6.  There is another way mentioned by optic writers, whereby they will have us judge of those distances, in respect of which the breadth of the pupil hath any sensible bigness:  And that is the greater or lesser divergency of the rays, which issuing from the visible point do fall on the pupil, that point being judged nearest which is seen by most diverging rays, and that remoter which is seen by less diverging rays:  and so on, the apparent distance still increasing, as the divergency of the rays decreases, till at length it becomes infinite, when the rays that fall on the pupil are to sense parallel.  And after this manner it is said we perceive distance when we look only with one eye.

7.  In this case also it is plain we are not beholding to experience:  it being a certain, necessary truth that the nearer the direct rays falling on the eye approach to a parallelism, the farther off is the point of their intersection, or the visible point from whence they flow.

8.  I have here set down the common, current accounts that are given of our perceiving near distances by sight, which, though they are unquestionably received for true by mathematicians, and accordingly made use of by them in determining the apparent places of objects, do, nevertheless seem to me very unsatisfactory:  and that for these following reasons:—­

9.  First, It is evident that when the mind perceives any idea, not immediately and of itself, it must be by the means of some other idea.  Thus, for instance, the passions which are in the mind of another are of themselves to me invisible.  I may nevertheless perceive them by sight, though not immediately, yet by means of the colours they produce in the countenance.  We often see shame or fear in the looks of a man, by perceiving the changes of his countenance to red or pale.

10.  Moreover it is evident that no idea which is not itself perceived can be the means of perceiving any other idea.  If I do not perceive the redness or paleness of a man’s face themselves, it is impossible I should perceive by them the passions which are in his mind.

11.  Now from sect. 2 it is plain that distance is in its own nature imperceptible, and yet it is perceived by sight.  It remains, therefore, that it be brought into view by means of some other idea that is itself immediately perceived in the act of vision.

12.  But those lines and angles, by means whereof some mathematicians pretend to explain the perception of distance, are themselves not at all perceived, nor are they in truth ever thought of by those unskilful in optics.  I appeal to anyone’s experience whether upon sight of an object he computes its distance by the bigness of the angle made by the meeting of the two optic axes?  Or whether he ever thinks of the greater or lesser divergency of the rays, which arrive from any point to his pupil?  Everyone is himself the best judge of what he perceives, and what not. in vain shall all the mathematicians in the world tell me, that I perceive certain lines and angles which introduce into my mind the various ideas of distance, so long as I myself am conscious of no such thing.