548 OBITUARY NOTICE OF JOSEPH JACKSON LISTER 



of a reversal of the relations to each other of the angles at which the rays of 

 light meet the different curves of the lens, the flint glass comes to operate with 

 less effect, the excess of correction diminishes, and at a point somewhat nearer 

 to the glass vanishes, and a second aplanatic focus appears, and from this point 

 onwards under-correction takes the place of over-correction, and increases till 

 the object touches the surface of the glass. Such a lens, then, has two aplanatic 

 foci : for all points between these foci it is over-corrected, but under-corrected 

 for points either nearer than the shorter or more distant than the longer focus. 

 A knowledge of these facts enables the optician to combine a pair of such lenses 

 with perfect security against spherical error. In order to do this, to quote from 

 my father's paper in the Philosophical Transactions, read on the 21st of January, 

 1830, ' the rays have only to be received by the front glass from its shorter 

 aplanatic focus, and transmitted in the direction of the longer correct pencil 

 of the other glass.' The light then proceeding through each glass, as if from 

 one of its aplanatic foci, is brought correctly to a focus by the combination. 

 Supposing two glasses to have been so arranged, if the front glass is carried 

 nearer to the back one, light proceeding from the shorter aplanatic focus of the 

 front glass will reach the back glass as if from a point nearer than its longer 

 aplanatic focus, that is to say, from a point between the foci, and therefore 

 the spherical error will be over-corrected. On the other hand, separation of 

 the glasses beyond their original interval produces under-correction. Thus, 

 by merely varying the distance between two such lenses, the correction of the 

 spherical error may be either increased or diminished at pleasure according 

 to a definite rule, and slight defects in the glasses can be remedied by simply 

 altering their relative position, the achromatism of the combination being 

 meanwhile happily little affected. 



Another beautiful circumstance connected with the aplanatic foci is that 

 of their relation to the coma. At the shorter focus the coma is inwards, at 

 the longer focus outwards ; and in a combination of two lenses arranged as 

 above described, the inward coma from the shorter focus of the front glass 

 destroys the outward coma from the longer focus of the back glass, and * the 

 whole field is rendered beautifully flat and distinct '. 



The same principle applies when the lenses are of different form, and when 

 more than two are combined. Thus the manufacture of the achromatic object- 

 glass was reduced from a matter of uncertainty and empiricism to a scientific 

 system, and has become susceptible of a degree of perfection that would other- 

 wise have been impossible. 



But though he had thus discovered the principle of construction, his own 

 abours were far from being concluded. The next section of his notes is labelled 



