GENERAL DETERMINATION OF LAWS 455 



\'\g. 1 ^s shows the three curves : 



(1) y vertically, xs horizontally ; for the law y = a + bx n . 



(2) - vertically, x horizontally ; for the law y = b (x + a) n . 



(3) y vertically, s horizontally ; for the law y = a + be"*. 



20- 



10 



Scale for jcs 



Scale far x 



Scal 



ix) I'l 12 |"5 - 



3 A 070 



FIG. 148. 



Of the three curves the third most nearly approaches a straight 

 line, and, therefore, y = a -f be is the law which suits the tabular 

 values of x and y the best. 



In order to find the constants of the law take three points on the 

 original curve ; for simplicity of calculation let these points be so 

 chosen that the values of x are equidistant. 



when x = 4, y = 20-1 and a + be* n = 20-1 

 when x = 8, y = 47-6 and a -f be* n = 47-6 

 when x = 12, y = 66-8 and a +be lZn = 66-8 

 subtracting (1) from (2) be* n (e* n - 1) = 27-5 

 subtracting (2) from (3) be* n (e* n - 1) = 19-2 



(1) 

 (2) 

 (3) 

 (4) 

 (5) 



dividing (5) by (4) 

 and 



1Q.O 



e* n = - = 0-6982 

 27-o 



rc= -0-0898. 



