The successor function used by Peano to define natural numbers is the prototype for a serial relation.
Bertrand Russell used serial relations in The Principles of Mathematics[1] (1903) as he explored the foundations of order theory and its applications.
A. Bernstein for an article showing that particular common axioms in order theory are nearly incompatible: connectedness, irreflexivity, and transitivity.
The prototype is Peano's successor function as a one-one relation on the natural numbers.
Russell's series may be finite or generated by a relation giving cyclic order.
"[1]: 181 To explain Meinong, Russell refers to the Cayley–Klein metric, which uses stretch coordinates in anharmonic ratios which determine distance by using logarithm.