566 



SCIENTIFIC THOUGHT. 



of quite recent writers ^ to place the whole matter 

 upon a thoroughly scientific basis. But it is not these 

 necessary technical refinements that interest us most 

 at present ; rather let us take note how the needs of 

 governments, as well as the uncertainty and risks of 

 life, have automatically led to the definition and study 

 of three distinct statistical conceptions, which in our 

 age govern a very large part of all our practical 

 12. enterprises. These three conceptions are the proba- 



Probability, ^ r i. 



co-^opera-^^ bility of future events based upon long series of past 

 buuon!*'^'^' experiences, the idea of reducing or averaging risks 

 by " amicable " co-operation, and the " equitable " dis- 

 tribution of the burdens of such co-operation according 

 to the individual units who co-operate."^ It will at 



^ It is generally admitted that 

 Prof. G. F. Knapp created a kind 

 of era in the more rigorous mathe- 

 matical treatment of the subject 

 by his various publications, dating 

 from the year 1868 with his tract 

 ' Ueber die Ermittelung der Sterb- 

 lichkeit aus den Aufzeichnungen 

 der Bevolkerungs -statistik.' M. 

 Block {loc.cit., p. 232) says: " Ce 

 livre a fait une veritaVjle sensation 

 parmi les hommes speciaux ; noii 

 que I'auteur ait apporte beaucoup 

 de uouvelles pierres a I'edifice, mais 

 il a donn^ h, ces pierres une ordou- 

 nance, une disposition qui les con- 

 stituent un monument." In the 

 year 1874 he published his ' Theorie 

 des Bevolkerungswechsels. ' Manj- 

 other writers have followed in the 

 new track, among whom I will only 

 mention Becker, Zeuner, and Lexis. 

 The graphical method is largely 

 employed by these authors, amongst 

 whom Zeuner resorts to a repre- 

 sentation in three dimensions with 

 some very elegant results. See his 

 ' Abhandlungen zur mathematischen 



Statistik' (Leipzig, 1869). A his- 

 torical and critical review of these 

 and older writings is given in the 

 last - named woik of Knapp, p. 

 5'3, &c. See also Prof. Lexis's 

 ' Einleitung in die Theorie der 

 Bevi ilkerungs-statistik ' (Strasburg, 

 1875). 



^ This is not the place to dis- 

 cuss the social and moral aspects 

 of co-operation, which by future 

 historians will possibly be looked 

 upon as one of the very few novel 

 political ideas which our century 

 lias evolved or at least elaborated 

 in a practical form ; the older co- 

 operative attempts, such as were 

 made under the influence of the 

 ideals of the great Revolution by 

 Fourier, Saint Simon, and Babeuf 

 in France, and by Robert Owen in 

 this country, not having contained 

 the elements of permanent success. 

 These elements seem to belong 

 almost exclusively to the line of 

 development started by the "Roch- 

 dale Pioneers." 



