Derived Quantities in Research

Using only the three quantities mentioned above, we can make a lot of measurements in the physical world. For instance, confin­ing ourselves to length alone, we can measure the area of a given (flat) surface. Consider an area whose length is 3 inches and the width is 2 inches. If we draw the lines at the markings of inch lengths, we get six area “pieces,” each piece having 1-inch length and 1-inch width.

If there is another area whose length is 5 inches and the width is 6 inches, drawing the lines as mentioned above, we get thirty area pieces, each 1 inch long and 1 inch wide. Similar “tri­als” with areas of different lengths and different widths should have led the first observer(s) long ago to the conclusion that area can be obtained by multiplying length by width, when both are measured in the same units. The logical process that led to that conclusion we now call induction, and we expect the elementary school student to be capable of it. It is interesting to note that the observation above is the basis of such induction, and in that sense, this “knowledge” is “experimental” in nature. Further, we should note that the width is measured and counted in inches, in the same way that the length is measured. Also, the resulting pieces of area are measured in inches, both the length and width of which are just 1, and designated as “1 square inch” or “1 inch square.” A similar construction, counting, and induction has led to the observation that volume, counted as the number of “1 cubic inch,” is given by multiplying length x width x height, all in inches. The fact that using any other unit of length instead of inches results in the corresponding square and cube is a rela­tively minor detail. Area and volume are quantities derived from one basic quantity: length.

Even more obvious are quantities that are derived from more than one basic quantity. For example, we can distinguish between an automobile moving fast and another moving slow. But when we want to specify what is “fast” and what is “slow,” that is, when we want to quantify the quality of “fastness,” we need to measure speed. Unlike length or weight, speed involves two basic quanti­ties that need to be separately measured: (1) the distance moved, and (2) the corresponding time elapsed. Then, by dividing the number of units of distance by the number of units of time, we obtain the defined quantity known as speed. Speed is thus a quantity, easily obtainable by a simple derivation, but not mea­surable independently; it is expressed as distance moved in unit time. Similarly, we distinguish that steel is heavier than alumi­num. But when we want to specify how much heavier, we need to know the density of each, which is obtained by measuring the weight and volume of each, then dividing the weight of each by the corresponding volume.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.