CONTENTS, xli 



CHAPTER XXI. 



THEORY OF APPROXIMATION. 



SECTION PAfiK 



1. Theory of Approximation 456 



2. Substitution of Simple Hypotheses 4;")8 



3. Approximation to Exact Laws 462 



4. Successive Approximations to Natural Conditions 465 



5. Discovery of Hypothetically Simple Laws 470 



6. Mathematical Principles of Approximation 471 



7. Approximate Independence of Small Effects 475 



8. Four Meanings of Equality 479 



9. Arithmetic of Approximate Quantities 481 



CHAPTER XXn. 



QTTANTITATIA'E INDUCTION. 



1. Quantitative Induction 483 



2. Probable Connexion of Varying Quantities 484 



3. Empirical Mathematical Laws 487 



4. Discovery of Rational Forraulfe 489 



5. The Graphical Method 4P2 



6. Interpolation and Extrapolation 495 



7. Illustrations of Empirical Quantitative Laws 499 



8. Simple Proportional Variation 601 



CHAPTER XXIII. 



THE USE OF HYPOTHESIS. 



1. The Use of Hypothesis .o04 



2. Requisites of a good Hypothesis 510 



3. Possibility of Deductive Reasoning 511 



4. Consistency with the Laws of Nature 514 



5. Conformity with Facts 516 



(>. Experimentum Crucis 518 



7. Descriptive Hypotheses 522 



