GENERAL DETERMINATION OF LAWS 453 



For example, the first law becomes y = bx n if a =- o ; or the second 



law becomes y = if n = 1. 



*+ a 



The selection of the best of these three laws can easily be effected, 

 because there is for each of them a simple relation connecting the 



variables, x and y, and the slope -~. 



CUB 



(1) Taking the law y = a + bx* 

 then y a --= bx n 



dij 



also - (or s] = nbx n ~ l 



ax 



,. . . y a x 



By division = - 



* n 



1 



or y = - xs + a 



Hence, if the tabular values of x and y suit the law, then a straight 

 line must be the result of plotting y vertically and xs horizontally. 



(2) Taking the law y = b (x + a) n 



-~- (or s) = rib (x + a)"- 1 



U X + CL 



By division 



s n 



1 a 



-- + - 



n n 



Hence, if the tabular values of x and y suit the law, then a straight 



11 

 line must be the result of plotting - vertically and x horizontally. 



S 



(3) Taking the law y = a + be?* 

 then y a = be?* 



-^ (or s) = nbe 

 dx v 



y a 



By division = n 



s 



or y = -ns + a 



Hence, if the tabular values of x and y suit the law, then a straight 

 line must be the result of plotting y vertically and s horizontally. 



Thus the discrimination can be carried out in the following 

 way : 



Draw the curve connecting the tabular values of x and y on 

 squared paper, and take a series of points on the curve. For each 



