ntrinsic to the event
or between such quantities and other quantities intrinsic to other
events. In the case of events of considerable spatio-temporal extension
this set of quantitative expressions is of bewildering complexity. If
e be an event, let us denote by q(e) the set of quantitative expressions
defining its character including its connexions with the rest of nature.
Let e_1, e_2, e_3, etc. be an abstractive set, the members being so
arranged that each member such as e_{n} extends over all the succeeding
members such as e_{n+1}, e_{n+2} and so on. Then corresponding to the
series

e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ...,

there is the series

q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ....

Call the series of events s and the series of quantitative expressions
q(s). The series s has no last term and no events which are contained
in every member of the series. Accordingly the series of events
converges to nothing. It is just itself. Also the series q(s) has no
last term. But the sets of homologous quantities running through the
various terms of the series do converge to definite limits. For example
if Q_1 be a quantitative measurement found in q(e_1), and Q_2 the homologue
to Q_1 to be found in q(e_2), and Q_3 the homologue to Q_1 and Q_2 to be
found in q(e_3), and so on, then the series

Q_1, Q_2, Q_3, ..., Q_{n}, Q_{n+1}, ...,

though it has no last term, does in general converge to a definite
limit. Accordingly there is a class of limits l(s) which is the
class of the limits of those members of q(e_{n}) which have
homologues throughout the series q(s) as n indefinitely increases.
We can represent this statement diagrammatically by using an arrow (-->)
to mean 'converges to.' Then

e_1, e_2, e_3, ..., e_{n}, e_{n+1}, ... --> nothing,

and

q(e_1), q(e_2), q(e_3), ..., q(e_{n}), q(e_{n+1}), ... --> l(s).

The mutual relations between the limits in the set l(s), and also
between these limits and the limits in other sets l(s'), l(s"), ...,
which arise from other abstractive sets s', s", etc., have a peculiar
simplicity.

Thus the set s does indicate an ideal simplicity of natural relations,
though this simplicity is not the character of any actual event in s.
We can make an approximation to such a simplicity which, as estimated
numerically, is as close as we like by considering an event which is far
enough down the series towards the small end. It will be noted that it
is