<P> In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms vs. grams) and tracking these dimensions as calculations or comparisons are performed . Converting from one dimensional unit to another is often somewhat complex . Dimensional analysis, or more specifically the factor - label method, also known as the unit - factor method, is a widely used technique for such conversions using the rules of algebra . </P> <P> The concept of physical dimension was introduced by Joseph Fourier in 1822 . Physical quantities that are of the same kind (also called commensurable), have the same dimension (length, time, mass) and can be directly compared to each other, even if they are originally expressed in differing units of measure (such as inches and meters, or pounds and newtons). If physical quantities have different dimensions (such as length vs. mass), they cannot be expressed in terms of similar units and cannot be compared in quantity (also called incommensurable). For example, asking whether a kilogram is greater than, equal to, or less than an hour is meaningless . </P>

What is the primary purpose of dimensional measurement