Mapping the Stars

One of the truisms of our time is the stunning pace of current technological change.  Another relates to the ability of modern scientists to extract the last possible decimal point of accuracy from their wonderful high-tech gear.

We compare ourselves, a bit smugly, to the way people were in the old days, when life moved at a more sedate pace, and people were willing to accept the crude results produced by a vastly more primitive technology.

Yeah, but…  When you really look inside the history of early science, you sometimes find just as great a drive to seize on the latest technology and an even greater talent for squeezing the last drop of data from it.  What the pioneers actually achieved, through brilliance, a solid understanding of their own technology, and capacity for tireless effort is every bit as remarkable as anything we can achieve today.

Today, we remember Galileo mostly for the discoveries he made when he built his own, incredibly crude model of that hot new invention, the telescope, and turned it toward the heavens.  He published them in 1610 in Sidereus Nuncius, forever securing his place in astronomical history and incidentally setting his feet on the path that led eventually to an appointment with the Inquisition.

But another Galileo discovery would also have a profound influence on astronomy:  The legend has a 17-year-old Galileo sitting one day in the cathedral at Pisa.  Bored, he found himself watching the swing of a lamp and noticing the odd fact that the time the lamp took to swing back and forth seemed to be the same no matter how large the arc.  He timed it by surreptitiously counting his own pulse.

That story is probably apocryphal.  But we do know that a 38-year-old Galileo finally took up the phenomenon of the pendulum in earnest in 1602.  He confirmed that its timing was, indeed, independent of the size of the swing.  Fascinated, he spread the news of his discovery among his friends.  He even found it had a practical use in his laboratory.  Using small, fast pendulums he was able to time his own experiments more accurately.

But he was still just counting the beats of a free pendulum.  It doesn’t seem to have crossed his mind to use his pendulum to control a clockwork until his old age.  He sketched a design for one just before he died in 1642, but never built it.

That accomplishment was left to Christiaan Huygens, who built the first pendulum clock fourteen years later, in 1656.  To really appreciate how revolutionary this new clock was, you have to know that its predecessor, called a foliot and verge clock, was accurate to perhaps plus or minus five minutes a day.  Huygens’ very first prototype clock had an error of less than a minute a day and it wasn’t too long before he got that down to eight seconds a day.  Pretty soon everyone around Europe was building his own version of Huygens’ new design.

That was particularly true in England, where the spread of their maritime commerce to all corners of the world had expanded everyone’s horizons.  Accurate navigation was recognized as the key to England’s future.  Suddenly even the very highest in society were becoming interested in things scientific.  In 1675, Charles II appointed one John Flamsteed as the first Astronomical Observer (later Astronomer Royal) to serve at a new Royal Observatory being built at Greenwich.  Christopher Wren was commissioned to design the octagonal Great Star Room there so the new Astronomer could make his observations in relative comfort.  (Unfortunately, Wren oriented the room a bit wrong, so Flamsteed was forced to do all of his observations from a shed he built in the garden.)

Flamsteed’s assigned task was to aid British navigation by making the first really accurate map of the visible stars.  In order to do that he knew he needed the latest versions of those two new devices, the telescope and the pendulum clock.  So he had a seven foot long telescope made to his own design and ordered two special clocks from Thomas Tompion, the finest clock and instrument maker in London.

The fact that Flamsteed needed a good telescope is probably obvious, given his astronomical assignment, but to understand the clock part, you need to know a bit about the process they used to locate heavenly bodies.

The first thing was to establish a frame of reference, then measure everything from that.  You did that by establishing the meridian for your observatory.  A meridian is any great circle line running from the north to the south pole.  Your own meridian is the one that is intersected by a line running from the center of the earth through where you are standing.  In other words, what you do is extend a plumb line from where you are right up into space; draw a line from the north pole intersecting your plumb line and continuing down around to the south pole.  That meridian line is the baseline on which you make all of your observations.  To insure this, you rigidly mount your telescope so that it always points toward the meridian line.  It is able to move vertically along the meridian line, but it is fixed horizontally.

Now if you want to map the location of a particular star, you have to record two bits of information.  First you adjust your telescope up or down on the meridian until it is aimed so that the star passes through the center of its field of view as the evening sky turns.  This angle, the angle of your telescope above the horizon that points to where the star’s path will cross your meridian, is the Declination for that star.

For the next part you have to have a very fine vertical line in the field of view of your telescope.  (To get the finest line possible, they were sometimes made of spider’s web, collected from the garden by that ever-useful tool, the apprentice).  Then you watch the star come into your field of view and move across that line.  When the star just crosses that line in your telescope, you note the time.  That time is called the Right Ascension and is the second half of the coordinates you need for mapping the star.

How accurately could they be expected to measure this event?  First, we have to look at their experimental situation.  Our planet moves at a nice, almost perfectly constant rate of 15 degrees per hour.  The inherent resolution of this experiment is clearly limited by the answer to this basic question: How long does it take the disk of a star to pass a fine line?  Did it flash by, too fast to measure?  Or is it so slow that you have to arbitrarily decide its exact “moment” of passage?

The answer is that, using a telescope like Flamsteed’s, it takes just about a second for a star’s disk to pass over a fine line.  And, since a second is quite a long time to someone freezing his rump on an English winter’s night, and since a star’s disk could be seen quite clearly, they were actually able to do better than simply recording the exact second.  With practice, they found they were able to interpolate that number down to tenths of a second with reasonable accuracy.  By repeating the experiment night after night, they eventually got averages that were very accurate, indeed.

But hold on, I hear you cry, these measurements started barely twenty years after Huygens made his first clock, the prototype, and I thought you said that Huygens’ best design was only good to eight seconds a day.  Surely trying to read tenths of a second accuracy in any signal that varies by that much is worse than useless.

And you’re right.  It would have been…if they had stopped where Huygens did.  But Flamsteed’s task clearly required better timing than that.  His problem was, first, how to make the best possible clock and, second, how to get the very best data out of that clock design.  Taking the second problem first, remember that Flamsteed shrewdly ordered two identical clocks.  By comparing them, he could play one against the other and get more accuracy than either offered alone.  Second, Flamsteed urged Tompion to improve on Huygens’ basic design.

In response, Tompion created a tour de force of both design and fabrication.  A mechanical clock works by retarding the drive and only letting it escape a tick at a time, with the release controlled by the pendulum.  Huygens escapement (the part that lets the gears move forward a step) actually drove the works backwards a bit before releasing it to run forward.  That created lots of friction which was a primary source of inaccuracy.  For Flamsteed, Tompion invented a brand new version of the escapement (called a dead beat escapement) that had no backward movement and therefore dramatically reduced the mechanical losses in his clocks.  Next, to time his new design he used a giant 13-foot-long pendulum.  This allowed him to keep the pendulum swing small in angular terms.  It kept it in the narrow region where a simple pendulum is both reliable and repeatable (the buzz term is isochronous).

In short, the two of them managed to both push the state of the art into some brand new areas while also shrewdly figuring out how to extract the most from what they had.  Using a combination of clever design invention, superb workmanship, and duplex timing, they were able to attain a timing accuracy that matched Flamsteed’s own ability to resolve the events he was observing.

Pushing the state of the art is always a bit unpredictable.  There were lots of early problems with the clocks.  But after a lengthy teething phase, Flamsteed was able to assure himself that his equipment was finally good enough for the task he was assigned.

Then the drudgery started.  Night after freezing night, Flamsteed and his assistants would sit at the telescope, timing one star in its transit, then another, and then another.  They had to repeat their experiments on the same stars night after night, to insure their measurements were reliable and so they could average their results.  Year after year, they kept at it, recording by night and calculating by day.  When it was finally published in 1725 as Coelestis Britannica, their report contained the positions in angles of declination and hours, minutes, and second of ascension, of an astounding 3,000 stars. (Flamsteed said he had actually mapped around 4,000, but only 3,000 to an accuracy he felt merited inclusion.)

I still consider this a model of the greatest of scientific achievements.  Refining tools only just invented, with nothing but human ingenuity, skill, and a persistence that defies belief, they revolutionized not only the astronomy of the heavens, but the idea of what precision men could reach.  A few years after this, building on what they had done, other astronomers would be arguing nonchalantly about the number of decimal places that should be shown in the difference between the mean solar and the sidereal day.

Their world had been changed, which is what technology does.  Fairly steadily from that day to this, technology has gotten better, knowledge had gotten wider, and our own expectations have insensibly risen to match them.  We are justly proud of what we can now accomplish.

Yet we shouldn’t forget that we do, indeed, stand on the shoulders of giants.

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