a. A. Baker — Loose Arenaceous Sediinents. S67 



In the search for a characteristic number to represent the 

 mechanical constitution of a sediment, the actual average diameter 

 of the grains in a sample, besides being exceedingly difhcult, if not 

 impossible to obtain, is useless, since it gives a result quite out 

 of keeping with the sizes of the grains in the bulk of the sample. 

 This arises from the fact that the clay grade in the sample, however 

 insignificant its percentage-weight may be, contains such an 

 enormous amount of tiny particles that the average diameter is 

 reduced to a figure of an order quite different from that sought. 

 Consequently a method is required which affords a result influenced 

 by the percentage-weights of the various grades present. 



(2) The "Equivalent Grade" of a Sediment. 



The plotting of the elutriation-curve of a sediment from the data 

 yielded by the mechanical analysis of it, affords a means of obtaining 

 graphically, the value of the definite integral of diameter of particles 

 with respect to percentage-weight. The value of this integral is 

 represented by the area under the curve enclosed between the first 

 and last ordinates and the first abscissa or base-line of the diagram. 

 It may readily be determined, with considerable accuracy, by the 

 use of the planimeter. The result is small or large, according as 

 the sediment under consideration is fine or coarse, since the coarser 

 the sediment the higher its curve climbs and the greater the area 

 enclosed beneath it. If we suppose the case of an ideal sediment in 

 which the grading is perfect (i.e. the sediment consists entirely of 

 grains of some one specified diameter), the elutriation-curve would 

 be a horizontal straight line (an abscissa), parallel to the first 

 abscissa and passing through the point on the first ordinate 

 representing the specified diameter. Let us suppose, for argument, 

 that all the grains in this ideal sediment are of diameter 0"2 mm. 

 Then the area under the curve is a rectangle whose area is a product 

 of the length representing 0'2 mm. and that representing 100 per 

 cent weight. .The figure sought as the representative average of 

 the diameters of the particles (taking into account percentage- 

 weights of grades) is obtained by dividing the area under the curve 

 by the length of the base-line representing 100 per cent weight, 

 and interpreting the length so obtained in terms of the scale of 

 lengths employed to represent diameters. Now, perfectly graded 

 sediments of this kind do not appear to occur in nature, but there is 

 no reason why we should not extend the argument, by analogy, to 

 apjjly to actual sediments. Consider an imperfectly graded natural 

 sediment. It gives a certain known value for the integral of diameter 

 of particles with respect to percentage-weight. Suppose it were 

 possible to substitute for this sediment a perfectly graded material 

 giving an equivalent value for the area under the curve. What would 

 be the diameter of the particles in this ideal sediment ? The answer 

 is supplied by finding the mean ordinate of the area under the curve, 



