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of small ridges and furrows, upon which (the total curvature 
not being zero) these axioms are not true. Similarly, he says, 
although the axioms of solid geometry are true within the 
limits of experiment for finite portions of our space, yet we 
have no reason to conclude that they are true for very small 
portions; and if any help can be got thereby for the expla- 
nation of physical phenomena, we may have reason to con- 
clude that they are not true for very small portions of space. 
I wish here to indicate a manner in which these specu- 
lations may be applied to the investigation of physical phe- 
nomena. I hold in fact 
(1) That small portions of space are in fact of a nature 
analogous to little hills on a surface which is on the average 
flat; namely, that the ordinary laws of geometry are not valid 
in them. 
(2) That this property of being curved or distorted is con- 
tinually being passed on from one portion of space to another 
after the manner of a wave. 
(3) That this variation of the curvature of space is what 
really happens in that phenomenon which we call the motion 
of matter, whether ponderable or etherial. 
(4) That in the physical world nothing else takes place 
but this variation, subject (possibly) to the law of continuity. 
I am endeavouring in a general way to explain the laws 
of double refraction on this hypothesis, but have not yet arrived 
at any results sufficiently decisive to be communicated. 
March 7, 1870. 
The President (Professor CAYLEY) in the Chair. 
New Fellows elected: 
W. G. Apams, M.A., St John’s College. 
A. T. CuapmMan, M.A., Emmanuel College. 
