Sig. Santini on Achromatic Telescopes. 



Ill 



For the mean rays nearest to the axis k v is a 0.317137, 

 which, compared with the above value of k y for the remote 

 mean rays, will give the remaining spherical aberration, 

 = 0.000899 ; that is, about ten times greater than what 

 writers on optics lay down as tolerable to the eye. 



Mr. Rogers extols, as one of the advantages of his new con- 

 struction, the power of removing the spherical aberration by a 

 slight separation of the second from the third lens, which is not 

 to be defined, but to be performed by means of a micrometrical 

 adjustment, until it is found by observation to be destroyed, or 

 at least rendered unappreciable to the eye. Although it does 

 not appear very commendable to allow a micrometrical motion 

 to this system of lenses, from which may arise errors of cen- 

 tering more dangerous than those it is sought to avoid, it does 

 not appear to me possible, at least in this example, to remove, 

 by this method, the spherical aberration. In fact, introducing 

 a small distance I d! between the second lens and the third, 

 the chromatic errors are reproduced which had been pre- 

 viously destroyed. We must, therefore, on this account, make 

 the distance d vary contemporaneously by a small arbitrary 

 quantity, £ d : calculating numerically the coefficients of £ d, 

 $ d' in the expression of A: v , as well for the proximate as the 

 remote rays, I obtain the following results : — 



For the nearest mean rays, k 1 = 0.317137 ■— 0.88962 Id — 28.8332 3 d! 

 For the nearest red rays, A' = 0.317121 — 0.80472 >d — 27.5364 W 

 For the remote mean rays, A* = 0.316238 — 1. 21610 St/ — 34.8746 \d' 



* So in the original, but this evidently should be 30° 28' 50.9".— Ed. 



