CHAP. IV. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS, _continued_.--OF THE DISCUSSION OF IDEAS 180 _Art._ 1. Successive Clearness, 2. Produced by Discussion. 3. Examples. 4. Disputes not useless, 5. Although "metaphysical." 6. Connected with Facts. CHAP. V. ANALYSIS OF THE PROCESS OF INDUCTION 186 _Sect._ I. _The Three Steps of Induction._ _Art._ 1. Methods may be useful. 2. The three Steps. 3. Examples. 4. Mathematical names of the Steps. _Sect._ II. _Of the Selection of the Fundamental Idea._ _Art._ 5. Examples. 6. The Idea to be found by trying, 7. Till the Discovery is made; 8. Preluded by Guesses. 9. Idea and Facts homogeneous. 10. Idea tested by the Facts. CHAP. VI. GENERAL RULES FOR THE CONSTRUCTION OF THE CONCEPTION 195 _Art._ 1. First: for Quantity. 2. Formula and Coefficients found together. 3. Example. Law of Cooling. 4. Determined by Experiment. 5. Progressive Series of Numbers. 6. Recurrent Series. 7. Use of Hypotheses. 8. Even with this there are difficulties. {xv} CHAP. VII. SPECIAL METHODS OF INDUCTION APPLICABLE TO QUANTITY 202 _Sect._ I. _The Method of Curves._ _Art._ 1. Its Process. 2. Its Use. 3. With imperfect Observations. 4. It corrects Observations. 5. _Obstacles_. (I.) Ignorance of the argument. 6. (II.) Combination of Laws. _Sect._ II. _The Method of Means._ _Art._ 7. Its Relation to the Method of Curves. 8. Its process. 9. _Argument_ required to be known. 10. Use of the Method. 11. Large masses of Observations used. 12. Proof of the Use of the Method. _Sect._ III. _The Method of Least Squares._ _Art._ 13. Is a Method of Means. 14. Example. _Sect._ IV. _The Method of Residues._ _Art._ 15. Occasion for its Use. 16. Its Process. 17. Examples. 18. Its Relation to the Method of Means. 19. Example. 20. "Residual Phenomena."