372 REPORT—1850. 
The accompanying Map (Plate V.) has been constructed principally 
from computations furnished to the Committee by Lieut. W. 8. 
Stratford, R.N., Superintendent of the Nautical Almanac, verified 
in some parts by duplicate computations made under the direction 
of the Astronomer Royal. 
The elements employed for computation of the geocentric places 
of the sun and moon are those of the Nautical Almanac. The sun’s 
semidiameter, as given in the Nautical Almanac, is increased by 
xdon part, the moon’s parallax by τοῖσυ, part, and the moon’s semi- 
diameter by 4,5 part, in conformity with the results of extensive 
investigations by the Astronomer Royal. It is to be: remarked that 
the semidiameter thus found for the moon is that corresponding to 
an illuminated moon seen on a dark sky: if the apparent semi- 
diameter when the dark moon is seen on the sun’s bright dise be 
sensibly smaller, the breadth of the shadow and the duration of 
total darkness will be less than those given in the map. 
The numbers in the Ist, 2nd, 3rd, 7th, and 8th columns are 
computed for the points opposite to them in the central line of 
shadow, but they will apply with sufficient accuracy for other neigh- 
bouring points within the shadow. The numbers in the 4th, 5th, 
and 6th columns are also computed for the points opposite to them 
in the central line of shadow; but they require large corrections to 
make them applicable to other points within the path of the shadow 
but not on its central lime. These corrections are given by the 
numbers at the top and bottom of the map, corresponding to the 
various lines drawn longitudinally through the shadow’s path. An 
example will best illustrate the mode of finding these corrections. 
It is required to find the duration of total darkness and the angles 
from the upper point of the sun’s disc for disappearance and reap- 
pearance, at Vladimir. 
Opposite Vladimir, the duration of total darkness on the central 
line is 189°. The longitudinal line passing through Vladimir, if 
traced to the bottom of the map, is found to correspond to the 
factor 0°7. Hence the duration of total darkness at Vladimir will 
be 189s x 0°7 = 182s. 
Opposite Vladimir, the angles from the sun’s upper point at dis- 
appearance and reappearance are respectively 64° and 116°. The 
longitudinal line passing through Vladimir, if traced to the top of 
the map, is found to correspond to the correction 46° towards S. 
Hence the angles from the sun’s upper point for disappearance and 
reappearance at Vladimir will be 
64° + 46° = 110° and 116° + 46° = 162°. 
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