174 Mr Lister on the improvement of the 



tral rays, and the colours of the violet side of the spectrum 

 into which each ray is refracted have also their foci shorter than 

 those of the red side ; if either of these errors is but partially 

 removed by the concave lens, the glass is said to be under-cor- 

 rected as to that aberration, and over-corrected if the opposite 

 error is produced by it. 



A large focal pencil free from all aberration is evidently the 

 great requisite for the object-glass of the compound microscope ; 

 a second point desirable to be attained is, that the field should 

 be flat and well defined throughout ; and a third, that the light 

 admitted should as much as possible be only such as goes to 

 form the picture, and should not be intercepted or diffused 

 oVer the field by too many reflections. 



The prominent obstacle to obtaining a sufficient pencil for 

 high powers by one object-glass of large aperture and deep 

 curves, is that the correction for the spherical figure by the 

 concave lens is greater for the rays of the circumference than 

 its due proportion to that for the more central ones ; so that 

 when such a glass is corrected for the mean of the pencil, if we 

 suppose its disk divided into a central space and three rings 

 surrounding it, the rays which pass through the central space, 

 and those of the second ring from it, will arrive at their focus 

 when those of the first ring will have just crossed the axis, and 

 those of the marginal ring will not quite have reached it. The 

 injury resulting to the defining power is in similar glasses in- 

 versely as the squares of their focal lengths, as far as regards 

 this cause of error, as well as those which arise from incorrigi- 

 ble colour and defects of workmanship. The effects upon the 

 pencil which have been before described, must not be included 

 under the same law. This excess of correction in the marginal 

 rays increases after a certain point so rapidly with a small en- 

 largement of the aperture of the glass, as soon to prescribe a 

 limit, beyond which it cannot be carried without injury to the 

 picture. 



With glasses of more contracted aperture, and at the seve- 

 ral surfaces of which the marginal refraction is moderate, the 

 effect alluded to is comparatively inconsiderable ; and conse- 

 quently, by dividing the refraction among two or more such 

 glasses corrected for the rays that pass through them, the pen- 



