320 TRANSACTIONS OF THE CANADIAN INSTITUTE. [Vou. VIII. 
is no such thing as a logical distinction between the motion of one thing 
say to the north and the motion of the whole universe with the exception 
of that one thing, in the opposite direction. That we usually attribute 
the motion to the smaller part, thinking the remainder of the universe at 
rest, as for instance in case of the Copernican System versus the Ptolemaic, 
is strictly speaking only a matter of economy of thought. Whether we 
say the earth turns around its axis or the whole extratelluric universe 
revolves round the earth, amounts to the same thing. The facts say the 
one as imuch as the other, they state nothing more than that space rela- 
tions between the earth and the rest of the universe are continuously 
changing in a certain way. 
The significance of the relativity of space magnitudes may be 
illustrated by a consideration, the first mention of which, if I am not 
mistaken, goes back to Condillac. Suppose the Lord should put us all 
into a deep sleep, and while we slept should reduce the spacial .extension 
of the whole universe, or at least that part which is .accessible to our 
senses and scientific instruments, to a hundred millionth part of its 
present extension without making the least change in the proportion of 
the objects and their parts. The earth would then have scarcely the 
size of a bowling ball, and we men would then be much smaller than the 
tiniest infusoria and bacteria. Now when awakened next morning 
would we not be astonished to find everything so small?) Not at all. 
We would not even notice a change, for all our standards would be 
reduced too. Men would still be five or six feet tall, and the Cathedral 
of Ulm, and the Washington Monument would still be about a hundred 
and sixty meters high. The Paris normal meter would deviate for the 
same fraction as before from the ten millionth part of a quadrant of the 
earth’s meridian. Itis even not necessary that the Lord should go through 
the trouble of putting us into a deep sleep; he can accomplish the whole. 
procedure before our eyes, and we could never notice anything. Since 
we could not possibly notice it if He did it, we have no right to say He 
does not do it. In fact the absolute size of the universe known to us, 
and everything in it may be subject to enormous fluctuations which 
we have no means of noticing or ascertaining. Against the above argu- 
ment the objection might be raised that it would be impossible to change 
the absolute magnitudes without damaging the proportions in time and 
gravity, but it will easily be seen that time does not enter into this question 
at all. Jf the orbits of the planets and the amplitudes of the waves of 
light and electricity are reduced in magnitude, the time magnitudes could 
remain the same as now, even absolutely, if that means anything. A little 
more intricate becomes the problem with regard to weight or gravity. 
Would gravity remain the same on a celestial body if the volume of that 
