from her actual motion, was less than the force of gravity at 
the earth s surface, in the exact ratio of the inverse square 
of the distance from the centre of the earth/" And Grant adds, 
in a note, “It is said that Newton became so much agitated 
as soon as he began to suspect the probable result of his cal- 
culation, that he was compelled to assign to a friend the task 
of bringing it to a conclusion."" * Grant very fairly notices, that 
in making this calculation, “ the force which retains the moon 
in her orbit is here supposed to act in the same direction during 
a very short space of time "" ; but he thinks “ this supposition, 
though not strictly true, cannot sensibly affect the result."" Now 
I beg to observe that the same fallacious supposition runs 
through all the demonstrations of the Principia , and is espe- 
cially patent in the first proposition, which is demonstrated by 
an illogical application of the laws of the parallelogram of 
forces or velocities to the solution of a problem which relates 
to a central or centripetal force ; and this, I say, does mate- 
rially affect the result, and, in fact, entirely alters it.f But I 
pass over this objection now, because there are others which 
claim priority over it namely, that the moon has no such 
orbit in reality, as was assumed for the basis of the calculation, 
if the earth goes round the sun ; that there was not any com- 
putation whatever “ deduced from the moon"s actual motion "" ; 
that there is no such fall from the tangent to her actual path ; 
in short, that all that depends upon this famous “ experiment am 
crucis "" (as it has been called), “which was to decide whether 
Newton had penetrated into the secret of the celestial motions, 
or whether he had been occupying his mind with speculations 
of a purely mathematical nature,"" J rests upon a series of false 
data and false suppositions, and upon consequent fallacious 
reasoning. This problem also, like that of “ the three bodies "" 
(§ 2), was only solved upon the false supposition that the moon 
has a nearly circular orbit round the earth, which could only 
be if the earth is at rest in space ; the moon’s actual path, ex 
hypothesi, if the earth goes round the sun, being an orbit, 
differing slightly from that of the earth, nearly in a circle round 
the sun. This is simply a fact, about which there can be no 
dispute among rational beings who understand the subject; 
and I need scarcely add that the force of gravitation, or any 
other force in the universe, can only produce or affect the 
actual motions of bodies; and the effects of such forces cannot 
possibly be truly measured by calculations based upon merely 
relative or apparent motions. This particular branch of this 
great subject, however, I have specially discussed in the Paper 
* Grant, p. 25. f Vide Vis Inertia Vida , § ix. passim X Grant, p. 2] 
VOL. IV. 2 E r 
