This argument may be summed up by the following disjunction: If bodies change their shapes in motion--and to some extent, since no body is perfectly rigid, they must all do so--then one of two cases must occur. _Either_ the changes of shape, as bodies move from place to place, follow no geometrical law, are not, for instance, functions of the amount or direction of motion; in which case the law of causation requires that they should not be effects of the change of place, but of some simultaneous non-geometrical change, such as temperature. _Or_ the changes are regular, and the shape _S_ becomes, in a new position _p_, _Sf_(_p_). In this case, the law of concomitant variations leads us to attribute the change of shape to the mere motion, and shape thus becomes a function of absolute position. But this is absurd, for position _means_ merely a relation or set of relations; it is impossible, therefore, that mere position should be able to effect changes in a body. Position is one term in a relation, not a thing _per se_; it cannot, therefore, act on a thing, nor exist by itself, apart from the other terms of the relation. Thus Helmholtz's view, that Congruence depends on the existence of rigid bodies, must, since it involves absolute position, be condemned as a logical fallacy. Congruence, in fact, as I shall prove more fully in Chapter III., is an _à priori_ deduction from the relativity of position. =71.= (2) The above argument seems to me to answer satisfactorily Helmholtz's contention in the precise form which he first gave it. The axiom of Congruence, we must agree, is logically distinguishable from the existence of rigid bodies. Nevertheless some reference to matter is logically involved in Geometry[90], but whether this reference makes Geometry empirical, or does not, rather, show an _à priori_ element in dynamics, is a further question.