10. Formulae for Relative Motion. 10.1 In transforming the equations of motion from the space of one member of the Newtonian group to the space of another member of that group, it must be remembered that the facts which are common to the two standpoints are the events, and that the ideally simple analysis exhibits events as dissected into collections of event-particles. Thus if and be the two consentient sets, the points of the -space are distinct from the points of the -space, but the same event-particle is at the point at the time in the -space and is at the point at the time in the -space. With the covert assumption of absolute space which is habitual in the traditional outlook, it is tacitly assumed that and are the same point and that there is a common time and common measurement of time which are the same for all consentient sets. The first assumption is evidently very badly founded and cannot easily be reconciled to the nominal scientific creed; the second assumption seems to embody a deeply rooted experience. The corresponding formulae of transformation which connect the measurements of space, velocity, and acceleration in the -system for space and time with the corresponding measurements in the -system certainly are those suggested by common sense and in their results they agree very closely with the result of careful observation. These formulae are the ordinary formulae of dynamical treatises. For such transformations the Newtonian equations are invariant within the Newtonian group. 10.2 But, as we have seen, this invariance, with these formulae for transformation, does not extend to Maxwell's equations for the electromagnetic field. The conclusion is that—still assuming these formulae for transformation—Maxwell's equations apply to the electromagnetic field as referred to one particular consentient set of the Newtonian group. It is natural to suppose that this set should be that one with respect to which the stagnant ether is at rest. Namely, stating the same fact conversely, the stagnant ether defines this consentient set. There would be no difficulty about this conclusion except for the speculative character of the material ether, and the failure to detect the evidences of the earth's motion through it. This consentient set defined by the ether would for all practical purposes define absolute space.