the infinite series, as it stretches away in unending succession
towards the small end, which is of importance. The arbitrarily large
event with which the series starts has no importance at all. We can
arbitrarily exclude any set of events at the big end of an abstractive
set without the loss of any important property to the set as thus
modified.

I call the limiting character of natural relations which is indicated by
an abstractive set, the 'intrinsic character' of the set; also the
properties, connected with the relation of whole and part as concerning
its members, by which an abstractive set is defined together form what I
call its 'extrinsic character.' The fact that the extrinsic character of
an abstractive set determines a definite intrinsic character is the
reason of the importance of the precise concepts of space and time. This
emergence of a definite intrinsic character from an abstractive set is
the precise meaning of the law of convergence.

For example, we see a train approaching during a minute. The event which
is the life of nature within that train during the minute is of great
complexity and the expression of its relations and of the ingredients of
its character baffles us. If we take one second of that minute, the more
limited event which is thus obtained is simpler in respect to its
ingredients, and shorter and shorter times such as a tenth of that
second, or a hundredth, or a thousandth--so long as we have a definite
rule giving a definite succession of diminishing events--give events
whose ingredient characters converge to the ideal simplicity of the
character of the train at a definite instant. Furthermore there are
different types of such convergence to simplicity. For example, we can
converge as above to the limiting character expressing nature at an
instant within the whole volume of the train at that instant, or to
nature at an instant within some portion of that volume--for example
within the boiler of the engine--or to nature at an instant on some area
of surface, or to nature at an instant on some line within the train, or
to nature at an instant at some point of the train. In the last case the
simple limiting characters arrived at will be expressed as densities,
specific gravities, and types of material. Furthermore we need not
necessarily converge to an abstraction which involves nature at an
instant. We may converge to the physical ingredients of a certain point
track throughout the whol