"8 EIGHTH REPORT 1838. 



laws of mechanics ; and he adds, that it is difficult to conceive how the 

 object could be seen in any other direction than that of a line perpen- 

 dicular to the curvature of the retina, at the point where it is really ex- 

 cited. He then proceeds to investigate mathematically how the ap- 

 parent magnitudes of objects would be affected, on the two suppositions, 

 that the line of visible direction coincided with the refracted ray, or 

 with a line perpendicular to the retina, at the point where the refracted 

 ray fell upon it. On the fii*st supposition, he finds that the apparent 

 magnitude of small objects would be increased about l-13th or l-16th, 

 if the anterior surface of the crystalline is supposed to have a radius of 

 six lines in place of four. On the second supposition, namely, that 

 of Porterfield and Reid, he finds that the apparent magnitude of objects 

 would be increased nearly one-third, which, as he remarks, being con- 

 trary to experience, we cannot suppose that vision is thus performed, 

 however natni-al the supposition may appear. " According to what 

 line then," he continues, " do we perceive objects or visible points, 

 which are not placed in the optic axis ? This is a point which it ap- 

 pears very difficult to determine exactly and rigorously. However, as 

 experience 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 follows, that the visible point, which sends a ray to the cornea, 

 is seen sensibly in its place, and, consequently, this visible point is seen 

 sensibly in the direction of a line joining the point itself and its image 

 on the retina. But why is this the case ? It is a fact which I will not 

 undertake to explain*." This abandonment of the inquiry will appear 

 the more remarkable, when we consider the assumptions from which 

 D'Alembert has deduced the preceding results. He takes for granted 

 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 dimensions of the eye, and any other refractive powers of the hu- 

 mours, which were within the limits of probability; and, above all, he 

 ought to have examined experimentally the truth of his fundamental 

 assumption, that visible points are really seen in their true places when 

 thev are not in the axis of vision. In submitting this assumption to 

 experiment, I had no difficulty in ascertaining that there exists an ocular 

 parallax, and that this parallax is the measure of the deviation of the 

 visible from the real direction of objects. It is nothing in the axis of 

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

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

 the head is immoveable, visible objects do not appear absolutely fixed, 

 and have an apparent magnitude greater than their real magnitude. 

 We are, consequently, not entitled to reject any law of visible direction, 

 on the ground of its giving a position to visible points, and a magnitude 



* Opuscules Matlicmatiqucs, toni. i. p. 2". 



