All the subscribers' lines are connected in order to jacks on the first two or three or four operators' positions, and these connexions are repeated or " multipled " upon each succeeding similar group of positions.
With the adoption of relays the signalling between the subscribers and the exchange became automatic, and, with the introduction of the principle of double and automatic supervision on the cord circuits, it became possible for the operators to tell at any instant the state of a connexion.
P operators D upon a monomial symmetric function is clear.
= exp,udl where exp denotes (by the rule over exp) that the multiplication of operators is symbolic as in Taylor's theorem.
F m +Z(D2f1) (Dif2)f3...fm+Z(D3f1) f 2 f fm, the summation in a term covering every distribution of the operators of the type presenting itself in the term.