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The accuracy with which this may be done depends upon the number of separate sizes into which the aggregates are divided. In this method the cement sometimes is considered as part of the sand; sometimes its curve is plotted and used in combination with those of the coarser materials. It is more important that the actual grading curve fit the ideal in the sand-cement portion than in that of the coarse aggregate. For best results the actual curve should intersect the theoretical approximately on the 40 per cent line. Here the dot and dash line represents the combination of the materials in the proportions stated, the measurements being by weight. In this case it was decided to make the actual curve coincide with the ideal at the 0.25 in. opening, about 37 percent. The 1916 Joint Committee recommended that "the proportions should be carefully determined by density experiments and the grading of the fine and coarse aggregates should be uniformly maintained, or the proportions changed to meet the varying sizes. For reinforced concrete construction, one part of cement to a total of six parts of fine and coarse aggregates, measured separately, should generally be used. For columns richer mixes are preferable. In massive masonry or rubble concrete a mixture of 1:9 or even 1:12 may be used. These proportions should be determined by the strength or other qualities required in the construction at the critical period of use." Density experiments are easily made by determining the heaviest of a series of trial mixes of equal volume, made with varying proportions of the ingredients, the cement ratio alone being fixed. It is important that all of these trial batches be of the same working consistency and compacted in the container in a uniform manner. Sometimes dry aggregates alone are combined and studied in this way. This is a very useful method of proportioning and one especially easy of application in checking the daily work in the field. It is generally used as a check on the method of Mechanical Analysis.

The 1916 Joint Committee Report gives the following table of the ultimate compressive strength that may be expected from different mixtures: In lbs. per sq. in. at an age of 28 days, testing cylinders 8 in. in diameter and 16 in. long, made, stored, and tested under laboratory conditions. * Combined volume fine and coarse aggregate measured separately. Professor Abrams states that "with given concrete materials and conditions of test the quantity of mixing water used determines the strength of the concrete, so long as the mix is of a workable plasticity." The equation expressing this relation he found to be for average conditions. It must be kept in mind that these equations hold only for a workable mix. The limitations in the application of the water- ratio theory indicated in the following quotation are largely met by the requirement that the concrete must be of workable consistency. "So far as these tests indicate, it may be concluded that the expression 14,000 divided by 7 raised to a power equal to the water-cement ratio, is a fair measure of the strength of concrete, provided that at least one-third of the aggregate is sand (that is smaller than a No. 4 sieve) and that the quantity of coarse aggregated any one size is not less than one-third as great as that of the next larger size. Other tests not included in the investigation indicate also that the sand should not be more than half the total aggregate in order to meet this criterion." Two and a half gallons of water are sufficient for the hydration of a sack of cement, usually taken to be hardened. �The diagrams and tables in this article and the next are from the pamphlet "Design and Control of Concrete Mixtures," published by the Portland Cement Association. Professor Abrams developed a measure of their size and grading which he named the Fineness Modulus. This modulus (or measure of fineness) is the sum of the percentages of the material coarser than the opening of each of the following standard series of sieves: 100, 50, 30, 16, 8, 4.