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of tlie second theorem, which merely reasons backwards on 
the first, purporting to show that when the radius vector of a 
revolving body describes equal areas in equal times, it is 
moved by a centripetal force ; and the conclusion drawn (from 
the same polygonal figure) is that “ it " — the so-called centri- 
petal force — “ acts, therefore, always in the direction of lines 
tending to the hnmovable point S. — Q. E. D ." And then we 
have, instead of any demonstration, merely this astounding 
assertion : — 
“Case 2. — And it is indifferent whether the surface in which a body 
describes a curvilinear figure is quiescent, or moves together with the body, 
with the figure described, and its point S, uniformly in a right line.” 
15. I crave leave to observe with reference to this, and I do 
so without meaning to sneer, that it is a too simply mathe- 
matical view of the case ! The atom of truth in it amounts to 
no more than this, that if the relative motions continued the 
same, whether the centre was in motion or not, it would not 
signify ! Or this, that if we draw some circles on a sheet of 
paper to represent the orbits of revolving bodies, it is in- 
different whether we carry the sheet of paper while we walk 
about peripatetically, or study it while quiescent on our desk, 
for the figures will still remain the same ! But as a dynamical 
or physical proposition it is ridiculously absurd. For, what 
does it amount to ? In the case of our earth it would amount 
to this. If the earth's orbital motion round the sun is (as we 
have been taught since September, 1863,) 65,000 miles an 
hour, the sun being regarded at rest, and if the sun's attrac- 
tion serves to hold it in its orbit while travelling with that 
velocity (only varying a few thousand miles an hour when in 
aphelion and perihelion) ; then we are to believe that it would 
be ie indifferent," if we were to start the sun off in a right line 
at the rate of 65,000 miles an hour; and that is a slow rate 
compared with that which some astronomers have assigned to 
the sun, for Bessel considered its motion two or three times as 
great, and Professor Airy's predecessor, Mr. Pond, assigned 
to it a velocity equal to that of light. Now, if the sun 
travelled onwards in space at the rate of only 65,000 miles an 
hour, and the earth kept revolving round it, what would then 
the motion of the earth necessarily be? Once every six 
months its motion would be at the rate of 130,000 miles an 
hour, — and how people can even conceive the sun's attrac- 
tion could then hold it, I know not ! — while every six months 
afterwards it would for a moment actually come to a dead 
stop ; and yet then, instead of falling into the sun by its 
gravity, we must suppose it would suddenly hop off again to 
career wildly round the sun as before ; its motion on this sup- 
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