35 



axis viz. 0'05°^^^ ami ОчИ"™. Their positions however are easily 

 calculated to be 4-32 and IV64 respectively, to the left of the 

 starting point. Thus , as the percentages of the ingredients 

 between 005 and 0*5 extend from 4'32 to 1, it is necessary, 

 in marking them off, to divide by 3*32 and employ the value 

 found as ordinate. The ingredients between O'Ol and 0"05°^°i 

 extend from 6"64 to 4*32, and the percentages for this size of 

 grain must therefore be divided by 2'32. The greatest difficulty 

 is met with in the representation of the finest ingredients below 

 O'Ol™™. If, we are to be able to mark off any definite height, 

 we must have a lower limit for this size of grain, and as we 

 cannot arrive at such a one in any empirical way, the choice 

 must be a somewhat arbitrary one. This circumstance however 

 will not influence us against the use of the curve, as our 

 attention must be specially directed to that part of the curve 

 which represents the finest particles; and if the lower hmit 

 is the same for all the samples any differences will be 

 very conspicuous. Here b'ioooo°™ is everywhere fixed as the 

 lower limit, so that, as this value lies 13'33 units to the left 

 of the starting point, the sizes of the grains below 0"01™™ will 

 extend over 6*69 units, and the percentages found, must be 

 divided by this number to determine the height the part of 

 the curve in question will attain. 



Where the heights determined for the curves are marked 

 off as horizontal lines, the curves will have a very jagged 

 appearance. As this representation of the case would be mis- 

 leading the curve has been smoothed throughout its length. If, 

 for instance, the size of a grain comes between two others, 

 one of which is present in very large, the other only in very 

 small quantities , the curve must slope evenly down from the 

 former to the latter. If a considerable number of one size of 

 grain is found , and smaller numbers of the two sizes repre- 

 .sented next to it, the curve must be highest at the middle, 

 and decrease gradually towards both ends. By actual examina- 



3* 



