xxv iii Contents. 



19, 20. Combination of testimony. 

 21, 22. Scientific meaning of a miracle. 



23, 24. Two distinct prepossessions in regard to miracles, and the logical 

 consequences of these. 



25. Difficulty of discussing by our rules cases in which arbitrary 



interference can be postulated. 



26, 27. Consequent inappropriateness of many arguments. 



CHAPTER XVIII. 



ON THE NATURE AND USE OF AN AVERAGE, AND ON THE 

 DIFFERENT KINDS OF AVERAGE. 



1. Preliminary rude notion of an average, 



2. More precise quantitative notion, yielding 

 (1) the Arithmetical Average, 



3. (2) the Geometrical. 



4. In asymmetrical curves of error the arithmetic average must be dis 



tinguished from, 



5. (3) the Maximum Ordinate average, 



6. (4) and the Median. 



7. Diagram in illustration. 



810. Average departure from the average, considered under the above 



heads, and under that of 



11. (5) The (average of) Mean Square of Error. 

 12 14. The objects of taking averages. 



15. Mr Gallon s practical method of determining the average. 



16, 17. No distinction between the average and the mean. 



18 20. Distinction between ivhat is necessary and what is experimental here. 



21, 22. Theoretical defects in the determination of the errors . 

 23. Practical escape from these. 



(Note about the units in the exponential equation and integral.) 



