IV CONTENTS. 



PAGE 



6. Signs from which an observed uniformity of sequence may 



be presumed to be resolvable . . .48 



7. Most, if not all, cases of sequence from very complex ante- 



cedents, are resolvable . . . .52 



8. Two kinds of empirical laws . . .54 



CHAPTER XVII. Of Chance, and its Elimination. 



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



chance . . . . , .56 



2. Chance defined and characterized . . .57 



3. The elimination of chance . . . .64 



4. Discovery of a residual phenomena by eliminating chance . 66 



5. The doctrine of chances . . . .86 



CHAPTER XVIII. Of the Calculation of Chances. 



1. The foundation of the doctrine of chances, as taught by 



Laplace, defective . . . .70 



2. The real foundation, what . . . .71 



3. Theorem of the doctrine of chances, which relates to the 



cause of a given event . . . .76 



4. In what cases the doctrine is practically applicable . 81 



5. How applicable to the elimination of chance . . 82 



CHAPTER XIX. Of the Extension of Derivative Laws to 

 adjacent Cases. 



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

 tingent upon collocations . . . .86 



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



the bounds of actual experience . . .88 



3. Those cases must be adjacent eases , . .90 



CHAPTER XX. Of Analogy. 



1. Various senses of the word analogy , .96 



2. Nature of analogical evidence . . .97 



3. On what circumstances its value depends . .103 



CHAPTER XXI. Of the Evidence of the Law of Universal 

 Causation. 



1. The law of causality rests upon an induction by simple 



enumeration . . . . .107 



2. In what cases such induction is allowable . .111 



3. The universal prevalence of the law of causality may once 



have been doubtful . . . .113 



4. Ground of its present certainty . . .115 

 o. Limits of the reliance due to it 117 



