BELATION OF CAPACITY TO SLOPE. 



119 



elated equations under condition of constant 

 width, namely, +0.12. So far as this moder- 

 ate difference in magnitude has significance, it 

 indicates that the index of relative variation, i t , 

 has the smaller range under the condition of 

 constant form ratio; for the index's range in 

 magnitude is a direct function of a. 



THE SYNTHETIC INDEX. 



Another mode of viewing the data of Table 

 21 ignores the middle term of the triple over- 

 lap and considers only the first and last. From 



the values of capacity and slope in these two 

 terms a value of the synthetic index can be 

 computed by equation (35). It is possible in 

 this way to broaden the range of data by in- 

 cluding the cases of simple overlap; and it is 

 possible to make many pertinent comparisons 

 by computing the corresponding values of the 

 synthetic index for observational series in 

 which the constant condition is width instead 

 of form ratio. The indexes with form ratio 

 constant and with width constant may be 

 symbolized severally by 7* and I w . 



TABLE 23. Values of synthetic index under condition that R is constant. (Is); u-ith coordinate mines, under condition that 



w is constant, (/ tt ). 



Table 23 contains values of 7* computed for 

 the 9 cases of overlap shown in Table 21 and 

 for 24 cases of simple overlap previously men- 

 tioned. Where the overlap is extensive, values 

 of Is were computed for two or more values 



of R. Each of these values is based on data of 

 two width-constant series, pertaining to differ- 

 ent trough widths, and whenever the extent 

 of such an associated width-constant series per- 

 mitted, a value of I w was computed from its 



