CONTENTS. xli 



CHAPTEK XXI. 



THEORY OF APPROXIMATION. 

 SECTION PAGE 



1. Theory of Approximation 456 



2. Substitution of Simple Hypotheses 458 



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 XXII. 



QUANTITATIVE INDUCTION. 



1. Quantitative Induction 483 



2. Probable Connexion of Varying Quantities . . . . . . .484 



3. Empirical Mathematical Laws 487 



4. Discovery of Rational Fornralse 489 



5. The Graphical Method 492 



6. Interpolation and Extrapolation 495 



7. Illustrations of Empirical Quantitative Laws 499 



8. Simple Proportional Variation 501 



CHAPTER XXIII. 



THE USE OF HYPOTHESIS. 



1. The Use of Hypothesis 504 



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 



6. Experimentum Crucis 518 



7. Descriptive Hypotheses . 522 



