350 SIR DAVID BREWSTER ON THE LAW OF VISIBLE POSITION 



The celebrated D'ALEMBERT, in his Doutes sur differents questions d'Optique, 

 maintains that the action of light upon the retina is conformable to the laws of me- 

 chanics ; and he adds, that it is difficult to conceive how an object could be seen in 

 any other direction than that of a line perpendicular to the curvature of the retina 

 at the point where it is really excited. He then investigates, mathematically, 

 how the apparent magnitudes of objects would be affected, on the two supposi- 

 tions that the line of visible direction coincides either with the refracted ray, or 

 with a line perpendicular to the retina at the point of excitement. On the first 

 of these suppositions, he finds that the apparent magnitude of small objects would 

 be increased about j^th, and on the second supposition, a little more than g, or 

 TJjjfi. This last result is, as D'ALEMBERT justly remarks, so contrary to expe- 

 rience, that we cannot suppose vision to be thus performed, however natural the 

 supposition may appear. " In the direction of what line, then," he adds, " do we 

 perceive objects, or visible points, which are not placed in the optical axis ? This 

 is a point which it appears very difficult to determine exactly and rigorously. As 

 experience, however, proves that objects of small extent, which are within the 

 range of our eyes, do not appear sensibly greater than they are in reality, it fol- 

 lows, that the visible point which sends a ray to the cornea, is seen sensibly in 

 its place, and consequently in the direction of a line joining the point itself and 

 its image on the retina. But why," D'ALEMBERT adds, " is this the case ? It is 

 a fact which I will not undertake to explain."* 



When we consider the data from which D'ALEMBERT has deduced the pre- 

 ceding results, it is not easy to account for his having abandoned the inquiry as 

 a hopeless one. He employs the dimensions of the eye as given by PETIT and 

 JURIN, and he assumes JURIN'S index of refraction for the human crystalline lens, 

 though it is almost exactly the same as that of an ox, as given by HAWKSBEE. 

 These, indeed, were the best data he could procure ; but he should have inquired 

 if the most probable law of visible direction was compatible with any other di- 

 mensions of the eye, and any other refractive powers of the humours which were 

 within the limits of probability ; and above all, he ought to have examined expe- 

 rimentally the truth of his fundamental assumption, that visible points are really 

 seen in their true places when they are not in the axis of vision. 



Now it is quite certain that these points are not seen in their true direction, 

 and that there is an ocular parallax* which is the measure of the deviation of the 

 visible from the true direction of objects. This parallax is nothing in the axis of 

 the eye, and it increases as the visible point is more and more distant from that 

 axis ; and hence it follows, that, during the motion of the eyeball, when the head 

 is immoveable, visible objects not only change their place, but also their form. 



Had the eye consisted of only two concentric coats, a cornea and a retina, 

 filled with a homogeneous fluid, vision would have been performed by centrical 



* Opuscules Mathematiques, Tom. I. Mem. ix. p. 266. 



