NO. H.] MECHANICAL COMPOSITION OF SAMPLES. 23 



rate better admits of being represented. The particles between - 05 and 0"5 mm. 

 extend over 9 divisions. They amount, in all, to 69 - 26 per cent, and thus the 

 height becomes 7*7 ; so that this size occasions no difficulty. The same may 

 be said of the particles between 0"01 and 0'05 mm. which occupy 0"8 of a 

 division; the percentage is 9"89, and the height consequently 12 - 36. But the 

 difficulty returns with the finest particles of less than 001 mm. As they oc- 

 cupy only 0*2 of a division, and are present to the amount of 19"42 per cent, 

 they would have to be marked at a height of 97'1, which is practically im- 

 possible, when a height of O022 has to be shown for the coarsest particles at 

 the same time. Even then we get no idea of the manner in which these 

 finest particles are distributed within the area they occupy. It is always 

 possible to see approximately in the microscope what is the size of the ma- 

 jority of the particles, and to observe that in this respect there is a consider- 

 able difference between the several samples. At some place or other the curve 

 must have a maximum, whence it descends regularly to both sides; and shades 

 of difference such as these cannot possibly be drawn in the space of - 2 of a 

 division, when at the same time there are to be 30 divisions. It will thus be 

 seen that with this mode of representation it will be impossible to include 

 either the finest or the coarsest particles, and it is clear that the case will be 

 much worse when the particles of less than 001 mm. rise to 100 °/o, or there- 

 abouts or when, on the other hand, stony particles appear in the sample. A 

 graphic representation with the sizes of the particles in arithmetical progres- 

 sion can thus be employed only when the samples dealt with, are very homo- 

 genous practically only with pure sand or gravel deposits, and it can only 

 be employed for purposes of comparison with other samples, when the latter 

 are very nearly of a similar composition. 



The case is altogether different when the figures for the sizes of the par- 

 ticles are given in a geometrical series. As will be seen from the tables, the 

 quotient 2 is here chosen as the unit. With 1 mm. as the starting-point, we 

 put Va, 1 /4, etc. on the left, and 2, 4, etc. on the right. The abscissa can thus 

 be continued indefinitely on both sides, but will in no case acquire a length 

 that is not applicable. The advantages of the method are best seen by look- 

 ing at the curves themselves. The greater compression of the coarser particles 

 in relation to the finer, enables even the smaller percentages that are as a rule 

 found, to be very clearly shown, and the curve can easily be extended to in- 



