630 TRANSACTIONS OF SECTION F. 



of measurement to aid the. judgment too immature to seize the significant funda- 

 mental fact concealed by its diverse manifestations. Purely arithmetical work is, 

 however, limited to the tabulation of exact records, where the whole field to be 

 surveyed can be covered, where no approximation or interpolation is necessary, 

 and where statistics becomes only another name for accountancy ; whereas the 

 application of mathematical principles makes it possible to measure the inac- 

 cessible, to describe the animal from the single bone, to make firm observations 

 from a shifting base, to dispense with the fixed meridian which the base practice 

 of industrial and oflacial needs obscures. 



Great progress has been made in recent years on what I am calling the 

 arithmetical side of statistics. With the encouragement of the very careful work 

 done by the International Institute of Statisticians, whose labours have been mainly 

 in this direction, official statisticians are aiming at logical systems of classification, 

 on such natural lines as may be applicable for the majority of civilised nations and 

 for long intervals of time. There are many difficulties in this direction : economic 

 categories — such as skilled and tuiskilled labour, manufactured goods and raw 

 materials, animal or vegetable products, occupied or imoccupied — do not admit of 

 such simple definition as divides an acid from an alkali ; statistical definitions are 

 rather the delimitation of boundaries, and it is a matter of convention on which 

 side particular persons or things are to be placed. Different conventions have 

 become established in different countries, and the rapid change of conditions 

 frequently induces an alteration in the conventions of a single country. Progress 

 is being made in the direction of uniformity as between country and country, and 

 it is here that the classifications of the International Institute are so important. 

 It is still the case, however, that we are so far from agreement, that it is impossible 

 to understand the published statistics of this or any other country without 

 intimate knowledge of the methods of compilation and classification in each 

 group. The comparison of wages or prices, for example, in England and Germany 

 is so difficult as to be hopelessly misleading, except in the hands of those few who 

 have made a special study of these statistics in both countries. 



It has till recently been the custom of departments publishing statistical 

 returns to issue them without explanation of the particular conventions adopted, 

 and then to complain that the ignorant public misquote them, till there was a 

 danger that statistics should be issued only by officials for officials, and even by an 

 official for himself alone, while the use of them (necessarily eiToneous) by the 

 general public was regarded as objectionable trespass in a private preserve. The 

 growth of popular interest, and of a certain blind and misguided confidence in 

 statistical statements, resulted in the printing of cautions that the statistics 

 did not mean what they appeared to mean ; and thus boards were erected to the 

 effect that this table was dangerous to statisticians and newspaper writers should 

 drive with caution ; but it did not for long occur to those responsible that 

 it was their business to put the public roads in good order for the convenience of 

 travellers. 



The Board of Trade — and especially the Labour Department — have gone a long 

 way now in the direction of explicitness of statement as to the exact meaning 

 of their tables, and of carefully-thought-out improvements in classification and 

 nomenclature ; and herculean efforts have been made to improve the Occupation 

 Census, the difficulties of which task have hardly been realised by its many critics. 

 The returns on a greatly altered basis for 1901 illustrate the permanent dilenoma 

 that compilers of periodic returns have to try to avoid. If the old classification 

 is retained, modern conditions throw it out of date ; if a new one is adopted, 

 comparisons may be made impossible. In 1881 veterinary surgeons and farriers 

 were classed together in the Census list of occupations ; in 1891 the latter were 

 put under ' Workers in Metals,' and in West Ham (for instance) were included 

 under the heading * Blacksmiths and Whitesmiths.' In 1901 whitesmiths are merged 

 either in * Others in Engineering' or in 'Miscellaneous Metal Trades,' blacksmiths 

 are given together with ' Strikers,' and the whole group of metal industries 

 reai'ranged. The result is that in comparing 1881 and 1 901 tjie smallest comparable 



