Cylindrical Eye.- This peculiarity of the organ of vision was first investigated and ex plained by the present Astronomer Royal. It depends on the curvature of the cornea being greater in the vertical plane than the hori zontal, whereby the rays are refracted to a nearer focus in a vertical than in a horizontal plane ; this gives rise to much confusion of vision, a point appearing a line, a circle an oval, and a square a parallelogram. In an in teresting case related by Dr. Robert Hamil ton*, the patient, when looking at a clock, was unable to distinguish the hands if they pointed perpendicularly, as at six o'clock, but if hori zontally he had no difficulty : so when looking at a wheel at a little distance, the horizontal spokes only could be seen. The patient was a coach painter by trade, and this peculiarity of vision greatly interfered with his business, for he could not draw vertical lines with any degree of correctness, and unwittingly made them slanting, a serious fault in heraldic de vices ; horizontal lines he drew with perfect precision. His method of correcting the per ceptions of perpendicular lines was to bend his head at right angles with his body, where upon upright bodies became distinct and accu rately represented. This man also practised a manoeuvre which forcibly reminds us of an act common to persons having conical cornew, that of placing the fore-finger at the outer angle of the eyelids and drawing them out wards whereby vision is improved.
To remedy the defect under which he laboured, Professor Airey made a pin-hole in a blackened card, which he caused to slide on a graduated scale ; then strongly illuminating a sheet of paper and holding the card between it and the eye, he had a lucid point on which he could make observations with ease and exactness. Then resting the end of the scale on the cheek bone he found that the point at the distance of 6 inches appeared a very well defined line inclined to the vertical about 35° and subtending an angle of 2°. Again, at the distance of 3 inches, it appeared a well-defined line at right. angles with the former, and of the same apparent length. It was therefore neces sary to make a lens which, when the parallel rays were incident, should cause them to diverge in one plane from the distance of 31. and in the other plane from the distance of 6 inches. The professor obtained a lens of which the radius of the spherical surface was 3k inches, of the cylindrical 4-1- inches, and with this he was able to read the smallest print.
In Dr. Hamilton's patient the relation of the horizontal to the vertical focus appeared to be as 51- inches to 61 inches, and on trying him with plano-concave cylindrical lenses, it was found that a lens of 24 inches focal length, the cylindrical surface being made to act ho rizontally, operated very beneficially. Besides this irregular refraction the man was myopic, but the lenses in question fitted as spectacles, enabled him to see well.
The defect of the cylindrical eye may be de tected by making a small pinhole a card which is to be moved from close to the eye to arm's length, the eye meanwhile being directed to the sky, or any bright object of sufficient size. With ordinary eyes the indistinct image of the hole remains circular at all distances, but to an eye having this peculiar defect it be comes elongated, and when the card is at a certain distance passes into a straight line.
On further removing the card the image be comes elongated in the perpendicular direc tion, and finally if the eye be not too long-sighted, passes into a straight line per pendicular to the former.
Professor Stokes has invented a highly ingenious instrument for determining the nature of the required lens, and the following is the proposition on which it is based.
Conceive a lens groand with two cylindrical surfaces of equal radius, one concave and the other convex, with their axes crossed at right angles ; call such a lens an astigmatic lens : let the reciprocal of its focal length in one of the principal planes be called its power, and a line parallel to the axis of the convex surface its astigmatic axis. Then if two thin astig matic lenses be combined t ith their axes inclined at any angle, they will be equivalent to a third astigmatic lens determined by the following construction.
From any point draw two straight lines representing in magnitude the powers of the respective lenses, and inclined to a fixed line drawn arbitrarily in a direction perpendicular to the axis of vision at angles equal to twice the inclinations of their astigmatic axes, and complete the parallelogram. Then the two lenses will be equivalent to a single astigmatic lens represented by the diagonal. of the pa rallelogram in the same way in which the single lenses are represented by the sides. A plano-cylindrical or spherico-cylindrical lens is equivalent to a common lens, the power of which is equal to the semi-sum of the reciprocals of the focal lengths in the two principal planes, combined with an astigmatic lens, the power of which is equal to their semi -difference. If two piano -cylindrical lenses of equal radius, one concave and the other convex, be fixed one in the lid and the other in the body of a small round wooden box, with a hole in the top and bottom, so as to be as nearly as possible in contact, the lenses will neutralise each other when the axes of the surfaces are parallel ; and by merely turning the lid round, an . astigmatic' lens may be formed of a power varying con tinuously from zero to twice the astigmatic power of either lens. When a person who has the defect in question has turned the lid till the power suits his eye, an extremely' simple numerical calculation, the data of which are furnished by the chord of double the angle through which the lid has been turned, enables him to calculate the curva ture of the cylindrical surface of a lens for a pair of spectacles which will correct the defect in his eye.* A curious case is related in the Annals d'Oculistiquet, of an anomaly of vision, which was probably the consgquence of a defect in the form of the cornea, such as that under consideration. M. Schnyder, the Pastor of Menzberg in the Canton of Lucerne, was presbyopic for horizontal lines and myopic for vertical. This he remedied by wearing spectacles the glasses of which were cylindric bi-convexes, with rectilinear, hori zontal and similar axes. These glasses obvi ated the preshyopia relative to the horizontal lines, and they were combined with sphero biconcave lenses to get rid of the myopia for vertical lines. Each of the glasses was made moveable for facility of cleaning.