Obliquely-crossed Cylindrical Lenses , 



317 



power of the eye is different in different meridians around 

 the optic axis. One process of examination of this defect 

 consists in ascertaining the position of the meridian of greatest 

 refractive power, and in then measuring that power; and, 

 this having been done, measuring the power in a meridian at 

 right angles to the former, that is to say in the meridian of 

 minimum refractive power. The difference between these 

 two powers gives in reality the amount of cylindricity to be 

 corrected. Or the excess of each over the normal spherical 

 refractive power of the eye might be separately corrected by 

 the choice of two appropriate cylindrical lenses which are 

 then superposed at right angles. Sometimes, however, 

 ophthalmic surgeons, whether through insufficient apprecia- 

 tion of the geometrical and optical principles involved, or 

 through some incidental cause, prescribe a lens with two 

 cylindrical curvatures on the respective faces of the lens, not 

 crossed at right-angles but at some oblique angle. As such 

 lenses are difficult of manufacture,, and as their optical effect 

 can be precisely reproduced by a suitably calculated and more 

 readily ground sphero-cylindrical lens, the optician desires 

 to have simple rules for 

 calculating the equivalent 

 sphero-cylinder. Hence the 

 present attempt to arrive at 

 easier rules for obliquely- 

 crossed cylindrical lenses. 

 To establish these rules it is 

 possible to proceed by a 

 simpler method than that of 

 Reusch, whose investigation 

 is exclusively based upon the 

 properties of parabolic lenses. 

 2. In the case of thin cylin- 

 drical lenses it is customary 

 to call a line drawn through 

 the lens, in a direction pa- 

 rallel to the axis of the gene- 

 rating cylinder of which its 

 curved surface forms a part, 

 " the axis " of that cylindrical 

 lens. Let there be two thin 

 cylindrical lenses placed in 

 contact behind one another, 

 so that their axes A A', B B' make an angle 6 with one 

 another. The optical axis of the system passes through 

 their intersection and is normal to the plane containing them. 



