1. Observation 399 2. Distinction of Observation and Experiment 400 3. Mental Conditions of Correct Observation 402 4. Instrumental and Sensual Conditions of Correct Observation 404 5. External Conditions of Correct Observation 407 6. Apparent Sequence of Events 409 7. Negative Arguments from Non-Observation 411 CHAPTER XIX. EXPERIMENT. 1. Experiment 416 2. Exclusion of Indifferent Circumstances 419 3. Simplification of Experiments 422 4. Failure in the Simplification of Experiments 424 5. Removal of Usual Conditions 426 6. Interference of Unsuspected Conditions 428 7. Blind or Test Experiments 433 8. Negative Results of Experiment 434 9. Limits of Experiment 437 CHAPTER XX. METHOD OF VARIATIONS. 1. Method of Variations 439 2. The Variable and the Variant 440 3. Measurement of the Variable 441 4. Maintenance of Similar Conditions 443 5. Collective Experiments 445 6. Periodic Variations 447 7. Combined Periodic Changes 450 8. Principle of Forced Vibrations 451 9. Integrated Variations 452 CHAPTER XXI. THEORY OF APPROXIMATION. 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 Formulæ 489 5. The Graphical Method 492 6. Interpolation and Extrapolation 495 7. Illustrations of Empirical Quantitative Laws 499