xvi CONTENTS. 



SECTION PAGE 



4. Method of Avoidance of Error .... 393 



5. Differential Method . . . . . .398 



6. Method of Correction ..... 400 



7. Method of Compensation ..... 406 



8. Method of Reversal . . . . .410 



CHAPTER XVI. 



THE METHOD OF MEANS. 



1. The Method of Means . . . . .414 



2. Several Uses of the Mean Result . . . .416 



3. The Significations of the Terms Mean and Average . .418 



4. On the Fictitious Mean or Average Result . . .422 



5. The Precise Mean Result . . . . .424 



6. Determination of the Zero Point by the Method of Means . 428 



7. Determination of Maximum Points . . . .431 



CHAPTER XVII. 



THE LAW OF ERROR. 



1. The Law of Error .... .434 



2. Establishment of the Law of Error .... 435 



3. Herschel s Geometrical Proof . . .437 



4. Laplace s and Quetelet s Proof of the Law of Error . . 438 



5. Derivation of the Law of Error from Simple Logical Prin 



ciples ....... 443 



6. Verification of the Law of Error . . 444 



7. Remarks on the General Law of Error . .447 



8. The Probable Mean Result as defined by the Law of Error . 447 



9. Weighted Observations . . .449 



10. The Probable Error of Mean Results . 451 



11. The Rejection of the Mean Result . . 454 



12. Method of Least Squares . .458 



13. Works upon the Theory of Probability and the Law of Error 459 



14. Detection of Constant Errors . . . 460 



