"uraa\!Mi7chi"?l<?o'.] ^oyoi MicYOSCo^ical Society. 139 



aplanatic focus appears, and from this point onwards under-correc- 

 tion 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 other's paper in the 'Philosophical Transactions,' read 

 January 21st, 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 cor- 

 rection of the spherical error may be either increased or diminished 

 at j)leasure 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 back glass, and " the whole field is rendered 

 beautifully flat and distinct." 



The same principle applies when the lenses are of difierent 

 form, and when more than two are combined. Thus the manu- 

 facture 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 otherwise have been 

 impossible. 



But though he had thus discovered the principle of construction, 

 his own labours were far from being concluded. The next section 

 of his notes is labelled " Memoranda on object-glasses made for 

 experiment, Dec. 1829 to May 1830." These include a great 

 number of interesting observations, such as trials of lenses of 

 different forms ; descriptions of the " colours of over, under, and 



