that its structure differs essentially from that of the Lorentzian
ether; whether the geometry of spaces of cosmic extent is approximately
Euclidean. But we can assert by reason of the relativistic equations
of gravitation that there must be a departure from Euclidean
relations, with spaces of cosmic order of magnitude, if there exists
a positive mean density, no matter how small, of the matter in the
universe. In this case the universe must of necessity be spatially
unbounded and of finite magnitude, its magnitude being determined
by the value of that mean density.

If we consider the gravitational field and the electromagnetic field
from the stand-point of the ether hypothesis, we find a remarkable
difference between the two. There can be no space nor any part
of space without gravitational potentials; for these confer upon
space its metrical qualities, without which it cannot be imagined
at all. The existence of the gravitational field is inseparably
bound up with the existence of space. On the other hand a part of
space may very well be imagined without an electromagnetic field;
thus in contrast with the gravitational field, the electromagnetic
field seems to be only secondarily linked to the ether, the formal
nature of the electromagnetic field being as yet in no way determined
by that of gravitational ether. From the present state of theory
it looks as if the electromagnetic field, as opposed to the
gravitational field, rests upon an entirely new formal _motif_,
as though nature might just as well have endowed the gravitational
ether with fields of quite another type, for example, with fields
of a scalar potential, instead of fields of the electromagnetic
type.

Since according to our present conceptions the elementary particles