The Law of Demand 79 



tions fall within =*= the root-mean-square deviation of 

 the observations from their mean value; 95 per cent., 

 between == twice the root-mean-square deviation; and 

 99.7 per cent, between =*= three times the root-mean- 

 square deviation. It is therefore possible, by means 

 of the Probability Integral, to affix the degree of prob- 

 ability that a deviation shall fall within any given 

 multiples or submultiples of the root-mean-square 

 deviation. In case of the use of the linear law of de- 

 mand for corn in the United States as a prediction 

 formula, the root-mean-square deviation of the ob- 

 servations about the demand curve was S = <r y ^\ r 2 = 

 15.92 per cent. That is to say, if we assume the law of 

 demand that was based upon observations from 1866 

 to 1911 to hold in 1912, then it is 95 to 5, or 19 to 1, that 

 the percentage variation in the actual price for 1912 

 from the percentage variation as calculated from the 

 law of demand will be between 2 (15.92), or 31.84 

 per cent. The calculated percentage change in the 

 price for 1912 was a fall of 13.06 per cent.; the actual 

 fall was 21.20 per cent., giving a difference of 7.14 per 

 cent. 



The precision with which the linear law of demand 

 may be used for the prediction of the price of corn in 

 the United States justifies the belief that for some pur- 

 poses it is unnecessary to seek a greater degree of 

 accuracy than is afforded by the simple linear laws. 

 But it is well to be able to reach the maximum degree 

 of precision, and for this reason we have fitted, to the 

 data of the Tables in the Appendix, the more complex 



