INTRODUCTION: Experimental work in science is frequently a study of the relationship between two interacting variables. For example the following questions might be answered from experimental data. How does the velocity of a falling body vary with time? What is the angular distribution of radiant energy transmitted through a small opening? What is the pressure response frequency characteristic of a crystal telephone receiver?
When experiments are performed, the independent variable, in these examples time, angle, and frequency, is progressively changed, and the corresponding values of the resulting dependent variable, velocity, intensity, and response respectively, are measured for a series of tests. These data are appropriately recorded in an organized table, that is, in tabular form.
A display of the data as a graph shows more clearly than the tabular form how the one quantity, or property, is related to the second. The graph also indicates probable experimental errors and provides values intermediate to the several readings.
The most powerful form in which the relationship of the variables can be expressed is a mathematical equation. Such equations permit various mathematical expansions and the deduction of additional information. A straight line curve on a graph may be converted quickly to the equation form. Obtaining a straight line curve may require the selection of suitable conversion factors for the axis values, or a special type of graph paper. These techniques, the basis of this discussion, reduce the laborious matching of curves of empirical equations to a reasonable “match” of the original graph form.
