415 
here it is flat like an orange.” That means that in one case the resisting 
medium was supposed to exist, and in the other was not ; and therefore 
there was confusion and discrepancy. But as regards the motion of the earth 
or planets, I mean simply that the influence of the resisting medium is 
inappreciable, and that it only becomes appreciable when it affects the orbit 
of a body so attenuated as a comet. And* therefore the question of the 
existence of a resisting medium does not invalidate the conclusions drawn 
with regard to the earth, the moon, the sun, and the planets 
Dr. Irons. — Would you apply the same remarks even to motion in the 
plenum ? Supposing the motion to get more and more intense, would it never 
be affected : is it so far attenuated that no amount of velocity would beat it ? 
Mr. Brooke. — That appears to be another question. I am speaking of 
the existing velocities in relation to the moon and sun ; but probably the 
attenuation of the medium is such that no velocity which has hitherto been 
imagined would be in the slightest degree affected by it. Mr. Beddie goes 
on to say, “ If there be really solar motion in space, and if there be a resist- 
ing medium, through which all the heavenly bodies must move, there is not 
a single demonstration in the Principia, whether sound or fallacious, which 
is in accordance with our ‘ current physical astronomy’ ; and no conclusion 
at which Newton arrived by 1 demonstration’ in his ‘ immortal work’ is now 
really accepted by modem astronomers.” There I entirely join issue with 
Mr. Reddie, because, as I have already said, I believe that the resistance of 
the assumed medium is so minute that it will not affect any of the deductions 
of modern physical astronomy, and therefore will not affect their relation to 
the demonstrations or anything else in the Principia. Mr. Reddie then 
says, “ The ‘ revolving body ’ is supposed to move in free space, ‘ void of 
resistance,’ and the areas are described ‘in one immovable plane’ ; and it is 
to these two points I especially desire to direct attention.” And, again, “ In 
the last of the corollaries it is said, ‘ The same thing holds good when the 
planes in which the bodies are moved, together with the centres of force, 
which are placed in those planes, are not at rest, but move uniformly in a 
right line.’ ” And this, he then remarks, is “ an astounding corollary.’’ 
But it is not astounding at all. Unless it can be shown that the results 
deduced from this hypothesis lead to conclusions which are at variance with 
the fact, there certainly is nothing astounding in the hypothesis as at present 
assumed 
Mr. Reddie. — A corollary is generally something obviously deduced from 
what has been previously demonstrated ; and I say there never was such a 
corollary as this in any strictly mathematical work. You will find no such 
contradictary corollary in “ Euclid” : first proving that the thing is true in 
one way, and then assuming that it is all the same if it is supposed to be 
quite another way ! 
Mr. Brooke. — The object of omitting a consideration in the first instance 
is to simplify the matter to be examined, and unless it can be shown that the 
neglect of that consideration would lead to an erroneous conclusion it appears 
to me to be perfectly legitimate. Mr. Reddie says, “ So, then, we are to 
VOL. IV. 2 F 
