Astigmatism and some other Ocular Defects. 429 



is often necessary to increase the latter. This is done by in- 

 serting at F the lens L. If /' be the focal length of this 

 lens, /2 





v~ P + /'~ P ' 



Thus we see that the insertion of the lens has no other effect 



P 

 than to remove the zero of divergence outwards by a distance J jj, 



which in units of the scale is — ~ir~*' 



[In the actual case this was 240 degrees of the scale, so that 

 when using the lens we must increase by 240 every number 

 read from the scale, but, in doing so, we must recollect that 

 the numbers from to B are negative,] 



It may be noted here that the power of any lens is the 

 displacement which its introduction at F causes on the scale. 



6. Suppose that we wish to ascertain the punctum remotum, 

 that is the least divergence suitable for the eye (in hyperme- 

 tropia, the greatest convergence). Begin with the table at 

 its farthest, and move it up slowly. Clearness at last appears 

 at the lower part of the object, that is, the narrow white interval 

 between two consecutive ellipses ceases to encroach on them. 

 This clearness gradually includes more and more of the object, 

 and the observer meanwhile has his attention occupied in 

 noticing the progress of its upper limit. Let him arrest the 

 motion when the upper limit of clearness arrives at the middle. 

 The scale now shows the divergence corresponding to the 

 punctum remotum. 



If the nearest point, or greatest useful divergence, has to be 

 observed, we may proceed in the same way but beginning at 

 the nearer end. For most eyes it will be necessary to insert 

 the lens L, and for some even a lens of shorter focal length. 



The difference between the two numbers read from the scale 

 gives the accommodating power. 



7. The object observed so far has been virtually a series of 

 horizontal lines, so that what has been determined as the least 

 divergence is the least divergence suitable for a vertical section 

 of the eye. Now let the inclined plane be laid on its side, the 

 major axes of the ellipses will become vertical, and the white 

 intervals may be called vertical lines. 



On determining afresh the least divergence it will often be 



* Each reading h of the scale should receive the small correction 

 — d^ a -rl000, 5 being distance of eye from F, in inches. 



Phil. Mag. 8. 5. Vol. 30. No. 186. Nov. 1890. 2 G 



