PHYSICAL ASTRONOMY. 123 
obtain by previous calculation, several places on the earth’s surface, where, 
for a given time of the place, a central (total or annular) eclipse will happen. 
In other words, it will be necessary to know beforehand the course of the 
centre of the moon’s shadow over the earth’s surface. Cut from thin brass 
plate or pasteboard a circle, whose diameter is equal to the diameter of the 
globe, multiplied by the difference of the apparent radii of the sun and 
moon, and divided by the parallax of the moon. Next, place horizontally 
upon the globe a ruler, and upon the ruler the above-mentioned circle. 
Let A be a place on the globe, which for a given local time has the sun in 
its zenith, and let B represent a place which, according to the preceding 
calculation, is to see a central eclipse at this same time ; adjust the globe in 
such a position that A occupies its highest point, and for this position of the 
globe, move the circle upon the inner horizontal ruler in such a manner 
that the centre of the circle shall lie perpendicularly above the point B. If 
we suppose straight lines to be drawn from all points in the circumference 
of the circle, perpendicular to its plane, then those vertically under the plane 
will inclose that space on the globe which, for the time in question, will be 
covered by the full shadow of the moon. We must now place the still 
horizontal ruler in such a manner that the centre of the circle shall con- 
stantly be vertically above the successive points B’, B”’, B’”, &c , which for 
given times have a central eclipse. The globe must be turned at the same 
time in such a manner that its highest point is continually that which at the 
given times has the sun in its zenith. We can thus mark the entire path 
of the full shadow and its bounds on the globe, from which it may be trans- 
ferred toa map. Cut now a circle whose diameter is equal to the diameter 
of the globe, multiplied by the sum of the apparent radii of the sun and 
moon, divided by the moon’s parallax, and proceed with this circle as 
before ; we shall in this manner obtain all those places which lie before the 
northern and southern borders of the half shadow, and which consequently 
only perceive a contact of the edges of the moon and of the sun. 
Ili.—Puysican AstTRoNomy. 
Rotation of the Earth; its Spheroidal Form ; Centrifugal Force; Simple 
Proof of the Spheroidal Shape of the Karth; Local Variation of Gravity. 
43. The daily motion of the starry heavens is only apparent, being a con- 
sequence of the actual turning of the earth on its axis, called its rotation. 
This rotation proceeds in a direction from west to east, since we see the 
apparent rotation of the heavens taking place in the opposite direction, or 
from east to west. Let, in fig. 7, pl. 6, the greater circle, KIHA/zh, repre- 
sent the stationary heavens, and the smaller circle, the rotating earth with 
its centre C. The point 0, in the upper part of the circle, will then, by its 
rotation, be made successively to assume the positions 0,0. The conse- 
quence will be, that the horizon of o will be first Hoh, then Joi, then Kok, 
123 
