Reduction of Observations. 141 



as most people have ever thought of asking for. When the 

 observations are indefinitely numerous, that is in general in 

 Class II., then an approximate treatment of the equation of de- 

 gree n — 1* incidental to this case becomes appropriate. With 

 regard to unsymmetric curves, the doubts which were before f 

 thrown out as to the application of the Poissonian analysis 

 to the solution of this case are confirmed, since the " abso- 





 lutely " best weights, the -r's of page 138, are not in general 



identical with the weights assigned by the " relative " analysis, 

 the inverses of Mr. Todhunter's U l (< Hist. Prob.' Art. 1002, 

 p. 565). 



There remains over the class of facility-curves which are 

 not known to possess either of the conditions required equally 

 by the absolute and relative method. In this case we must 

 fall back upon the general remarks above offered (/3, y, S). 

 Many of the applications of Probabilities to the social sciences 

 belong to this category. In balancing Testimony numerical 

 precision, as Mr. Venn has justly $ insisted, is out of the ques- 

 tion. But we may obtain what the same writer, in reference 

 to the theory of belief, calls a " logical foothold," by perceiving 

 that the problem of Testimony may be regarded as a degraded 

 case of the problem of observations ; in which, instead of an 

 indefinite number of degrees presented by the continual varia- 

 tion of our scale (the abscissa w) } we have only two degrees — 

 Truth and Falsehood. The measurement of the Useful in 

 general (including the Beautiful) is more like the problem of 

 physical observations in respect of number of degrees ; but it 

 differs more from it in this respect — that in the moral mea- 

 surements there is never an objectively real value ; and there- 

 fore that the weight of authorities cannot even conceivably be 

 tested in this case, as in physics, by their divergence (in pre- 

 vious experience) from an objective real point. For us, how- 

 ever, who hold that the divergence of a source of observations 

 does always, even in Physics, theoretically involve§ a subjec- 

 tive estimate of advantage, the difference in question is not of 

 paramount importance. But this is not the place to pursue 

 these reflections. 



King's College, London. 



i 



* Phil. Mag. 1883, p. 371. t Ibid, p 373. 

 % ' Logic of Chance,' Chap ,xix. 

 § Phil. Mag. 1883, p. 364. 



