the limits of
being from 1 to
, or from 0 to
,
Perhaps it may be thought that this notation is merely a circuitous way of expressing what was more simply and as effectually expressed before; and, in the above example, there may be some truth in this. But there is another description of cycles which can only effectually be expressed, in a condensed form, by the preceding notation. We shall call them varying cycles. They are of frequent occurrence, and include successive cycles of operations of the following nature:—