REFERENCES:

section 11.2, last Note on p 126:

[a] "The calendar reform instituted by

Pope Gregory XIII [Inter Gravissimas]

deleted 10 days from the

Gregorian calendar, starting on

5 October 1582."

[b] "The previous calendar day had

index 577 739 on the Julian calendar,

computed as 1581 years of 365 days

plus 395 leap days + 279 days

from 1 January 1852 to

5 October 1582."

[c] "The following day was

15 October 1582."

[d] "From that date to the Convention du

Mètre on 20 May 1875, there were

106 870 calendar days including

leap days."

section 11.7, in a Note on p 141:

[e] "685 263 is the index of

1 January 1601,

computed as 684 609 (index of

15 October 1582) plus 6654 days from

15 October 1582 through

1 January 1601."

section 11.7, in the 2nd Example on p 141:

[f] "The first calendar day of 2010

is Gregorian day 830 991"

PROBLEMS:

The assertion in [a] is misunderstandable:

no days were deleted from the Gregorian

calendar by any pope. In fact, the

proleptic Gregorian calendar without

any "deletions" is

used by ISO 8601:2004, by computer

software and by some historians.

What really is meant is:

'The calendar reform instituted by

Pope Gregory XIII and promulgated in

the bull [Inter Gravissimas] started

the use of the Gregorian calendar with

the date 15 October 1582, which is the

same as 05 October 1582 in the Julian

calendar.'

As for [b]: The "previous calendar day"

would be 1582 Oct 04 in the Julian

calendar, not 1582 Oct 05 as suggested in

[b]. Whichever of the two is meant, the

following computation in [b] is

incorrect: the number of days from

1582 Jan 01 until 1582 Oct 05 is 277 and

not 279, as can be read directly from

[table 11.3, p 146].

As for [c]: It appears as if the

"following day" means the day

after J1582-10-05. This

following day is

J1582-10-06 = G1582-10-16,

not G1582-10-15 as asserted.

(We use prefixes

J and G to distinguish Julian and

Gregorian calendars.)

The computation in [d] is incorrect: the

number of days from G1582-10-15 to

G1875-05-20 is 106 868, not 106 870

as asserted,

because G1582-10-15 = JD 2299 160.5

and G1875-05-20 = JD 2406 028.5.

Assertion [e] is clearly

self-contradictory since

685 263 - 684 609 is not 6654.

Inconsistencies between [b, e, f]: If

1 January 1601 is the day number 685 263

as asserted in [e] then

day 0 is JD 1620 550.5 = G-0276-10-25,

and if day 684 609 is G1582-10-15 as

also asserted in [e] then

day 0 is JD 1614 551.5 = G-0292-05-23.

Still another zero point follows from [f]:

day 0 is JD 1624 206.5 = G-0266-10-29

and finally, if [b] is meant to refer to

G1582-10-14 as day number 577 739, then

day 0 is JD 1721 420.5 = G0000-12-27.

That last date might indicate that day 0

was actually meant to be still another

date, viz J0001-01-01 = G0000-12-30,

but this is just a wild guess of mine.

ANALYSIS OF THE ISSUES:

The inconsistencies may come from

several sources:

from typos (though I am not able to

figure out which);

from the error in the formula for

the duration of successive Gregorian

years (eg in [d]);

from the use of intervals on the

"time axis" instead of points on it.

The time axis is an affine space whose

translation space, formed by the

differences T - T' for points T, T' on

the time axis, is the vector space of

"duration values". Intervals of

lengths > 0 s, however, do not form an

affine space. So one has to take the

lower or the upper bounds of the involved

intervals consistently to arrive at valid

date arithmetic (eg, satisfying the rule

T - T" = (T - T') + (T'- T")).

An error in numerical examples for

non-trivial specifications is particularly

unfortunate because such examples are

often taken as the very first test cases

for an implementation. It is therefore

appropriate to check all the examples

before publishing. Many calendrical

calculators are available online for that

purpose; the one at [http://emr.cs.iit.edu

/home/reingold

/calendar-book/Calendrica.html]

is particularly useful.