Some previous editions of the Hurley text distinguished among the direct, the inverse and the double methods of agreement. This edition does not.
The method of agreement detects a cause in the sense of a necessary condition. The method consists of a search for a single factor common to a number of situations in which the same event occured.
If there are a number of possible causes for a phenomenon and exactly one of them is present whenever the event is present, then it is a necessary condition. Since we do not know whether the linkage occurs in every case, we cannot claim that it is a sufficient condition. Nor do we have evidence that there are not other causes as well so that we have discovered just one necessary condition. But in the circumstances examined, this condition is necessary.
For example, suppose a student took three exams one Friday and got two A's and one C. The student studied a great deal for the exams on which an A was earned and hardly at all for the one on which a C was received. This makes it look as if a lot of studying is a cause of getting a good grade. But, it is necessary not sufficient for we do not know whether the student will always get an A after studying a lot (what if they study the wrong material?) or whether there were other factors involved (such as the order in which the topics were studied).