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It may be interesting to look at the seasonal variations in daily rate
of an ordinary battery powered wall clock. I check this clock monthly,
so the values are the average daily rate for the month. All values are
positive, i.e., the clock always runs fast.

      2006  2007  2008
Jan   .40   .38*  .37
Feb   .40   .45   .39
Mar   .38   .46   .44
Apr   .43   .46   .45
May   .47   .50   .50
Jun   .48   .52   .52*
Jul   .40   .48   .50
Aug   .48   .48   .49
Sep   .47   .50   .52
Oct   .44   .47   .49
Nov   .41   .41   .46
Dec   .35   .38   .41

* new battery installed at beginning of this month


And here are values for a $25 Timex digital watch I bought in 2000. It
still has the original battery. I don't wear this watch a lot; probably
less than 5 hours per week.

      2006  2007  2008
Jan   .43   .41   .42
Feb   .40   .42   .42
Mar   .41   .43   .45
Apr   .41   .41   .43
May   .39   .41   .42
Jun   .34   .40   .38
Jul   .26   .35   .34
Aug   .35   .34   .34
Sep   .40   .40   .40
Oct   .43   .45   .43
Nov   .43   .44   .46
Dec   .41   .43   .44


The time checks are by eye and ear using WWV on a cell phone. By
comparing the phone audio to the audio from a shortwave receiver I've
found that the phone is consistently 1/4 second late, as well as I can
estimate, so this constant is disregarded.

My monthly error checks are accurate to perhaps 1/4 second, so the
corresponding daily rate is probably accurate to plus or minus .01 second.

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