182 ADAMS— THE EINSTEIN THEORY. 



extension by Weyl of the Einstein theory, which is really a logical 

 extension of the Riemann geometry. In Riemann's geometry the 

 scale of measurement is fixed ; a line element at one place can be 

 compared directly with a line element at a distance. But in a system 

 of geometry to remain true to the idea of direct action as opposed 

 to action at a distance this assumption appears unwarranted. And 

 so Weyl assumes that the scale of measurement varies from point to 

 point in the four-dimensional universe. This hypothesis results in 

 another differential form which characterizes the metrical proper- 

 ties of space — this time a linear differential form — and Weyl shows 

 how the electric and magnetic state of space can be interpreted in 

 terms of the coefficients which enter into this expression. 



All that I have attempted to do in the foregoing is to show what 

 kind of a theory the Einstein theory is ; how radically it differs in 

 principle from what we are accustomed to ask for in a physical 

 theory. This theory opens up to the study of natural phenomena a 

 new universe, a universe in which geometry and physics cannot be 

 regarded as independent sciences. This universe is a four-dimen- 

 sional metrical manifold ; physical phenomena are determined by 

 the metrical properties of this universe. There is no reason that 

 I can see why this generalized space of the Einstein theory should 

 not be named " the ether." But giving it a name does not help in 

 understanding its properties, and it is a wholly different ether from 

 that to which we have grown accustomed. 



It is interesting to note that the possibility of space having a 

 dynamical property was suggested by Riemann, although it was 

 left for Einstein to develop the consequences of such a conception. 

 In fact, Riemann went farther, and suggested the possibility of 

 space being a discrete manifold instead of a continuum, and this 

 suggestion is of particular interest at the present time in view o'f 

 the growing importance of the quantum theory which is founded 

 on the idea of discreteness somewhere as opposed to continuity. 



The difficulties in understanding the Einstein theory are not so 

 much mathematical difficulties ; they arise from the vain attempt to 

 picture to our minds the kind of space required by the theory. We 

 instinctively try to form a model of some mechanism which will 



