account out there that addresses what I'm asking for?
EDIT: The most detailed description of H4 that I have found starts on page 49 of The Marine Chronometer: Its History and Development by <PERSON>. Contrary to my preconceived expectations, there were no features in H4 that were obviously designed to be specifically robust to a ship’s unpredictable accelerations. If anything, H1, H2, and H3 seemingly had more “ship-specific” features than H4 did, but they were ultimately less successful than H4. The harmonic oscillator in H4 was a fairly standard-looking balance wheel with a balance spring, whose period must (I assume) have been naturally robust to accelerations.
It is possible that the physical size of H4 was carefully chosen with the marine setting in mind. Smaller mechanical clocks seem to be inherently less accurate even on land, and perhaps a larger version of H4 would have been more vulnerable to impulses. <PERSON> says that the escapement of H4 was a complicated modification of a verge escapement, which is usually considered to be inferior to a grasshopper escapement. But <PERSON> also says that a grasshopper escapement would have been impossible “in a machine of such small size,” so there may have been other reasons for making H4 as small as it was. So far, I have not found any discussion of this point anywhere. 484