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might just as well consider them as actually falling stars, because they are 
like the stars in heaven ; for although we call them falling stars, we know 
they have nothing in common with stars. I am sure Mr. Mitchell’s account 
will be a most valuable record on the subject in our Transactions , and it will 
very likely complete No. 4 of our Journal. 
Professor Oliver Byrne. — I have a few remarks to offer to you, and 
they are based upon demonstration, and not conjecture. I am going to base 
what I have to say upon what Archimedes based his mechanics. It is, “ the 
law of sufficient reason,” carried out by Leibnitz, and made great use of by 
Laplace. It is known to all philosophers, who make use of it to prove one 
thing, but reject it when you want to prove another. Leibnitz made great 
use of it, and I should have said that our very learned and worthy Vice- 
President has brought before us a subject that requires our most serious con- 
sideration, because it is the only index we have left, it is really the only 
weather-vane by which men can discover the motions of the heavens. Now, 
I have taken 13 of the principal stars, and I have calculated their positions 
up to the 1st January, 1867, and their proper motions and declinations. It 
was a great deal of labour, and I am sure that each of these stars loses place, 
as regards the observer, by 600 or 700 yards. The pole star and others have 
travelled 666 yards out of their places. These stars all move, and there is a 
delusion in astronomers about them ; they all say they have a proper motion, 
and it is a curious thing that all the negative quantities of these 13 great 
stars differ but 16" from all the positive motions of the larger stars in the 
heavens — 
The Chairman. — The difference between the positive and the negative 
quantities. 
Professor Byrne. — This motion takes place, which I am going to prove 
by the law of sufficient reason. No philosopher has ever been able to prove 
the parallelogram of forces ; and all attempts to prove have failed when the 
quantities compared are incommensurable. If these had relations to one 
another, we could get a law, but it is impossible. If you give me the diagonal 
of the square, no one can tell the length of the side— the diagonal may bo 
20 feet, but you cannot tell the length of the side — that seems simple, yet it 
is impossible that any one can find it out. The diameter of a circle may be 
10 feet, no one can tell the circumference. There is no law for the incom- 
mensurability of quantities, and the law of sufficient reason will not apply. 
What I am going to prove will be proved with the exception that I am 
not taking incommensurable quantities, and the only specimen of human 
reasoning totally perfect is the 5th Book of Euclid, because it takes in the 
doctrine of incommensurable quantities altogether ; and consequently what I 
am going to say is subject, not to comparison with incommensurable quan- 
tities, but quantities that can be measured by practice. I suppose I have taken 
the right motion of the stars ; but to show I have not done so, my empirical 
rule differs 16 seconds, which is very small. We will take 13 of the larger 
stars, and each one in its turn operates upon its neighbour. The question is 
this, — the conclusion I am coming to, the object I wish to prove is this, — and 
