d between the visible taps of
a hammer, is, to my mind, exactly like the relation of succession
between the tangible taps; the unlikeness between red and blue is a
mental phenomenon of the same order as the unlikeness between rough
and smooth. Two points visibly distant are so, because one or more
units of visible length _(minima visibilia_) are interposed between
them; and as two points tangibly distant are so, because one or more
units of tangible length _(minima tangibilia_) are interposed between
them, it is clear that the notion of interposition of units of
sensibility, or _minima sensibilia_, is an idea common to the two. And
whether I see a point move across the field of vision towards another
point, or feel the like motion, the idea of the gradual diminution of
the number of sensible units between the two points appears to me to
be common to both kinds of motion.

Hence, I conceive, that though it be true that there is no likeness
between the primary feelings given by sight and those given by touch,
yet there is a complete likeness between the secondary feelings
aroused by each sense.

Indeed, if it were not so, how could Logic, which deals with those
forms of thought which are applicable to every kind of subject-matter,
be possible? How could numerical proportion be as true of _visibilia_,
as of _tangibilia_, unless there were some ideas common to the two?
And to come directly to the heart of the matter, is there any more
difference between the relations between tangible sensations which we
call place and direction, and those between visible sensations which
go by the same name, than there is between those relations of tangible
and visible sensations which we call succession? And if there be
none, why is Geometry not just as much a matter of _visibilia_ as of
_tangibilia_?

Moreover, as a matter of fact, it is certain that the muscular sense
is so closely connected with both the visual and the tactile senses,
that, by the ordinary laws of association, the ideas which it suggests
must needs be common to both.

From what has been said it will follow that the ninth proposition
falls to the ground; and that vision, combined with the muscular
sensations produced by the movement of the eyes, gives us as complete
a notion of corporeal separation and of distance in the third
dimension of space, as touch, combined with the muscular sensations
produced by the movements of the hand, does. The tenth proposition
seems