The emergence of dimensional analysis in the 19th c

Dimensional analysis was developed in the 19th c. It can be viewed as a reformulation of the principle of homogeneity following the emergence of numerical equations, implying a redefinition of the concept of dimension. The principle of homogeneity holds that some operations can only be performed on quantities of a similar nature, where dimensions define the latter. Instead, Fourier substituted rules which ensure that equations remain invariant under a change of units, and identified dimensions with the power to which conversion factors of derived units must be raised when a fundamental unit is changed. To what extent this new definition of ``dimension'' concurs with the former is not obvious, and tension between the two conceptions motivated much of the debates regarding dimensional analysis throughout the 19th c.