*bears to the unit of velocity [acceleration] on the ratio or according as the motion is parallel to I or perpendicular to I (MVLR).*

Let us use *F* to denote force. Then from the dimensional equation

we shall be able to draw an interesting conclusion concerning the measurement of force.

Suppose that an observer *B* on a system carries out some observations concerning a certain rectilinear motion, measuring the quantities *M', L', T',* so that he has the equation

Another observer *A* on a system (having with respect to the velocity *v* in the line *l*) measures the same force, calling it *F*. Required the value of *F* in terms of , when the motion is parallel to *l* and when it is perpendicular to *l*, the estimate being made by *A*.

When the motion is perpendicular to *l* — that is, when the force acts in a line perpendicular to *l* — we have

When the motion is parallel to *l* we have

These results may be stated in the following theorem:

Theorem IV. *In the same systems of reference as in theorem III., let an observer on measure a given force F' in a direction perpendicular to l and in a direction parallel to l, and let and be the values of this force as measured in the first and second cases respectively by an observer on . Then we have*

It is obvious that a similar use may be made of the dimensional equation of any derived unit in determining the relation which exists between this unit in two relatively moving systems of reference.