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 OP 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 



