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 CHAPTER XXIV. EMPIRICAL KNOWLEDGE, EXPLANATION AND PREDICTION. 1. Empirical Knowledge, Explanation and Prediction 525 2. Empirical Knowledge 526 3. Accidental Discovery 529 4. Empirical Observations subsequently Explained 532 5. Overlooked Results of Theory 534 6. Predicted Discoveries 536 7. Predictions in the Science of Light 538 8. Predictions from the Theory of Undulations 540 9. Prediction in other Sciences 542 10. Prediction by Inversion of Cause and Effect 545 11. Facts known only by Theory 547 CHAPTER XXV. ACCORDANCE OF QUANTITATIVE THEORIES. 1. Accordance of Quantitative Theories 551 2. Empirical Measurements 552 3. Quantities indicated by Theory, but Empirically Measured 553 4. Explained Results of Measurement 554 5. Quantities determined by Theory and verified by Measurement 555 6. Quantities determined by Theory and not verified 556 7. Discordance of Theory and Experiment 558 8. Accordance of Measurements of Astronomical Distances 560 9. Selection of the best Mode of Measurement 563 10. Agreement of Distinct Modes of Measurement 564 11. Residual Phenomena 569 CHAPTER XXVI. CHARACTER OF THE EXPERIMENTALIST. 1. Character of the Experimentalist 574 2. Error of the Baconian Method 576 3. Freedom of Theorising 577 4. The Newtonian Method, the True Organum 581 5. Candour and Courage of the Philosophic Mind 586 6. The Philosophic Character of Faraday 587 7. Reservation of Judgment 592 BOOK V. GENERALISATION, ANALOGY, AND CLASSIFICATION. CHAPTER XXVII. GENERALISATION.