RELATION OF VARIABLES. 97 



any particular scientific inquiry have been observed and described 

 with thoroughness and classified into empirical laws and generaliza- 

 tions, it is proper and desirable to employ the deductive method and 

 ascertain the extent to which that particular natural system conforms 

 to a logical one. But, it not infrequently happens that the specialist 

 extends theories that have proved useful in his restricted researches 

 to classes of phenomena with which he is unfamiliar without first 

 making a critical examination as to their applicability. This tendency 

 is manifested especially by the isolated or individual investigator 

 whose attention is necessarily restricted to the limjted observations 

 he can make and to relevant data others may have gathered. When 

 confronted with a problem calling for extensive observation in the 

 field he is prone to carry it into the laboratory in an attempt, on the 

 basis of theory and carefully conducted experiments, to reach an 

 explanation of phenomena never observed. The deductive method 

 thus becomes a process of inventing facts to fit theories, instead of 

 theories to fit facts. The empirical method, on the other hand, being 

 concerned primarily with direct observation, often demands that 

 investigation be carried on by an organized group of individuals work- 

 ing in cooperation for the purpose of obtaining as wide a range of 

 relevant observations as possible. Each method has its place in all 

 investigations, and each has its limitations; and it is only by com- 

 bining all relevant observations with induction and deduction that 

 one can use his full powers of cognition and approach complete solu- 

 tion of any problem in natural science. 



2. General Statement of Problem and Mode of Attack. 



How can the values of a variable, for example the yield of wheat 

 per acre of a given region, measured at equal intervals of time, say 

 annually, be used for predicting the yield for the ensuing year? The 

 frec^uency with which the wheat yield has been observed to fall within 

 given limits, divided by the total number of observations, is the em- 

 pirical probability that the next yield of wheat will fall within those 

 limits. Obviously, the more frequently the wheat yield has been 

 observed to fall within given limits the larger will be this empirical 

 probability, and the greater the total number of observ^ttions the 

 nearer will this empirical probability approximate the true proba- 

 bility, i. e., the frequency ratio that would have resulted had the 



