vi CONTENTS. 



CHAPTER XXVIII. 



ANALOGY. 

 SECTION PAGE 



1. Analogy . . . . . . . 



2. Analogy as a Guide in Discovery 



3. Analogy in the Mathematical Sciences 



4. Analogy in the Theory of Undulations 



5. Use of Analogy in Astronomy 



6. Failures of Analogy ...... 



CHAPTER XXIX. 



EXCEPTIONAL PHENOMENA. 



1. Exceptional Phenomena ..... 



2. Imaginary or False Exceptions ..... 



3. Apparent but Congruent Exceptions . . . .313 



4. Singular Exceptions . . . . . . .316 



5. Divergent Exceptions ..... 320 



6. Accidental Exceptions . . . . . . .324 



7. Novel and Unexplained Exceptions .... 



8. Limiting Exceptions ....... 



9. Real Exceptions to Supposed Laws .... 

 10. Unclassed Exceptions ..... 



CHAPTER XXX. 



CLASSIFICATION. 



1. Classification ......... 344 



2. Classification involving Induction ..... 346 



3. Multiplicity of Modes of Classification . . . .348 



4. Natural and Artificial Systems of Classification . . .351 



5. Correlation of Properties . . . . . . .353 



6. Classification in Crystallography ...... 359 



7. Classification an Inverse and Tentative Operation . . 364 



8. Symbolic Statement of the Theory of Classification . . 367 



9. Bifurcate Classification . 371 



10. The Five Predicates 375 



11. Summun Genus and Infima Species . . . . .379 



12. The Tree of Porphyry 381 



13. Does Abstraction imply Generalization ? . . . .389 



14. Discovery of Marks or Characteristics ..... 394 



15. Diagnostic Systems of Classification ..... 396 



16. Index Classifications ........ 400 



17. Classification in the Biological Sciences .... 405 



18. Classification by Types . . . . . . .411 



19. Natural Genera and Species . . . . . .414 



20. Unique or Exceptional Objects . . . . . .418 



21. Limits of Classification . 421 



