At the same time the genuine sensational form of the lines before us can, in all the cases of distortion by suggested perspective, be felt correctly by a mind able to abstract from the notion of perspective altogether. Individuals differ in this abstracting power. Artistic training improves it, so that after a little while errors in vertical bisection, in estimating height relatively to breadth, etc., become impossible. In other words, we learn to take the optical sensation before us _pure_.[255] _We may then sum up our study of illusions by saying that they in no wise undermine our view that every spatial determination of things is originally given in the shape of a sensation of the eyes._ They only show how very potent certain _imagined_ sensations of the eyes may become. These sensations, so far as they bring definite forms to the mind, appear to be retinal exclusively. The movements of the eyeballs play a great part in educating our perception, it is true; but they have nothing to do with _constituting_ any one feeling of form. Their function is limited to _exciting_ the various feelings of form, by tracing retinal streaks; and to _comparing_ them, and _measuring_ them off against each other, by applying different parts of the retinal surface to the same objective thing. Helmholtz's analysis of the facts of our '_measurement of the field of view_' is, bating a lapse or two, masterly, and seems to prove that the movements of the eye have had some part in bringing our sense of retinal equivalencies about--_equivalencies_, mind, of different retinal forms and sizes, not forms and sizes themselves. _Superposition_ is the way in which the eye-movements accomplish this result. An object traces the line AB on a peripheral tract of the retina. Quickly we move the eye so that the same object traces the line _ab_ on a central tract. Forthwith, to our mind, AB and _ab_ are judged equivalent. But, as Helmholtz admits, the equivalence-judgment is independent of the way in which we may feel the form and length of the several retinal pictures themselves: "The retina is like a pair of compasses, whose points we apply in succession to the ends of several lines to see whether they agree or not in length. All we need know meanwhile about the compasses is that the distance of their points remains unchanged. What that distance is, and what is the shape of the compasses, is a matter of no account."[256]