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tides, that I am able to guarantee the result of my calculation of the 
time of high water, within a few minutes :— 
From twelve o’clock, noon, of the 23rd April, 1014, to noon of the 
12th December, 1860, allowing for the change of style and leap years, 
there were 309,223 real days. 
The synodical period of the moon is 29.530588715 days, and new 
moon occurred on the 12th December, 1860, at 47.6 minutes after noon. 
Multiplying the length of the synodical month by 10472 months, we 
find 
29°530588715 x 10472 = 309244°325 days. 
From which, subtracting the number of days from 23rd April, 1014, to 
12th December, 1860, or 309223 days, we find 
21-325 days, or 21° 7° 48™ 
It follows from this calculation that new moon occurred at 
April, . . . 23% O° 47.6™—1014, A. D. 
Minus .. . 21% 7 48™ 
Or,at . . . 14 16% 59°6™—April, 1014, A. D. 
2. é. at 5 o’clock on the morning of the second of April. 
Therefore full moon occurred at 
April, . . . 12 16" 59-6™ 
Plus obec eas. A Q1e6 
164 11" 21:™2 
Therefore the astronomical, or true full moon, occurred at 21 minutes 
past eleven at night of the 16th April, 1014. 
- Calculating by the established rules, the calendar or ecclesiastical 
full moon occurred on the 18th April, 1014 (Sunday), which would 
therefore make Easter Day fall on the 25th April, and make the 28rd 
April Good Friday, agreeable to the traditions of the battle of Clontarf. 
I shall now show that the calculation of the tides makes it quite 
certain that the date 1014 falls in with all the physical circumstances 
related of the battle. 
It appears from the calculation that I have given already that 
The age of the moon at noon on the 23rd April, 1014, was 21.292 days, 
or 21° 7* nearly. 
The tide was therefore a neap tide, and the moon in her third 
quarter. 
From the Academy’s observations, it appears that on such a day of 
the moon’s age, at the spring equinox, the itide at Kingstown is full at 
5" 22™ in the morning, 
from which it follows that the tide along the Clontarf shore, when not 
