CONTENTS. xli 



CHAPTER XXI. 



THEORY OF APPROXIMATION. 

 SECTION PAGK 



1 Theory of Approximation ....... ... 456 



Substitution of Simple hypotneses ......... 458 



Approximation to Exact Laws ........... 462 



Successive Approximations to Natural Conditions ..... 465 



Discovery of Hypothetically Simple Laws ....... 470 



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. 



THE USE OF HYPOTHESIS. 



1. The Use of Hypothesis 



2. Requisites of a good Hypothesis . . 



3. Possibility of Deductive Reasoning . 



4. Consistency with the Laws of Nature . 



5. Conformity with Facts 



6. Experimentum Crucis 



7. Descriptive Hypotheses . ; . 



504 

 510 

 511 

 514 

 516 

 518 



