VI CONTENTS. 



PAGE 



4. Hence empirical laws cannot be relied on beyond the 



limits of actual experience . . . .41 



5. Generalizations which rest only on the Method of Agree- 



ment can only be received as empirical laws . . 43 



6. Signs from which an observed uniformity of sequence 



may be presumed to be resolvable. . . .44 



7. Two kinds of empirical laws . . , 47 



CHAPTER XVII. Of Chance, and its Elimination. 



1. The proof of empirical laws depends on the theory of 



chance . , . , . . .49 



2. Chance defined and characterized . . . .50 



3. The elimination of chance . . . . .55 



4. Discovery of residual phenomena by eliminating chance . 57 



5. The doctrine of chances . . . . .59 



CHAPTER XVIII. Of the Calculation of Chances. 



1. Foundation of the doctrine of chances, as taught by 



mathematics . . . . . .61 



2. The doctrine tenable . . . . .63 



3. On what foundation it really rests . . .64 



4. Its ultimate dependence on causation . . .68 



5. Theorem of the doctrine of chances which relates to the 



cause of a given event .. . .. . .72 



6. How applicable to the elimination of chance . . 74 



CHAPTER, XIX. Of the Extension of Derivative Laws to Adjacent 



Cases. 



1. Derivative laws, when not casual, are almost always con- 

 tingent on collocations . . . . .78 



2. On what grounds they can be extended to cases beyond 



the bounds of actual experience . . . .80 



3. Those cases must be adjacent cases . . .82 



CHAPTER XX. Of Analogy. 



1. Various senses of the word analogy . . .86 



2. Nature of analogical evidence . . , .87 



3. On what circumstances its value depends . . 91 



