point B, the object A appears nearly in its own natural place, if the point B is taken in the glass, or at the same distance, if in the speculum.  The eye being brought back to O, the object seems to draw near:  and being come to P it beholds it still nearer.  And so on little and little, till at length the eye being placed somewhere, suppose at Q, the object appearing extremely near, begins to vanish into mere confusion.  All which doth seem repugnant to our principles, at least not rightly to agree with them.  Nor is our tenet alone struck at by this experiment, but likewise all others that ever came to my knowledge are, every whit as much, endangered by it.  The ancient one especially (which is most commonly received, and comes nearest to mine) seems to be so effectually overthrown thereby that the most learned Tacquet has been forced to reject that principle, as false and uncertain, on which alone he had built almost his whole catoptrics; and consequently by taking away the foundation, hath himself pulled down the superstructure he had raised on it.  Which, nevertheless, I do not believe he would have done had he but considered the whole matter more thoroughly, and examined the difficulty to the bottom.  But as for me, neither this nor any other difficulty shall have so great an influence on me as to make me renounce that which I know to be manifestly agreeable to reason:  especially when, as it here falls out, the difficulty is founded in the peculiar nature of a certain odd and particular case.  For in the present case something peculiar lies hid, which being involved in the subtilty of nature will, perhaps, hardly be discovered till such time as the manner of vision is more perfectly made known.  Concerning which, I must own, I have hitherto been able to find out nothing that has the least show of probability, not to mention certainty.  I shall, therefore, leave this knot to be untied by you, wishing you may have better success in it than I have had.’

30.  The ancient and received principle, which Dr. Barrow here mentions as the main foundation of Tacquet’s catoptrics, is that:  ’every visible point seen by reflection from a speculum shall appear placed at the intersection of the reflected ray, and the perpendicular of incidence:’  which intersection in the present case, happening to be behind the eye, it greatly shakes the authority of that principle, whereon the aforementioned author proceeds throughout his whole catoptrics in determining the apparent place of objects seen by reflection from any kind of speculum.