In proportioning the quantities of matrix to aggregate the ideal to be aimed at is to get a concrete in which the voids or air-spaces shall be as small as possible; and as the lime or cement is usually by far the most expensive item, it is desir able to use as little of it as is consistent with strength.
For this purpose a large can, whose volume is known, is filled loosely with stones, and the volume of the voids between them is determined by measuring how much water the can will hold in addition to the stones.
For example, suppose it is resolved to use 2 parts of sand to i of cement, and suppose that experiment shows that in a pailful of stones two-fifths of the volume consists of voids, then 2 parts of sand (or sand with cement) will fill voids in 5 parts of stones, and the proportion of cement, sand, stones becomes 1:2:5.
It is important in all fire-proofing of columns and girders, and in all floor construction, furring and partitions, that there shall be no continuous voids, either vertical or horizontal, which may possibly serve as flues for the spread of heat or flame in case of fire.
At the base of every system of astronomical observation is the law that, in the voids of space, a ray of light moves in a right line.
Moreover, the volume of sand and cement together is generally assumed to be equal to that of the sand alone, as the cement to a large extent fills up voids in the sand.