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changed and complicated, by the hypothesis of the earth’s revolution round 
the sun. On that hypothesis we may not longer simply take this rate of the 
moon’s motion during an eclipse, namely of 67,000 miles an hour, and mul- 
tiply it by 24 to give the moon’s path in a day, and again by 30 to obtain 
her path approximately in a month ; because although, upon the data assumed, 
67.000 miles is truly the velocity per hour of the moon when in opposition, 
it is by no means or approximately the rate of her whole motion during a 
lunation, as the rate of 2,000 miles an hour almost truly was upon the simpler 
hypothesis that the earth is at rest. Upon the heliocentric hypothesis, with 
the earth in rapid motion, and the moon passing round it while it thus moves, 
the moon must indeed travel 2,000 miles an hour more swiftly than the earth 
when at the full, and she must retain a greater velocity than the earth in 
order to get before it and arrive at her place in her last quadrature ; but it 
is equally a necessity of the hypothesis, that when there her velocity must 
diminish to less than that of the earth, that she may fall back to her place 
in conjunction between the earth and the sun, and that she must continue to 
move with a velocity less than the earth till she falls behind the earth in its 
orbit, and so reaches her place in her first quarter ; so that, just as the moon 
required to travel at the rate of 67,000 miles an hour, or 2,000 miles faster 
than the earth, in order to pass through its shadow in four hours when in oppo- 
sition ; — so when she is in conjunction, and falling behind the earth as much 
as before she exceeded it in velocity, her rate of motion must become reduced 
to 63,000 miles an hour, or 2,000 miles an hour less than that of the earth. 
9. Thus we see, that upon the geocentric system, the moon’s motion, com- 
puted from the duration of a lunar eclipse, was very nearly at a uniform rate 
of about 2,000 miles an hour ; but, from precisely the same data, when we 
change the hypothesis, and assign to the earth a mean orbital motion of 
65.000 miles an hour, then the moon’s velocity must of necessity vary during 
each lunation no less than 4,000 miles an hour, her speed, when she is full or 
in opposition to the sun, being 67,000 miles, and when she is dark or in con- 
junction with the sun, 63,000 miles an hour only. Reasoning from the same 
one initial fact of observation, namely, that during a lunar eclipse the moon 
traverses the earth’s shadow in about four hours, I repeat, that upon the 
geocentric hypothesis the moon’s real motion is very little more than 2,000 
miles an hour throughout, and is nearly the same in every part of her orbit, 
the variation being comparatively slight ; while upon the heliocentric hypo- 
thesis her mean velocity is not only increased by the whole velocity of the 
earth in its orbit, but it actually becomes 4,000 miles an hour greater and 
less at one time than another. The moon’s real velocity during a lunar 
eclipse, and always when she is full and furthest from the sun, upon the 
heliocentric hypothesis, is no less than 4,000 miles an hour greater than it is 
at the time of a solar eclipse, and always when she is nearest the sun imme- 
diately before new moon. This great variation in her velocity also occurs, 
though her distance from the earth is supposed to be nearly the same at 
these two times. 
10. But not only is the rate of the moon’s real motion thus altered, 
and its comparatively uniform motion changed, so materially as to differ 
by no less than 4,000 miles an hour at one time and another each luna- 
tion, when we abandon the Ptolemaic system, but the actual path of the 
moon is also entirely altered, and the very direction in which she moves is 
thereby changed, and even at times reversed. She no longer describes a 
nearly circular or oval path both in space and round the earth every month, 
at a radial distance of less than 240,000 miles, but she moves in an enor- 
mously larger orbit with a radius some 380 times greater ; and this nearly 
circular orbit she now describes, not monthly round the earth, but round the 
sun once a year. Theu her path during each lunation, though she still 
