OONTEKTS. xli 



CHAPTER XXI. 



THEORY OF APPROXIMATION. 

 SECTION PAUK 



1. Theory of Approximation - .".' ! '. . . 456 



2. Substitution of Simple hypotheses . . . . 'i V .. . .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 Formulae 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. 



THB USE OF HYPOTHESIS. 



