**Systematic overview of why
Sir Robert Anderson's calculations in
The Coming Prince (with regards to the the prophecy of Daniel 9)
are in error for subtracting Julian Leap Days from the result.**

10/20/99

-Paul C. Smith

This article assumes a working knowledge of
the terms Julian Calendar, Gregorian Calendar, JDN, solar day,
solar year, revolution and rotation. For introductory
explanations and basic definitions, see:http://genealogy.org/~scottlee/cal-overview.html, http://www.execulink.com/~idris/calendar7.html provides information pertinent to a preliminary understanding of the difference between solar days and solar years. |

*Criticisms and objections will be
handled, see footnote at
bottom of article*.

**Introductory premise:
**A popular and frequently quoted source by amateur Christian apologists in defense

of the validity of messianic prophecy is Sir Robert Anderson of Scottland Yard, from

his book

by finding exactly 173,880 days, or sixty-nine "weeks" ("sevens") of 360-day prophetic

years, between March 14, 445 BC and April 6, AD. 32 in the Julian calendar.

This article addresses only one problem with this claim
of precision: there are not

173,880 days between these two Julian dates; there are 173,883 (including day one).

Anderson found his "solution" by subtracting three days from the result to
"correct" for

the fact that there are 3 more leap years counted in the old Julian calendar than what

is required to accurately synchronize with a solar year. Our modern calendar,

the Gregorian, handles this more accurately by making only every fourth centennial

year a leap year. It is this adjustment to his result that this article intends to

show the invalidity of.

Anderson's calculations are flawed primarily
because calculations of dates and years

only need to accomodate leap year rules in a calendar when one is trying to calculate:

- a precise count of solar years
*from*a span of time given in calendar days - a precise count of calendar days
*from*a timespan given in solar years

Sir Robert Anderson is not doing either of these -- he is
trying to calculate a precise count

of solar days *from* a span of time given in... solar days. Converting that
count of days into

solar years in order to immediately divide again and allow leap years into the calculation

is a superflous, unnecessary and erroneous step in the process. The claim of precise
(to-the-day)

prophectic success is based upon a prophetic year of 360 solar days of 24 hours.
Therefore,

one may simply count days in any calendar using whatever leap year rule that calendar

happened to implement, accurate or not relative to a solar year. The only criterion
is that

you count days by accurately following the rules of the calendar you are picking the start
and

end dates in. I will grant without argument the legitimacy of the 360-day year, as

well as the accuracy of Anderson's fixing of the starting and ending events as described
in

Daniel 9:24ff.

It is shown axiomatically and confirmed experimentally
below that Anderson's calculations

do not accurately count the number of solar days during the timespan he claims to count.

Identity of some terms as used herein:24 hours, defined by an earth's rotation on its own axis

A Solar Day =365.242199 Solar Days, defined by one earth revolution around the sun.

A Solar Year =

**Proposition 1**:

One can accurately count days between two Julian Calendar

Dates using the Julian Calendar alone, without subtracting

from the result for leap years.

Given any calendar (including the Julian, which did not track

solar years accurately), one does not have to subtract any days

from a count between two dates in order to determine how many

solar days (rotations of the earth on its own axis, which is what

calendar days count) elapsed between the two dates. All you

need to know is the rules of that particular calendar, erroneous

or not, which for the Julian means that a leap-day is added to every

fourth year.A very simple example of why this is so is provided at:

http://people.ce.mediaone.net/paulsmith68/DeleteDays.html

**Proposition 2**:

The Julian Day Numbering system (which is NOT the same as Julian

Calendar Dates), or JDN, is merely a sequential count of solar days

starting with November 25, 4714 BC in the Gregorian Calendar.

It is not meaningful to ask how JDNs deal with leap years, or how many leap years

they include. It is also not meaningful to ask of a JDN whether that number refers

to a Julian date or to a Gregorian date; it will have a corresponding date inboth

calendars, although those dates may be different. Mistakes in understanding on

this often result from the erroneous belief that a date in the Gregorian calendar

will coincide in time with the same date in the Julian calendar. This is not so; take

for example today (the day I am writing this). It is October 20, 1999 in the Gregorian

calender. However, it is October 7 in the Julian calendar. Nevertheless, the JDN 2451472

refers to today, and that JDN has counterparts in both calendars.

So A Julian Day Number (JDN) represents a single DAY IN TIME, and any given event in

time can only have happened onone JDN, it does not happen on one JDN for the

Julian calendar and then on another JDN for the Gregorian calendar, since doing so

would constitute the event being dated to two different days in time, given the definition

of a JDN.

**Proposition 3**:

One can accurately count days elapsed between two JDNs

by subracting the lower JDN from the higher, without subtracting

from the result for leap years.

As long as I pick two dates from the

same calendar, I

can use theJDN numbers for those two datesto calculate the number

of days between them; no further adjustments for leap years are necessary.

A Julian Day Number (JDN) represents a single DAY IN TIME.

It does not and cannot "include" or "exclude" "leap years" because

there is no "year" in the JDN system. JDNs are nothing more than a

sequential count of days elapsed since November 25, 4714 BC

in the Gregorian calendar. JDNs are neither "Julian days" nor

"Gregorian days" nor even "Jewish days." JDNs are merely

solar days (24 hour cycles) that have elapsed since the assigned

starting date.When

different calendars(such as the Julian and Gregorian) drift from each

other, they will havedifferent dates corresponding to the same JDN.For instance, as I write this...

it isJDN 2451472,

it isOctober 20, 1999in theGregorian Calendar,

and it isOctober 7, 1999in theJulian Calendar.Thus as long as I pick two dates from the

same calendar (for

example, two different Julian Calendar dates, two different

Gregorian dates, or two different Jewish dates) , I can

use the JDN numbers for these two dates to calculate the number

of days between them; it would be erroneous to adjust this

calculation any further to account for leap-year anomalies.A very simple example of why this is so is provided at:

http://people.ce.mediaone.net/paulsmith68/OneNumberTwoCalendars.html

**Proposition 4**:

A calendar's accuracy or inaccuracy with respect to solar years does

not affect the number of solar days between two dates in that calendar.

The Julian Calendar's error in calculating leap years would make

it inaccurate only with respect tosolar years, which can be defined either

with reference to the earth's revolutions around the sun, or alternately with

reference to the maximum of the earth's axial tilt. When counting thesolar days

(rotations of the earth on its own axis, which correspond directly to calendar dates)

betweenJulian calendar dates, that calendar's inaccuracy with maintaining

synchronicity withsolar yearsis irrelevant to the math.

**Proposition 5**:

It follows from 1, 2 and 3 that every calendar will count the same number

of solar days between the same two physical days in time.

If propositions 1, 2 and 3 are true, then

every calendarshould yield the

same count of datesbetween twodays in timewhen one determines

therules of the calendar, and thedate that the calendar assigned to the(which can be referenced by JDN). One must not forget

two physical days in time

that two calendars can assign differing dates to the same physical day in time;

I will repeat the example:as I write this...

it isJDN 2451472,

it isOctober 20, 1999in theGregorian Calendar,

and it isOctober 7, 1999in theJulian Calendar.

**Proposition 6**:

We are in possession of Anderson's starting date, ending date,

and the rules of the calendars in question; the result is 173,883,

and it is immutable.

ANDERSON'S START DATE:

JDN:1558960

Julian Calendar:Mar 14, 445 BC

Gregorian Calendar:Mar 9, 445 BC

ANDERSON'S END DATE:

JDN:1732842

Julian Calendar:Apr 6, 32 AD

Gregorian Calendar:Apr 4, 32 ADSince we have established in proposition 2 that using the

JDN system will yield an accurate count, we can simply

subtract 1558960 from 1732842 (and add 1 since we are

including the first day in the number of days elapsed).Therefore, 1558960 - 1732842 = 173,882, and

173,882 + 1 =173,883.Propositions 2, 3 and 4 have shown that no adjustments to

this number are necessary or warranted; to alter the result

according to how many Julian Leap Years did not occur in

either asolar year or in theGregorian Calendaris to miscount

the actual number ofsolar dayselapsed between the two

physical days in time.

**Proposition 7**:

We can achieve further experimental confirmation of propositions

5 and 6 by physically counting the dates each calendar includes between

JDN 1558960 and JDN 1732842. Doing this experiment confirms

that all calendars coincide in counting 173,883 elapsed days for

the timespan in question.

It will be necessary to download a file to view the experimental

confirmation results. You can obtain this file at:

www.theism.net/public/anderson.zip. See the readme for output instructions.

The text file it creates (called "anderson.txt" ) is a table consisting of an

enumeration of every Julian Date, Gregorian Date, Jewish Date, and JDN,

for the period in question, with the respective Day of Week listed as well.An examination of this table will confirm the following:

a) Every date is accurately and sequentially enumerated in the Jewish Calendar*

b) Every date is accurately and sequentially enumerated in the Julian Calendar

c) Every date is accurately and sequentially enumerated in the Gregorian Calendar

d) Every date is accurately and sequentially enumerated in the JDN System

e) Each line of the table has correct associations between the corresponding Julian Date,

Gregorian Date, Jewish Date and JDN.

[f through i: Including the first enumerated day...]

f) ...there are 173,883 enumerated dates in the Jewish Calendar

g) ...there are 173,883 enumerated dates in the Julian Calendar

h) ...there are 173,883 enumerated dates in the Gregorian Calendar

i) ...there are 173,883 enumerated dates in the JDN SystemSince a) through i) are true, propositions 5 & 6 are experimentally confirmed.

*Jewish dates were often observationally set, rather than following a strict

algorithm. Therefore, no calculations in this article are based on the Jewish

dates due to probable inaccuracies with them.

**Proposition 8**:

We can achieve even more experimental confirmation of propositions

5 and 6 by physically counting the LEAP dates and NON LEAP DATES

each calendar includes between JDN 1558960 and JDN 1732842.

Doing this experiment confirms that the "extra" leap days in the Julian

Calendar for the period are offset by an absence of an equal number of

non-leap days; thus, any further adjustment to the result is superflous.

(This also refers to computations performed on the above mentioned file;

computations were performed in Microsoft Access. Click here for instructions

on how to do this yourself.)An examination of this table will confirm the following for the period between:

ANDERSON'S START DATE:

JDN:1558960

Julian Calendar:Mar 14, 445 BC

Gregorian Calendar:Mar 9, 445 BC

...AND ANDERSON'S END DATE:

JDN:1732842

Julian Calendar:Apr 6, 32 AD

Gregorian Calendar:Apr 4, 32 ADThere are

119 LEAP DAYSin theJulian calendar

for the period between Julian March 14, 445 BC and Julian April 6, 32 AD.

There are173,764 NON-LEAP DAYSin theJulian calendar

for the period between Julian March 14, 445 BC and Julian April 6, 32 AD.

119 + 173,764 =173,883There are

116 LEAP DAYSin theGregorian calendar

for the period between Gregorian March 9, 445 BC and Gregorian April 4, 32 AD.

There are173,767 NON-LEAP DAYSin theGregorian calendar

for the period between Gregorian March 9, 445 BC and Gregorian April 4, 32 AD.

173,767 + 116 =173,883Thus it is further experimentally confirmed that the leap year differences

between the inaccurate Julian calendar and the more-accurate Gregorian

calendar cancel each other out. We can see that there are an identical

number of calendar days between the two physical days in time in both

calendars, and that this number is in fact 173,883. Thus two seperate

methods confirm propositions 5 & 6, and thus the final result.

**Conclusion**:

Sir Anderson erred by subtracting three days from his result to account

for the three Julian Leap years that do not occur in the Gregorian calendar

and mis-track the solar year. The prophetic success of his calculations was

never based on solar years in the first place, but rather on 360-day "prophetic"

years which he finds Biblical support for. Thus, we must count **solar**
**days**

and divide by 360 rather than counting solar or axial years. The sixty-nine

"sevens" of Daniel 9 is reasonably interpreted to mean some sort of seven-year

period, so 69 x 7 x 360 of Anderson's years would be 173,880 days.

The legitimacy of the 360-day year can be granted without
argument.

The problem is that in using a year consisting of 360 solar days, it becomes

irrelevant whether or not the calendar used to count the days accurately

maintains synchronicity with the solar or axial year; these calendars could

miscalculate solar years by 11 months, and yet we could accurately

count the number of solar days between two calendar dates without

having to account for anything related to the duration of a solar or axial year.

The unfortunate result of this is that Anderson's
oft-quoted calculations which

find **precision** in the fulfillment of Daniel 9:24ff are erroneous.
Thinking Christians

should analyze this data very carefully -- we have a responsibility to think soberly

before offering anectodal confirmation of our faith which we do not know is true.

Christians should be among the first to eschew dogmatic obstinacy and welcome

honest analysis.

This article remains open to criticism. I do not
expect such a popular document

as Anderson's work to be discarded flippantly; however, I am extremely

confident that the above analysis leaves no room for other conclusions. It should

also be noted that even without this particular finding of error, many Christian

scholars find this research of Anderson's flawed in other ways; thus, acceptance

of Anderson as a reliable source is hardly universal within Evangelical Christendom.

Many well-studied Christians find altogether different scenarios more plausible

for evaluating this prophetic success; I list two web references below (these pose

entirely different scenarios for computing Daniel's "69 weeks"):

from http://www.themoorings.org/apologetics/69weeks/weeks1.html:

[...B]y treating each week of the sixty-nine as seven 360-day years, Sir Robert Anderson calculated that the period of weeks came to a close on April 6, AD 32; Sir Robert Anderson,The Coming Prince,10th ed. (repr., Grand Rapids, Mich.: Kregel Publications, 1984), 127. [...] Unfortunately, Anderson made several errors. [...H]e guessed that Nisan 1 was March 14 (ibid., 123). Actually, it was April 13[!]; Richard A. Parker and Waldo H. Dubberstein,Babylonian Chronology 626 BC-AD 75(Providence, RI: Brown University Press, 1956)

[This author goes on to elucidate problems with the crucifixion date as well]from http://www.sentex.net/~tcc/dan70.html:

[...O]ne cannot assume, "the Jewish year had only 360 days" for interpreting Daniel's 70 Weeks prophecy. The old year ended and a new one began at a new moon, not after so many days had elapsed, as in our calendars. This fact appears to undermine the interpretation of the 70 Weeks of Daniel popularized by Sir Robert Anderson, ingeneous though it may be.

We must not be obstinate about contending for falsehoods.
I personally have chosen

the Christian faith in part because I feel it is a choice that is rationally justifiable
by the

available data. Many others have done the same. The world will be far less
inclined

to even consider following in our footsteps if we show ourselves to be unteachable

when facts disagree with some favorable assumption. Friends, it's time we put this

claim to rest and stopped quoting the "to-the-day" precision of Sir Robert
Anderson's

calculations as a reason to believe.

God bless,

Paul C. Smith

October 20, 1999

*If anyone has a logical objection to any of the
propositions or underlying presuppositions in this article, I welcome the opportunity to
address them. With the exception of duplications, all objections will be published
and answered on the objections page for this article.*

*Please submit objections individually, clearly and
concisely to webmaster@theism.net for consideration. A
clear, cogent refutation of a specific proposition, a demonstration of how a proposition
is based upon a false premise, or a demonstration of how I have misunderstood Anderson's
calculations are expected with any requests for me to retract this article. Please
submit each objection as a separate message, to assist us in keeping track of what issues
have been answered. I am confident that the reasons for this will be understood and
accepted by the reader.*