RELATION OF VARIABLES. 133 



of observations and groups increases each point tends to coincide 

 with a point on the curve corresponding to the true functional rela- 

 tion, and each line tends to coincide with the tangent at that point. 

 In case regressions are not used, the result is simply a series of points 

 determining the curve. 



Lastly, as is the case in applying any statistical method, the end 

 result gives the relation of dependent variable not to each measured 

 independent one, as such, but to a correlated system of unobserved 

 variables which each measured one represents. In other words each 

 observed variable is an index of a certain complex consisting of a 

 number of unknown elements, and a statistical method merely serves 

 to eliminate the effects of all but one of these complexes at a time and, 

 by synthesis, to determine the effect of any combination of them. 

 The method of successive approximation offers no exception to this 

 rule, and, in order to further disentangle these complexes, additional 

 variables must be measured and the number of observations increased. 



6. Literature Cited. 



Blair, T. A. 



1913. Rainfall and spring wheat. Mo. Weather Rev., 41: 



1515-1517. 

 1915. Temperature and spring wheat in the Dakotas. Mo. 



Weather Rev., 43: 24-26. 

 1918. Partial correlation applied to Dakota data on weather 



and wheat yield. Mo. Weather Rev., 46: 71-73. 



Bocher, M. 



1909. An introduction to the study of Integral Equations. 

 Cambridge Tracts in Mathematics and Mathematical 

 Physics. No. 10, 71 pp. 



Fredholm. L. 



1900. Sur une nouvelle methode pour la resolution du probleme 

 de Dirichlet. Ofr. Kongl. Vet. Ak. Forh. Stockholm, 

 57: 39^6 



1903. Sur une classe d'equations fonctionnelles. Acta Math., 

 27: 365-390. 



