Chapter III: Book III

OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.

CHAP. I. INTRODUCTION 141
_Art._ 1. Object of this Book.
2. An Art of Discovery not possible.
3. Use of Methods.
4. Series of Six Processes.
5. Methods of Observation and Induction.

CHAP. II. OF METHODS OF OBSERVATION 145
_Art._ 1. Referring to Number, Space, and Time.
2. Observations are never perfect.
3. (I.) _Number is naturally exact_.
4. (II.) _Measurement of Space_.
5. Instruments Invented in Astronomy,
6. And improved.
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_Art._ 7. Goniometer.
8. Standard of Length.
10. (III.) _Measurement of Time_.
11. Unit of Time.
12. Transit Instrument.
13. Chronometers.
14. (IV.) _Conversion of Space and Time_.
15. Space may Measure Time.
16. Time may Measure Space.
17. (V.) _The Method of Repetition_.
18. The Method of Coincidences.
19. Applied to Pendulums.
20. (VI.) _Measurement of Weight_.
21. Standard of Weight.
22. (VII.) _Measurement of Secondary Qualities_.
23. "The Howl" in Harmonics.
24. (VIII.) _Manipulation_.
25. Examples in Optics.
26. (IX.) _The Education of the Senses_,
27. By the Study of Natural History.
28. Preparation for Ideas.

CHAP. III. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS;
_and first_ OF INTELLECTUAL EDUCATION 164
_Art._ 1. (I.) _Idea of Space_.
2. Education by Geometry.
3. (II.) _Idea of Number_.
4. Effect of the usual Education.
5. (III.) _Idea of Force_.
6. Study of Mechanics needed,
7. To make Newton intelligible.
8. No _Popular_ Road.
9. (IV.) _Chemical Ideas_.
10. (V.) _Natural History Ideas_.
11. Natural Classes to be taught.
12. Mathematical Prejudices,
13. To be corrected by Natural History.
14. Method of Natural History,
15. Resembles common language.
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_Art._ 16. Its Lessons.
17. (VI.) _Well-established Ideas alone to be used_.
18. How are Ideas cleared?

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.
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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."

CHAP. VIII. METHODS OF INDUCTION DEPENDING ON RESEMBLANCE 220
_Sect._ I. _The Law of Continuity._
_Art._ 1. Its Nature and Application,
2. To Falling Bodies,
3. To Hard Bodies,
4. To Gravitation.
5. The Evidence.
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_Sect._ II. _The Method of Gradation._
_Art._ 6. Occasions of its Use.
7. Examples.
8. Not enjoined by Bacon.
9. Other Examples.
10. Its Value in Geology.
11. Limited Results.
_Sect._ III. _The Method of Natural Classification._
_Art._ 12. Examples of its Use.
13. Its Process.
14. Negative Results.
15. Is opposed to Arbitrary Definitions.
16. Propositions and Definitions correlative.
17. Definitions only provisional.

CHAP. IX. OF THE APPLICATION OF INDUCTIVE TRUTHS 233
_Art._ 1. This forms the Sequel of Discovery.
2. Systematic Verification of Discoveries.
3. Correction of Coefficients.
4. Astronomy a Model.
5. Verification by new cases.
6. Often requires fresh calculation.
7. Cause of Dew.
8. Useful Applications.

CHAP. X. OF THE INDUCTION OF CAUSES 247
_Art._ 1. Is to be pursued.
2. Induction of Substance.
3. Induction of Force.
4. Induction of Polarity.
5. Is Gravity Polar?
6. Induction of Ulterior Causes.
7. Of the Supreme Cause.
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BOOK IV, OF THE LANGUAGE OF SCIENCE.