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Final Answers
© 2000-2020 Gérard P. Michon, Ph.D.

 Huygens

Horology

Time doesn't exist.  Watches do.

 Michon
 
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On this site, see also :

Related Links (Outside this Site)

Horology - The index  (originally by  Fortunat F. Mueller-Maerki)
British Horological Institute   |   Royal Observatory Greenwich
Kelloseppakoulu:  The Finnish School of Watchmaking.
NIST Time and Frequency DivisionHistory.
US Naval Observatory:  Time Service Department  (Tycho).

Bibliography :

Wheel and Pinion Cutting in Horology   by  J. Malcolm Wild, FBHI (b. 19??)
The Crowood Press Ltd, 2001.  Hardcover reprint 2012, 253 pp.  (ISBN 0-978-1-86126-245-5).  Appendix includes extracts from relevant Swiss standards  (NIHS)  20-01, 20-02, 20-10, 20-25  and British standard  BS 978-2 (1952).

Videos :

How it's made:  Luxury Watches
 
Making the first watch:  Life story of  George Daniels (1926-2011)
[ Unrelated to Henry Daniels (1912-2000) who helped him with the Space Traveller's Watch. ]

 
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Horology


(2012-11-19)   Horology
Approximating astronomical ratios with gears.

Horologists are primarily concerned with the measurement of mean solar time  (there are  approximately  86400 atomic seconds in a mean solar day).  To design a mechanical watch that would keep both mean solar time and sidereal time, we need a good approximation of their ratio.  The value at  J2000.0  was approximately:

1.002737909350795   =   [ 1; 365, 4, 7, 1, 2, 1, 361 ... ]

This  continued fraction expansion  (CFE)  is clearly  begging  to be trunctated just before the last term quoted above.  This yields:

[ 1; 365, 4, 7, 1, 2, 1 ]   =   46879 / 46751   =   1.00273790934953263...

Remarkably, although the actual ratio does vary, the above rational approximation will remain  optimal  for more than a century  (well beyond the warranty period of any mechanical clock or watch).  For a watchmaker, the problem is that the denominator of that fraction is  prime  and can only be produced by a wheel with at least that many teeth  (clockmakers call them  leaves).  Making a wheel with  46751  leaves is out of the question...

So, we have to settle for somehing less.  Here are good approximations to  46879 / 46751  that can be attained with wheels that have no more than  n  teeth.  The error in the last column is expressed in seconds per day.

Approximating  46879 / 46751   with
at most  m  wheels of  n  teeth or fewer
 :
mnNumerator  Denominator    Error  
  3    46751    (7 . 37) . 181    46751  0
246879(7 . 37 . 181)467510

Space Traveller's Watch  by  George Daniels (1926-2011) with the help of Henry Daniels, FRS (1912-2000).
(In this video, George Daniels misquotes the above ratio as "1.002737942", which it ain't.)


(2012-11-19)  Daniels Coaxial Escapement 
The most notable innovation of the 20th Century in mechanical horology.

 Come back later, we're
 still working on this one...

Escapement   |   Co-axial escapement
 
Daniels Chronograph (2:27)  presented by its maker,  George Daniels (1929-2011).

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visits since August 4, 2019
 (c) Copyright 2000-2020, Gerard P. Michon, Ph.D.