Re: [Phys-l] Help! An explanation for the laity

[Bernard Cleyet <bernardcleyet@redshift.com>]

Thanks John, however, I mislead (unintentionally).  What he means is why 
is a log used period.   I  initially gave him the series for his 
calculation;  ln (x) ~ x-1 - [(x-1)^2]/2  + [(x-1)^3]/3 ....

Then plugged in and decided for all the likely clocks, better would be 
the series:

2 * { (x-1)/(x+1)  + <[(x-1)/(x+1)]^3>/3 + ...}   With only three terms 
sufficient for ~ one part per million, IIRC.  (The limit of his least 
expensive device.  He has a GPS one that is significantly better!)

He is (has) programming (ed) his device upgrade prototype to use the 
"Cleyet" method *, which is more apprehensible.  He want to additionally 
add the "Bateman" method, which uses the log. decrement; this he doesn't 
understand.


* Horological Science Newsletter 2007-4

bc

John Denker wrote:

> On 12/04/2007 09:31 PM, Bernard Cleyet wrote:
>
>  
>
> > "Why is the natural log used?"
> >    
>
> 1) Because 
>   ln(1.001) = .001                [1]     
>
> 2) You can use any log you want, but unnatural logs
> just make the formula more complicated-looking.
>
>  log10(1.001) = 0.00043           [2]
>
>
>
> Which would you rather remember, [1] or [2]?
>
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