First, let us all agree on one thing: there's no such thing as a hundred per cent accurate time measuring machine. Not even the almighty atomic clocks. Even those have errors (although, on the most perfect ones this means gaining or losing one second in a hundred million years interval). Presently, the champion of precision seems to be the Quantum clocks technology, with a precision of about (take it or leave it two or three hundred million years :-) ) 3.4 billion years. Now, that's accuracy. But still far from perfection, since the estimated age of the Universe is (according to scholars) about 14 billion years. So, these watches are still not error-free, despite looking at this fact with a metaphysical approach.
So, forgetting these marquee players, what are the time-measuring instruments that we all know?
Well, two comes into our minds: the watches and the clocks.
What's the difference between the two? Well, I'm no horologist... but I'd say that it has something to do with portability. A clock is a time-measuring instrument that (due to its size and weight) is supposed to be fixed somewhere (be that the hall of your home, the bridge of a ship or an airplane's cockpit). On the other hand, the watch is a portable one (e.g. a wristwatch or a pocket watch).
And both of them can be (but not necessarily) chronometers. So... what's a chronometer, anyway? Since the web is a little bit short of interesting definitions, let's pick up one from my times as a nautical student (because these instruments were, in fact, created for navigation purposes), in Paço de Arcos, authored by our first year navigation professor.
Definition of a chronometer.
A chronometer is a time-measuring instrument, or (I think, more correctly) machine, which rate (or "marcha", in Portuguese), for a given condition of atmospheric temperature, humidity and pressure, is regular. That is: it gains or looses a certain amount of time over a period of (normally) twenty-four hours. This "amount" of time lost or gained is, usually, expressed in full seconds or in its fractions. How is this defined?
Well, there is no actual standard worldwide. And many nations have their own chronometer testing institutes (among the most famous, one comes to our mind: the Swiss COSC). But they all agree on one thing: these (government) institutions are the market regulators in terms of time-measuring machines. So, any common watch - or clock - secretly wishing to be promoted to chronometer has to be subjected to the battery of tests imposed by the national authority on the matter. And, only after passing all of them with flying colours will the wannabe receive the so desired Chronometer Certificate. It's a bit like college: you study, you train and you pass the exams. In the end, you'll have your Degree.
By this time, you are already looking at your cheap automatic Invicta with suspicion, thinking that you should have bought a Rolex or a Jaeger-LeCoultre instead. Well, don't.
The fact that you don't own a Chronometer Certificated (C.C.) time machine does not necessarily mean that it's not up to chronometer standards. It just means that the testing of your particular watch or clock was not requested by its maker to the reference institution. Why? Because it costs money. Money that you, the consumer, will pay in the end price. And since most of the watchmakers are already working on high standards, they don't feel the need for an additional expense, leading to a costlier product.
Fact is: the Chronometer Certificate is only valid for the time and place of testing. You leave the laboratory with your newly-certified chronometer and it's already (in a microscope point of view, granted!) behaving differently.
So, what's the use, for the normal people, of a C.C. watch? None, except vanity. In (professional) navigation things are a bit different. Just because in this industry, everything has to be certified. Chronometers are just one thing more in the endless list of certificates that we have to carry on board, ranging from life rafts to shackles.
Chronometers were born to conserve (interesting concept) the time on board with the purpose of longitude calculation.
On the eighteen century, when its use became popular, and while at sea, there was no way to check their accuracy. Hence the need for a high precision movement. Back in those days, a ship would leave the port of Lisboa and would arrive to Rio de Janeiro one month later with no way to check the local time in between. They could only rely on the accuracy of the ships chronometer to all the duties involving time (including the astronomy calculations, for navigation purposes). That was the basis for the C.C.'s: assurance and reliability for the mariners.
They had to know the limits of their clocks for their daily routine aboard. Lets not forget that before this technological advance, everybody was checking time with a sandglass.
Nowadays, things are different.
When I was a Second Mate, on freighters, one of my duties, around noon (besides the bloody Noon Sight astronomical calculation) was to check the daily chronometer rate. For that matter, we would listen one radio station from the USA (but there are others) synchronized with an atomic clock and giving the time signal in the form ...poc... poc... poc............... piiiinnnng... ten hours-twenty-two minutes... poc... poc... poc............ piiinngggg.... etc.
By this (mandatory) procedure, we had the chronometer error updated every twenty-four hours making the need for a certificate of accuracy less important, unless we are talking of a really piece of cr.. time measuring machine.
Talking about precision.
Lets face it: any cheap Casio digital watch existing today can have an accuracy of (plus or minus) twenty seconds per month. The quartz technology revolutionized the industry. My Quartz Solar-Powered Casio Riseman G-Shock GW9200 even has Multi-Band Atomic Timekeeping; that is, it makes automatically what I had to do manually as a Second Mate: receives the atomic time signal of several radio stations worldwide and synchronizes, several times a day, with them (as long as you are located within their transmission range). It's virtually errorless. I paid for it 250 Euros. A COSC certified Omega will cost you over three thousand. Which one do you prefer? I know. I do too :-)
The point is a Certified Chronometer is supposed (theoretically) to have a regular rate, by testing standards. That is if it advances it advances, if it looses it looses. On the contrary, a non-certified watch has a non-measured error. It may (or may not) gain one or two seconds in one day, and it may loose that same amount on the next. It may reach the end of a month with exactly the same time of the other. But for accurate work, we have to discard it since we don't have a base to start from. It has nothing to do with precision. It's only a matter of standard testing.
Speaking about precision: you know what is the value of one second of arc in meters, at Equator level, for astronomical navigation purposes?
A little navigation.
At Equator level, the Earth has about 40000 kms (or 40.000.000 mts) of circumference, right? And the good ol' Earth is a sphere, right? Since it is circular in shape, we can divide it in 360 degrees, and each degree in 60 minutes and each minute in 60 seconds, right?
Let's do that: 40.000.000/360/60/60 = about 30 mts.
That's the error that you may get in your nautical calculations for every second that your watch forgets.
Today, ships with ten times that distance in length are becoming common. It's a bit funny, if we think of it. You are calculating the position of your bridge wing, not of the ship as a whole (her bow is two hundred meters away).
On the other hand, the best I've managed, in astronomical navigation, was a chart plotting precision, with sextant and chronometer, of roughly half a mile (nearly 900 mts). And believe me: I've trained a lot as a Cadet. I had a Captain that insisted on it.
You know what this value means in terms of time? Thirty seconds. You always have more chances to make a sextant (optical) error than a time one.
I rest my case.
I rest my case.