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(316) _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. 31. Let us now see how this phenomenon agrees with our tenets(317). The eye, the nearer it is placed to the point _B_ in the above figures, the more distinct is the appearance of the object: but, as it recedes to _O_, the appearance grows more confused; and at _P_ it sees the object yet more confused; and so on, till the eye, being brought back to _Z_, sees the object in the greatest confusion of all. Wherefore, by sect. 21, the object should seem to approach the eye gradually, as it recedes from the point _B_; that is, at _O_ it should (in consequence of the principle I have laid down in the aforesaid section) seem nearer than it did at _B_, and at _P_ nearer than at _O_, and at _Q_ nearer than at _P_, and so on, till it quite vanishes at _Z_. Which is the very matter of fact, as any one that pleases may easily satisfy himself by experiment.