198 



EEPOKI — 1888. 



inaccuracy of the weights ; and the iBequality of the price-returns more 

 than the inequality of the weights. 



The only proof of the theory which can be offered to the unmathema- 

 tical reader is to verify it by actual trial. We may assume a certain set 

 of data as perfectly correct : then affect each of them with an error such 

 that the modified datum is, say, as likely as not to be in excess or defect 

 by 10 per cent. ; is very unlikely to be out by 30 or 40 per cent. ; and 

 cannot, humanly speaking, be out by more than 50 per cent. A simple 

 method of affecting a given set of figures with an error of this degree is 

 to multiply each of them with a figure formed by adding together twenty 

 digits taken at random from mathematical tables or statistical returns ; 

 dividing each product by 90 (the mean about which aggregates of twenty 

 random digits hover). The data thus artificially aff'ected with error are 

 now to be used in the computation of an index-number, an erroneous 

 number, which is to be compared with the result assumed to be true as 

 having been deduced from the unfalsified data. A great number of such 

 trials having been made, it will appear that the erroneous index-numbers 

 deviate from the true one with the fi-equency and to the extent predicted 

 by theory. 



A specimen of this verificatory process is subjoined here. The data 

 employed by Mr. Palgrave in his computation of an index-number for 

 1885 ' are assumed to be correct ; then each datum is displaced or falsi- 



' See above, p. 195. 



