rectilinear motion with velocity varying as _f(t)_, except in so far as it is compelled to alter that state by the action of external forces. Such a hypothesis _is_ mathematically possible, but, like the similar one for space, it is excluded logically by the comparative nature of the judgment of quantity, and philosophically by the fact that it involves absolute time, as a determining agent in change, whereas time can never, philosophically, be anything but a passive form, abstracted from change. I have introduced this parallel from time, not as directly bearing on the argument, but as a simpler case which may serve to illustrate my reasoning in the more complex case of space. For since time, in mathematics, is one-dimensional, the mathematical difficulties are simpler than in Geometry; and although nothing accurately corresponds to congruence, there is a very similar mixture of mathematical and philosophical necessity, giving, finally, a thoroughly definite axiom as the basis of time-measurement, corresponding to congruence as the basis of space-measurement[159]. =152.= (3) The case of time-measurement suggests the third of the above objections to the absolute necessity of the axiom of Free Mobility. Psycho-physics has shown that we have an approximate power, by means of what may be called the sense of duration, of immediately estimating equal short times. This establishes a rough measure independent of any assumed uniform motion, and in space also, it may be said, we have a similar power of immediate comparison. We can see, by immediate inspection, that the sub-divisions on a foot rule are not grossly inaccurate; and so, it may be said, we both have a measure independent of congruence, and also could discover, by experience, any gross departure from Free Mobility. Against this view, however, there is at the outset a very fundamental psychological objection. It has been urged that all our comparison of spatial magnitudes proceeds by ideal superposition. Thus James says (Psychology, Vol. II. p. 152): "Even where we only feel one sub-division to be vaguely larger or less, the mind must pass rapidly between it and the other sub-division, and receive the immediate sensible shock of the more," and "so far as the sub-divisions of a sense-space are to be _measured_ exactly against each other, objective forms occupying one sub-division must be directly or indirectly superposed upon the other[160]."