CHAP. I.] NATURE AND DESIGN OF THIS WORK. 19 



were the data of experience alone employed present results of 

 this character. To obtain a definite solution it is necessary, in 

 such cases, to have recourse to hypotheses possessing more or less 

 of independent probability, but incapable of exact verification. 

 Generally speaking, such hypotheses will differ from the imme- 

 diate results of experience in partaking of a logical rather than of a 

 numerical character ; in prescribing the conditions under which 

 phaenomena occur, rather than assigning the relative frequency 

 of their occurrence. This circumstance is, however, unimportant. 

 Whatever their nature may be, the hypotheses assumed must 

 thenceforth be regarded as belonging to the actual data, although 

 tending, as is obvious, to give to the solution itself somewhat of 

 a hypothetical character. With this understanding as to the 

 possible sources of the data actually employed, the method is 

 perfectly general, but for the correctness of the hypothetical ele- 

 ments introduced it is of course no more responsible than for the 

 correctness of the numerical data derived from experience. 



In illustration of these remarks we may observe that the 

 theory of the reduction of astronomical observations* rests, in 

 part, upon hypothetical grounds. It assumes certain positions 

 as to the nature of error, the equal probabilities of its occurrence 

 in the form of excess or defect, &c., without which it would be 

 impossible to obtain any definite conclusions from a system of 

 conflicting observations. But granting such positions as the 

 above, the residue of the investigation falls strictly within the 

 province of the theory of Probabilities. Similar observations 

 apply to the important problem which proposes to deduce from 

 the records of the majorities of a deliberative assembly the mean 

 probability of correct judgment in one of its members. If the 

 method of this treatise be applied to the mere numerical data, 

 the solution obtained is of that wholly indefinite kind above de- 

 scribed. And to show in a more eminent degree the insufficiency 

 of those data by themselves, the interpretation of the arbitrary 

 constants (I. 16) which appear in the solution, merely produces 



* The author designs to treat this subject either in a separate work or in a 

 future Appendix. In the present treatise he avoids the use of the integral 

 calculus. 



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