"The Calendar" by David Ewing Duncan: Numerous Errors?

I have recently read "The Calendar" by David Ewing Duncan. It is an
excellent book, and one that often had me going back over the pages to
check or compare what I was currently reading with what I had read
earlier. In doing so, however, I found several discrepancies that I
couldn't explain. The question is, are these errors, or have I simply
misunderstood?

My copy is a paperback edition published by Fourth Estate, London, in
1999. I can only quote page numbers from my book, so my apologies if
your page numbers are different. In the order that they appear in the
book, my queries are as follows;

1. Calendar Index, page vi - The year as amended by Pope Gregory XIII
(the Gregorian calendar): 365 days, 5 hours, 48 minutes, 20 seconds.
Shouldn't this be 365 days, 5 hours, 49 minutes, 12 seconds?

2. Calendar Index, page vi - Length of time the Gregorian calendar is
off from the true solar year: 25.96768 seconds. Deducting this from
the figure I have assumed in item 1 above, the true solar year would
be 365 days, 5 hours, 48 minutes, 46.03232 seconds. Why be so
precise, and then get it wrong? According to some sources, this
figure corresponds to the 1840's, not 1900, 1996, 1999 or 2000 (all
years considered to be current at various locations in the book).

3. Calendar Index, page vi - The year as measured in oscillations of
atomic cesium: 290,091,200,500,000,000. If Cesium oscillates
9,192,631,770 times per second, then there are 794,243,384,928,000
oscillations in a day. Is the year really an exact multiple of
500,000,000 oscillations?

4. Timeline, page xxi, Year 1100 - The year by Omar Khayyam is given
as 365d 5h 49m 12s (and the same again on page 278), but on page 190
it is given as 365.24219858156 days. This converts to 365d 5h 48m
45.96s, so why the difference? I believe that the first figure is
actually the Gregorian year. The second figure is 99.99999% of that
given for the atomic year.

5. Time Stands Still, page 97 - In the table, 6 Kalends April is given
as 26th March, whereas other sources give this as 27th March. Which
is correct?

6. Time Stands Still, page 98. The formula 22 + 11 + 33 - 30 + 3,
should read 22 + 11 = 33 - 30 = 3?

7. The Strange Journey of 365.242199, page 154 - He (Aryabhata)
estimates the length of the solar year at 365.3586805 days, some 2
hours 47 minutes and 44 seconds off from the true year in Aryabhata's
era, which equalled 365.244583 days. The footnote says that this is
about 7 seconds shorter than our current year. Only three errors
here! These are (i) 365.3586805 days is 2 hours 47 minutes and 44
seconds off our era, not the year in 499; (ii) 365.244583 days equals
365 days, 5 hours, 52 minutes, 12 seconds, which is actually 3 minutes
26 seconds longer than 365.242199 days; and (iii) In 499, the year
would have been about 7 seconds longer, not shorter, than our current
year.

8. From the House of Wisdom to Darkest Europe, page 190 - Omar Khayyam
appears to have calculated the year to within 4 seconds of what it was
in 1079. Duncan doesn't make this point, but just brushes it of as
'overly precise'. Any comments?

9. From the House of Wisdom to Darkest Europe, page 190-191 - Ulugh
Beg gave a measurement for the length of the year that came to 365
days, 5 hours, 49 minutes and 15 seconds, just 25 seconds too long. I
make this figure about 29 seconds longer than our time, and 27 seconds
longer than in 1440. Where does the 25 seconds come from?

10. Solving the Riddle of Time, page 277-278 - The table contains two
differences from what is given elsewhere in the book. The
measurements for Omar Khayyam and the Gregorian calendar are not as
quoted on pages 190 and 277 respectively. See items 4 and 1 above for
further details.

My conclusions? It's a great book, that probably took Duncan many
years to research. However, next time, he should get somebody to
check his mathematics!

Regards,



Philip Clarke