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kept in London and Borda’s standard metre — change in length 
from time to time as the Earth changes its direction of motion 
through space and through the aether, or as these bars are turned 
about in the laboratories in which they are kept. We have no 
means of measuring our speed relative to the aether. For all we 
know to the contrary our Earth may at the present instant have 
a speed of, say, 190,000 miles per second relative to the aether. If 
it has this velocity, then a man who is 5ft. Sin. high when he 
stands up at right angles to this relative motion will be only 
4ft. 9in. in height when he lies in the direction of the motion. We 
could not tell this difference bv the eye, because the retina of our 
eye would have undergone a similar contraction in the same direc- 
tion and the image of the 4ft. him man would cover the same pro- 
portion of the retina in that direction as the image of the 5ft. Sin. 
man would cover in the other direction. We fail to observe this 
actual change which takes place in the dimensions of what we call 
rigid bodies, not because it is possibly small (it may be great as a 
matter of fact), but because it is of such a character as to baffle 
all ordinary tests, although it is revealed indirectly by such 
peculiarly applied tests as the Micbelson-Morley experiment. The 
change will not appear just so difficult for us to admit when we 
remember that in all probability the forces of cohesion which bind 
together a rigid body are of the nature of electrical forces and 
thus act through the aether with its drift relative to the rigid body. 
We commonly speak of space as having three dimensions, the 
directions which we popularly term up-and-down, to-and-fro, 
right-and-left. We can, however, imagine a flat or two-dimensional 
universe inhabited by flat beings who would fail to realise what 
was meant by the third dimension of up-and-down. And 
mathematicians find it just as easy to make calculations for four 
dimensions as for only three. It is possible for us, therefore, to 
imagine a model (we cannot actually construct it) which would 
introduce a fourth dimension, in a two-dimensional diagram we 
can show in a graph how the lengths and widths of rectangles of 
the same shape as this page are connected. In a three-dimensional 
model we could show how the lengths, breadths, and thicknesses 
of books of similar shape to this volume are connected. And in a 
four-dimensional model we could show in the same way how the 
lengths, breadths, and thicknesses of the volumes of Proceedings 
of this Society had varied at different times. The mathematician 
can, therefore, picture a model in which are indicated by distances 
in four directions, mutually at right angles, what we may call 
length, breadth, height, and (say) time. But owing to the curva- 
ture of the surface of our spherical Earth, the direction which we 
call in Perth purely height is a direction in space which is equiva- 
lent partly to height and partly to (say) breadth in Sydney, and 
equivalent partly to height and partly to (say) length in Roe- 
