The Marine Chronometer

Time is a position

Latitude was never the hard problem at sea. The height of the noon sun, or of the pole star, above the horizon tells you how far north or south you are, and a sextant measures that angle well.

Longitude is different, because the Earth turns underneath the sky. It spins 360° every 24 hours, 15° every hour, so an east–west position is really a question about time. When the sun reaches its highest point over the ship, it is local noon. If you know, at that same instant, what time it is at a reference meridian such as Greenwich, the difference between the two times is your longitude.

Move the ship with the slider. The view looks down on the North Pole, with the sun to the right; the figure always shows the moment of the ship’s local noon:

Observing local noon is straightforward. Knowing Greenwich time in the middle of an ocean is not: you have to carry it with you, in a clock that keeps going through months of motion, damp and heat.

The arithmetic is unforgiving. An hour of time is 15° of longitude, a minute is a quarter of a degree, and a single second is a quarter of a nautical mile at the equator (less toward the poles, where the meridians crowd together). A clock that gains a couple of seconds a day is superb by domestic standards; after six weeks at sea it has quietly moved the ship twenty miles.

John Harrison’s fourth timekeeper, H4, beat that standard on its 1761–62 trial voyage to Jamaica. But H4 was a single, intricate masterpiece that few could copy. The instrument that actually went to sea by the thousand through the nineteenth and twentieth centuries came from a different line of development, running through Pierre Le Roy in France and John Arnold and Thomas Earnshaw in London. That standard form is what we’ll build: a fusee-driven chronometer with a spring detent escapement, a bimetallic balance and a helical balance spring, hung in gimbals in a wooden box.

An oscillator that ignores the sea

Every clock is an oscillator plus a counter. On land the best oscillator was the pendulum, but a pendulum measures time against gravity, and a rolling ship adds accelerations of the same order as gravity itself. A pendulum clock on a deck is hopeless.

The chronometer uses a balance: a wheel that rotates back and forth about its own axis, pushed back toward its rest position by a spring. Because the wheel is balanced about its axis, a sideways jolt pushes equally on both sides of it and produces no turning force. Only rotation of the ship itself can disturb it, and the gimbals we’ll meet later take care of most of that.

The period of a balance depends on two things: its moment of inertia I, which grows with the mass of the rim and with how far out that mass sits, and the stiffness κ of the spring. For small swings the period is T = 2π√(I/κ). A heavier rim swings more slowly; a stiffer spring swings faster.

Many marine chronometers complete a full oscillation in half a second. Watchmakers count each swing in one direction as a vibration, so that’s 14,400 vibrations an hour. As we’ll see, the escapement gives the balance one push per full oscillation, which is why a chronometer ticks in half-seconds.

The spring that breathes

An ideal oscillator is isochronous: its period doesn’t depend on how widely it swings. The formula above assumes this, and a real balance only approximates it. That matters, because the amplitude never stays put. It changes as the mainspring runs down, as oil thickens, as temperature shifts friction. Any link between amplitude and period turns each of those effects into an error in rate.

Most watches use a flat spiral balance spring. Chronometers usually use a helical spring, a coil shaped like a tiny cylinder, with its two ends bent inward in terminal curves so they attach close to the axis. When the balance turns, the coils wind up and unwind. With well-shaped terminal curves they stay centred on the balance staff while they do it, so the spring only ever twists the balance. Without the curves, the coil’s centre wanders off to one side as it winds, pushing the balance pivots sideways and adding friction that depends on amplitude.

Arnold was using curved ends on helical springs by the 1770s and 80s, found largely by experiment. A full mathematical treatment of the curves came much later, from the French engineer Édouard Phillips in the 1860s.

Heat

Temperature was the chronometer’s chief enemy. When a steel spring warms, it gets less stiff. At the same time the balance expands, which puts its mass further from the axis and raises its moment of inertia. Both effects slow the clock. A plain brass balance with a steel spring loses on the order of ten seconds a day for every degree Celsius, and a ship sailing from the English Channel to the tropics can see a swing of twenty degrees or more.

The cure was to make the balance change shape. Its rim is a strip of two metals fused together, brass on the outside and steel on the inside, cut through near each end of the crossbar so each half of the rim has a free end. Brass expands more than steel, so when the temperature rises the free ends curl inward. That pulls mass toward the axis and lowers the inertia, just enough to offset the weakening spring. The heavy weights on the rim are slid along it to set how much correction each degree produces.

The correction is not perfect. The bimetallic rim changes the inertia roughly in proportion to temperature, while the spring’s loss of stiffness has a significant quadratic part. A chronometer can be adjusted to keep time at two temperatures, but it then gains between them and loses outside them. This middle temperature error, typically a second or two a day, occupied chronometer makers for most of the nineteenth century. They built many “auxiliary compensation” devices to reduce it before Charles-Édouard Guillaume’s nickel-steel alloys largely solved the problem around 1900.

Constant force

The energy to run the chronometer is stored in a coiled mainspring inside a drum called the barrel. A typical chronometer runs for about two days on one winding, yet it is wound every day at the same hour, so it always works on the upper, more consistent part of the spring.

Even so, a spring pulls harder when fully wound than when nearly run down. More force means wider swings of the balance, and since no balance is perfectly isochronous, the rate would drift with the state of wind. The chronometer borrows a much older solution, the fusee: a grooved cone connected to the barrel by a fine steel chain.

When the chronometer is fully wound, the chain pulls on the narrow end of the cone, where it has the least leverage, just when the spring is strongest. As the spring weakens, the chain comes off the cone at ever larger radii. Force times lever arm stays nearly constant.

Winding reverses all of this. The key turns the fusee backward, drawing the chain off the barrel and onto the cone, which tightens the spring. For as long as the key is turning, though, the fusee is no longer pushing the train forward. To keep the clock from stopping or faltering, chronometers carry maintaining power, Harrison’s invention: a small auxiliary spring inside the fusee that keeps driving the train while the main drive is interrupted.

Counting

From the fusee, a chain of gears called the train both slows things down and counts. The fusee’s great wheel drives the centre wheel, which turns once an hour and carries the minute hand. Each following wheel drives the next faster: the third wheel, then the fourth wheel, which turns once a minute and carries the seconds hand, and finally the escape wheel.

The tooth counts in this figure are illustrative, but the ratios are the ones a half-second chronometer needs. The escape wheel has 16 teeth, as on the Hamilton Model 21, and releases one of them per oscillation of the balance, 120 times a minute, so it turns once every 8 seconds.

At normal speed the motion isn’t smooth. The whole train stands still, then jumps, twice a second. That is the escapement at work, and in a chronometer it is the most distinctive part of all.

The detent

An escapement has two jobs. It lets the train advance one tooth at a time, and it gives the balance a small push to replace the energy lost to friction. Every contact disturbs the balance a little, so the ideal escapement touches it as rarely and as briefly as possible. The detent escapement comes very close. It pushes the balance in only one direction of swing, and for the rest of each oscillation the balance swings almost entirely free.

Here is one full cycle, seen from above, drawn to scale from the Hamilton Model 21, the American chronometer made in large numbers for the US Navy during the Second World War. The escape wheel, 13.2 mm across, is held still by a jewel, the locking stone, mounted on the detent: a slender blade whose foot is clamped to a fixed block, joined to it by a thin, flexible spring at the point of flexure so that it can swing slightly. A stop button on the block sets how far the detent can fall back. The balance staff carries two rollers, each with a jewelled pallet.

As the balance swings counterclockwise, the small discharging pallet strikes the tip of the fine passing spring. That spring rests against a horn on the detent, so the push lifts the whole detent off its stop. The locking stone moves clear, the wheel leaps forward, and a tooth drops into a notch cut in the large roller, its crescent, where it catches the impulse pallet and drives the balance on its way. By then the detent has sprung back, ready to catch the next tooth.

On the return swing the discharging pallet meets the passing spring from the other side. This time the passing spring simply bends away from the horn. The detent never moves, the wheel stays locked, and the balance passes with almost no resistance.

All of this happens in a few degrees of a swing of some 250° each way, and the tolerances are fine. The US Navy’s overhaul manual for the Model 21 gives a repairer the figures to set, measured as angles of the balance. The lock, from the moment the detent leaves its stop until the tooth drops off the stone, should be about 6°. The wheel’s drop onto the impulse pallet should be about 2°. The whole contact on both swings together, the overall, should be 26° to 30°. The impulse roller, 6.3 mm across, clears the teeth on either side of it by only 0.05 mm, and the horn clears the discharging pallet by a quarter of a millimetre. The figure above meets every one of those settings: its lock is 6.1°, its drop 2.1° and its overall 27.8°.

Hamilton also chose its materials for the job. The detent is beryllium copper, a springy alloy that doesn’t rust, and the passing spring is Elinvar, a nickel-steel whose stiffness hardly changes with temperature. In English chronometers the passing spring was usually gold.

The design has a price. A detent escapement isn’t self-starting: if the balance stops, it has to be swung by hand to set it going again. A hard jolt can also knock the detent and let the wheel slip a tooth. In a padded box in a ship’s chart room that’s an acceptable trade, and it is one reason the design stayed in the box instead of moving to the wrist.

Level on a moving ship

A balance’s rate varies slightly with its orientation, so the chronometer is adjusted to run in one position: dial up, balance horizontal. The brass bowl holding the movement hangs in gimbals, a ring pivoted in the box along one axis, with the bowl pivoted inside the ring along the perpendicular axis. The bowl is weighted low, so it hangs level while the box rolls and pitches around it.

The whole instrument

Here is everything together. Open the lid, then lift the movement out of its bowl and turn it over to see the balance side. The dial shows the time where you are now.

On a real voyage, the chronometer’s value lay less in having no error than in having a predictable one. Before sailing, the navigator established its rate, say a steady gain of 1.3 seconds a day, and applied it to every reading. A chronometer that gains steadily is perfectly usable; one whose rate wanders is not. Ships that could afford it carried two or three, compared daily, so that one misbehaving instrument would give itself away.

For one real instrument built part by part, see the working model of the Hamilton Model 21. Its layout is fitted to photographs of the movement and its escapement is checked against the manual; every part can be picked out and named, and the hands keep your local time.

Radio time signals in the early twentieth century, and satellite navigation later, finally retired the chronometer from its job. The instrument itself, a few ounces of oscillating brass keeping a ship’s place on the planet, remains one of the most elegant solutions ever built to a problem that once cost thousands of lives.

Further reading. Manual for Overhaul, Repair and Handling of Hamilton Ship Chronometer, NAVSHIPS 250-624, Bureau of Ships (1948), the source of the escapement figures above. Rupert T. Gould, The Marine Chronometer: Its History and Development (1923). David Boettcher’s notes on middle temperature error. Bartosz Ciechanowski, Mechanical Watch, whose approach inspired this page.