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These two dimensionless products describe, as in Ecological application 3.2d, the critical length x and the characteristic time t as:

Ecological application 3.3b

A second example provides an easy solution to the problem which confronted Paloheimo & Dickie (1965), concerning the synthesis of data on the growth of fish with respect to food intake. The question was discussed at length in Ecological application 3.2e, which led to three scale factors, for food ration, mass, and time. These scale factors were used by the authors to compare diversified data from the ecological literature.

The solution is found directly, here, using the dimensional matrix of the six variables involved in the problem: time t, mass W, food ration R, rate of oxygen consumption T, rate of metabolic expenditure a, and coefficient b. The variables to be isolated being t, W, and R, they are in the first three columns of the dimensional matrix:

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