Sec. 4.5 



RECTIFICATION OF THE NORMAL CURVE 



103 



ment of either, or both, x and y so that the new graph of y = f(x) 

 becomes a straight line. That is, a curved line is straightened out by 

 a change of scale. 



Because the reader is assumed to be familiar with logarithms, the 

 description of a method for rectifying a normal curve will be pre- 

 ceded by a similar discussion regarding logarithmic and exponential 

 curves. If Y — logio X, as in Table 4.51 for selected X's, the pairs 

 of values (X, Y — logio X) plot on the curve of Figure 4.51. 



TABLE 4.51 



Some Pairs of Numbers Which Satisfy the Equation Y = logio X 



X Y X Y X Y 



100 200 300 400 500 600 700 800 900 1000 

 X 



Figure 4.51. Graph of Y = log 10 X for X in the interval 1 s£ X ^ 1000. 



It is obvious that as the size of X increases, the size of Y = logio 

 X increases less and less for equal increases in A". For example, 

 when X changes from 500 to 600, log X changes by 0.08; but when 

 X changes from 900 to 1000 (another increase of 100), log X 

 changes by only 0.05. It is typical of straight-line (linear) mathe- 

 matical relationships that Y changes the same amount for equal 

 increases in X. In other words, Y changes uniformly with increas- 

 ing X. If log X is put on a uniform scale, as in Figure 4.52, and 



