24.  What seems to have misled the writers of optics in this matter is that they imagine men judge of distance as they do of a conclusion in mathematics, betwixt which and the premises it is indeed absolutely requisite there be an apparent, necessary connection:  but it is far otherwise in the sudden judgments men make of distance.  We are not to think that brutes and children, or even grown reasonable men, whenever they perceive an object to approach, or depart from them, do it by virtue of geometry and demonstration.

25.  That one idea may suggest another to the mind it will suffice that they have been observed to go together, without any demonstration of the necessity of their coexistence, or without so much as knowing what it is that makes them so to coexist.  Of this there are innumerable instances of which no one can be ignorant.

26.  Thus, greater confusion having been constantly attended with nearer distance, no sooner is the former idea perceived, but it suggests the latter to our thoughts.  And if it had been the ordinary course of Nature that the farther off an object were placed, the more confused it should appear, it is certain the very same perception that now makes us think an object approaches would then have made us to imagine it went farther off.  That perception, abstracting from custom and experience, being equally fitted to produce the idea of great distance, or small distance, or no distance at all.

27.  Thirdly, an object being placed at the distance above specified, and brought nearer to the eye, we may nevertheless prevent, at least for some time, the appearances growing more confused, by straining the eye.  In which case that sensation supplies the place of confused vision in aiding the mind to judge of the distance of the object; it being esteemed so much the nearer by how much the effort or straining of the eye in order to distinct vision is greater.

28.  I have here set down those sensations or ideas that seem to be the constant and general occasions of introducing into the mind the different ideas of near distance.  It is true in most cases that divers other circumstances contribute to frame our idea of distance, to wit, the particular number, size, kind, etc., of the things seen.  Concerning which, as well as all other the forementioned occasions which suggest distance, I shall only observe they have none of them, in their own nature, any relation or connection with it:  nor is it possible they should ever signify the various degrees thereof, otherwise than as by experience they have been found to be connected with them.

29.  I shall proceed upon these principles to account for a phenomenon which has hitherto strangely puzzled the writers of optics, and is so far from being accounted for by any of their theories of vision that it is, by their own confession, plainly repugnant to them; and of consequence, if nothing else could be objected, were alone sufficient to bring their credit in question.  The whole difficulty I shall lay before you in the words of the learned Dr. Barrow, with which he concludes his optic lectures:—­