2. When m = 1 the fraction becomes 2/3; i.e. the odds are 2 to 1 in favour of recurrence. And there are writers who accept this result. For instance, Jevons (_Principles of Science_ p. 258) says "Thus on the first occasion on which a person sees a shark, and notices that it is accompanied by a little pilot fish, the odds are 2 to 1 that the next shark will be so accompanied." To say nothing of the fact that recognizing and naming the fish implies that they have often been seen before, how many of the observed characteristics of that single 'event' are to be considered essential? Must the pilot precede; and at the same distance? Must we consider the latitude, the ocean, the season, the species of shark, as matter also of repetition on the next occasion? and so on. I cannot see how the Inductive problem can be even intelligibly stated, for quantitative purposes, on the first occurrence of any event. 3. See in _Mind_ (x. 454) Mr Jacob's account of the researches of Herr Ebbinghaus as described in his work _Ueber das Gedächtniss_. CHAPTER IX. _INDUCTION AND ITS CONNECTION WITH PROBABILITY._ 1. We were occupied, during the last chapter, with the examination of a rule, the object of which was to enable us to make inferences about instances as yet unexamined. It was professedly, therefore, a rule of an inductive character. But, in the form in which it is commonly expressed, it was found to fail utterly. It is reasonable therefore to enquire at this point whether Probability is entirely a formal or deductive science, or whether, on the other hand, we are able, by means of it, to make valid inferences about instances as yet unexamined. This question has been already in part answered by implication in the course of the last two chapters. It is proposed in the present chapter to devote a fuller investigation to this subject, and to describe, as minutely as limits will allow, the nature of the connection between Probability and Induction. We shall find it advisable for clearness of conception to commence our enquiry at a somewhat early stage. We will travel over the ground, however, as rapidly as possible, until we approach the boundary of what can properly be termed Probability.