Monday, December 10, 2007

Origin of our 24-hour day

Days, months and years are all based on easily observed natural events. But where did the "hour" come from? Why 24?

According to a book I have, the origin lies with the ancient Egyptians and comes to us via the Babylonians, Greeks and the Romans.

Sometime in the third millenium (3000 - 2000 B.C.) the Egyptian administration felt the need for an official year, nicely sub-divided. They observed (most likely) that the "first rising" of the star Sirius was an annual event, synchronous, but not co-incident with the annual flooding of the Nile. This "first rising", known more properly as the heliacal rising, is when both the Sun and a Star rise at the same time in the dawn hours. They counted 365 days to the next heliacal rising of Sirius, and then divided the year into 36 official weeks of 10 days each - the odd five days being discounted.

Why 36 weeks? They, or the Babylonians (not sure which), also identified 35 other stars or star groups which had more or less evenly-spaced heliacal risings throughout the year.

Then they proceeded to divide the night into hours, based on those same star groups which should have led to an 18-hour (half of 36) night! However, on many nights, only 12 of those 36 stars or star groups were reliably visible as they rose, therefore the night was evenly divided into 12 hours and so was the day.

Thus, about 5000 years ago, the 24-hour day was born!

Best regards,


Thursday, November 22, 2007

Scratches inside your vintage watch?

From time to time, I find lines scratched inside vintage watches. I even posted a pic last year of my 1906 Waltham wire lug watch bezel but nobody seemed to know back then.

The penny finally dropped as I took it apart yesterday and made notes, as I do these days. I duly noted down the Wadsworth case serial number xxx9394 and then removed the bezel. By chance, the scratches were lit and oriented such that it looked like VIIII III VIIII IIII - and in Roman numerals that's the last 4 digits of the above serial number! The inscriber hadn't closed the bottom of the V's so, from other angles, it wasn't at all obvious what the scratches represented.

One slightly interesting thing about these particular numerals is that the inscriber didn't use the "subtractive" method, ie IX for 9 and of course, IV for 4 - the which has often been discussed ref. dial numbers. I guess that a V is easier to scribe than a X, and an I is easier than a V.

Ed Ueberall (The Escapement) agreed:
Many of the watch case companies did this in order to keep matching parts together as they traveled around the factory. Often the center section will also have the last four (or more) Arabic digits stamped on the rim, while the bezel had the hand scratched (Roman) numerals. The back cover(s) had the full number stamped inside.

Cary Hurt also mentioned:
You'll also find this on Hamilton wristwatch cases made by both Wadsworth and Fahy's. Though (as Ed says above) this was originally done as an inventory aid during production, it now serves as an easy way to validate the originality of bezel-midsection-back combinations.

This is increasingly important as the rarity of original two-tone watches makes it unfortunately more attractive for mismatched sets to be presented as genuine.
It also can help to identify when a gold-filled bezel is mated to a solid gold back.

I've seen it on Wadsworth cases by Elgin, Waltham and Gruen as well.

Terry Hall just added:
If you find an upside down V, that is a Zero.....

Happy Holidays!


Wednesday, November 14, 2007

Can Vibration break your Wristwatch?

Probably not, I'm pleased to say.  Please read on . . .

This question came to mind while I was mowing the lawn.  I had glanced down at my wrist to check the time and, to my horror, I saw that, instead of my Traser "beater", I was wearing a vintage 1929 Bulova cut-corner watch with no shock protection on the balance jewels.  Not only that but, because of the unbalanced mower blade and general crappy state of the machine, the vibration was actually blurring the watch with about a 1/8 inch amplitude! I just had to do the calcs - and here are the results . .

Machinery Vibration and the Strength of Materials can both get pretty complicated, especially if you don't know the steel alloy used to make a balance staff, so I simplified the problem and assumed that any breakage would be to a balance staff pivot by a shearing force, i.e. applied at right angles to to the staff axis (centerline). Then I assumed that the pivots were good fits in the jewels and that the oil would cushion any tendency for the staff to "rattle" under vibration.  I also assumed that the watch itself being moving in a sinusoidal manner which eased the calculation a lot.  The mower runs at about 600 rpm which equals a vibration frequency of 10 Hz.  The first job was to calculate the peak force on the balance . .

For that, it was necessary to weigh the balance.  Presenting it to the 0-500g kitchen scales proved to be a waste of time, as one might expect!  The needle didn't even budge.  Fortunately, I still had the beam-balance scales that I use for re-loading gun cartridges.  The balance weighed in at 1.3 grains (there are 7000 grains to 1 lb).  Next I measured the balance pivot diameter which was 0.09mm or 90um.

Now, if we knew the peak acceleration, we could calculate the force on the pivots.  Fortunately, that is a common enough calculation in the world of machinery protection and, these days, there are calculators like this available on the 'net.  Using that calculator and entering 10Hz and 3mm, the result was 0.6 G's.  Didn't seem a lot but, just to be sure, the next step was to calculate the stress on the pivots.

As a worst case, I assumed that the watch was vertical.  That way, it is necessary to add 1 G (the constant force of gravity) to the acceleration figure obtained previously, which gives a total acceleration of 1.6 G's. Then, the formula for Stress is simply Stress = Force/Area.  The force is simply 1.6 x the weight (in Newtons).  The balance weight of 1.3 grains converts to 826uN (micro-newtons), and so the force is 826uN x 1.6 = 1.322mN (milli-Newtons).  (The use of Newtons in metric engineering calculations is commonly done to distinguish between force and mass.)  With a pivot diameter of only 0.09mm, the area will be very small.  (Small areas give high stresses - consider the case of the fat lady tottering along on stiletto heels!).  However,we will be doubling it because the force is assumed to be shared equally between the two pivots.  The pivot cross-sectional area (from πD2/4) came out to 6.362nm2, twice that being 12.72nm2.  Therefore, the Stress is 1.322mN/12.72nm2 = 104 kPa or 15 psi.

15 psi doesn't sound much to me.  To make any judgement though, we need to know what level of Stress steel can withstand.  As stated above, it's not easy to find an exact value beyond which a pivot would suddenly snap.  However, a lot of Googling suggested that somewhere around 200,000 kPa (Shear Yield Stress) would be a reasonable guess which is 29,000 psi.  From that, it's obvious that you can mow the grass with a lawnmower way worse than mine while wearing even the most delicate wristwatch from your collection.



Monday, November 5, 2007

Some ice in your watch, Sir?

Somebody said on a popular watch forum:
I've heard the best way to keep a watch for a long time - especially allowing the lubricant's condition - is to pack it in a vacuum [bag] and store it in a freezer (-18 degrees C).

Myself, I think it's pretty good way to mess up a watch . .
1) Take an expensive watch at room temperature 20 C and a not unreasonable 60% relative humidity (RH) inside the watch.
2) Place it in the freezer (baggie or not, makes little difference). As the temperature inside the watch falls, the relative humdity increases. Condensation starts at +12 C (the dew point for 60% RH) and continues down to O C when it will freeze. However, condensation will still continue to occur as the temperature falls, building up as more ice until the internal temperature stabilizes at -18 C or whatever. See here for proof.
3) The watch will have stopped by this point because the oil will be too viscous.
4) Now take out the watch: as your fine timepiece warms up, the ice melts and the water will probably emulsify the oil rendering it essentially useless and bringing forward your next service date to tomorrow.

I do keep my watches in the kitchen but certainly not in the freezer, nor even the fridge for that matter!


Tuesday, October 23, 2007

The Equation of Time

This is really about the different ways of representing "the equation", but first a little preamble. (or you could Google "equation of time" and view all 94,700 results :wink:)

Watches are, of course, mainly instruments to measure the passage of "time". However, "time" in that context is a man-made concept and is dependent on the machinations of atomic clocks and such-like. Furthermore, the division of the planet into time zones, although good for commerce and the punctuality of trains, has also helped to divorce us even further from the reality of the time by which humanity once lived i.e. solar time; for example - when it is noon at Greenwich (by "noon" I mean when the Sun is at it's highest, not 12 o/clock), the Sun over Rockall Island still has yet to climb quite a bit, even though it's in the same time zone. This also explains why using your watch to find North can send you wandering up to 15 degs off, and that's not including the 6 deg penalty for forgetting to correct for Summer Time (who, me?).

Anyway, the "equation of time" represents the imperfect motion of our planet around the Sun. The equation itself is horrendous, don't even bother to look at it. Generally, we tend to use the term to mean it's result for any given day of the year. Lindbergh used such a result on his epic flight to Paris. The equation of time is also of significance to garden gnomes, strangely enough. "What's the time, Grumpy?" - "Bloody 'ell have I got to climb up the sundial again??". You see, if you set a sundial to your watch on Feb 14th to please SWMBO, I guarantee it will be a half-hour fast when you next look at it on Nov 5 between fireworks.

So, without further ado, here are several ways from worst to best to represent this "equation of time" . . . ta daaa . . !!

The most seriously boring way is a table:

Part of a Sun Data table . . .
Col. 1: Date
Col. 2: Equation of Time. Number of minutes and seconds the Sun is off compared with an accurate clock which shows local mean time.
Col. 3: fast or slow (Sun).
Col. 4: Declination of the Sun in degrees and minutes. When negative, the Sun is south of the celestial equator; when positive, north. Values are averaged over the 4 year leap year cycle.


A little better - a graph

I prefer, at the very least, a visual approach. Here's the equation plotted out on bog-roll. You'll notice that clocks do agree with the Sun four times a year but it's not really obvious why in this graph form.

equation of time in graph form

Better yet

If the graph is plotted against the angle of the Sun instead of against the time of year, the effect of our wobbly orbit, etc becomes immediately apparent.

The figure below is called an "analemma" (no jokes, please).

graphic figure of eqn of time

and there's an even prettier one on our family globe, I didn't even know what it was until yesterday:

However it does look like the folks below knew all about it. It's a Jaeger-LeCoultre Gyrotourbillon (photo by Ron DeCorte, taken from The cam rotates just once per year, as you should expect by now ;-) - if anyone knows what the months cam does, please leave a comment to this post.

jeager le coultre eqn of time cam

However I like this one the best. Straight from nature - a time-lapsed sequence of the Sun at 8:30 AM for a year, by Dennis di Cicco

time lapse of Sun at 8:80 am for one year

Here's quite a good site on the subject

Monday, October 22, 2007

An Accidental Sparkle!

As I recall, you can buy a special filter to get the sunburst effect - but the tiny sparkle below, just above the balance jewel, was completely accidental and no filter was used!

gruen movement

My setup uses three lamps, hence the six-pointer. You'll notice that the angles between the points and the point intensities are not equal because of my unequal lamp placements and distances.

So, how did the sparkle appear? The light from each lamp hits the curved bevel on the regulator and is reflected up into the camera's field of view. Even though the lamps have diffusers on them, the single curvature concentrates the reflected light and gives a fan shaped reflection beam rather than a spot beam. The "accident" occurred due to the exposure setting used. It was enough to saturate the image at the center of the sparkle but to have less and less saturated area going outwards along each reflection beam.



Thursday, October 18, 2007

The risk of getting humidity in a watch

People tend to fear that all kinds of nasty stuff will rush into their watches the moment the slightest opening appears, such as when setting the time.  Rest easy - it just ain't so.  Stuff only gets in if air flows in.  Air only flows if there is a pressure difference to cause it to do so.  Usually there is no difference in pressure between the inside and outside of your watch - even sealed ones! No pressure difference = no flow.  Therefore, that horribly humid air will stay outside of your horological masterpiece for the short period during which you'll be setting the time.

But if you leave the crown pulled out and it is unsealed (unlikely) another process takes place.  The humidity (by this I mean absolute humidity, not the kind given in weather forecasts) inside and out will equalize by a process called diffusion.  This is less good.   Picture the following:

In hot and humid Bahrain, due to an interruption, you leave your watch on the Hotel balcony for a week with it's unsealed crown pulled out.  Just before leaving your room to check out, you spot the watch, throw it in your bag & rush off to the airport.  I guarantee that there will be liquid water inside your watch before you get through your first Jack Daniels!

It's the drop in temperature that does it.  Have a look at the psychrometric chart here  (Opens in a new tab, click on the chart there to enlarge it).  Let's say it's 36 deg C and 80% relative humidity (RH) inside your watch.  Find that point on the curve for 80% RH.  Now move to the left until you reach the 100% curve - this is the so-called dew-point temperature for a water content of 0.030 as shown by the scale on the right.  The distance you moved is only 4 deg C.  Any cooling after that causes condensation inside your watch and, as you know, water+oxygen+steel=rust  ;-(

best regards,