VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 343 



But the case is widely different with regard to the eye-glasses ; for though they 

 are very much affected by both the aberrations before mentioned, yet by a proper 

 combination of several together, their errors may be in a great measure corrected. 

 If any one, for instance, would have the visual angle of a telescope to contain 

 20 degrees, the extreme pencils of the field must be bent or refracted in an angle 

 of 10 degrees; which, if it be performed by one eye-glass, will cause an aberra- 

 tion from the figure, in proportion to the cube of that angle : but if 2 glasses be 

 so proportioned and situated, as that the refraction may be equally divided be- 

 tween them, they will each of them produce a refraction equal to half the re- 

 quired angle ; and therefore, the aberration being in proportion to the cube of 

 half the angle taken twice over, will be but a 4th part of that which is in pro- 

 portion to the cube of the whole angle ; because twice the cube of one is but + 

 of the cube of 2 ; so the aberration from the figure, where 2 eye-glasses are 

 rightly proportioned, is but a 4th of what must unavoidably be, where the whole 

 is performed by a single eye-glass. By the same way of reasoning, when the 

 refraction is divided among 3 glasses, the aberration will be found to be but the 

 gth part of what would be produced from a single glass ; because 3 times the 

 cube of one is but one gth of the cube of 3. Whence it appears, that by in- 

 creasing the number of eye-glasses, the indistinctness, which is observed near 

 the borders of the field of a telescope, may be very much diminished, though not 

 entirely taken away. 



The method of correcting the errors arising from the different refrangibility of 

 light, is of a different consideration from the former ; for whereas the errors 

 from the figure can only be diminished in a certain proportion to the number of 

 glasses, in this they may be entirely corrected, by the addition of only one glass ; 

 as we find in the astronomical telescope, that 2 eye-glasses, rightly proportioned, 

 will cause the edges of objects to appear free from colours quite to the borders of 

 the field. Also in the day-telescope, where no more than 2 eye-glasses are ab- 

 solutely necessary for erecting the object, we find, by the addition of a 3d rightly 

 situated, that the colours, which would otherwise confuse the image, are en- 

 tirely removed : but this is to be understood with some limitation ; for though 

 the different colours, which the extreme pencils must necessarily be divided into 

 by the edges of the eye-glasses, may in this manner be brought to the eye in a 

 direction parallel to each other, so as, by the humours thereof, to be converged 

 to a point in the retina ; yet, if the glasses exceed a certain length, the colours 

 may be spread too wide to be capable of being admitted through the pupil or 

 aperture of the eye ; which is the reason, that in long telescopes, constructed 

 in the common manner, with 3 eye-glasses, the field is always very much con- 

 tracted. 



