Improvements in the Microscope. 59 



After numerous experiments, I am satisfied, that the principal de- 

 fect in the achromatic microscope, is not the color of the secondary 

 spectrum, as appears to have been generally supposed, but that it is 

 what may be called the Secondary Aberration of Figure : which is 

 occasioned by the spherical aberration increasing in a greater ratio, 

 from the center of the concave, than it does in the convex lenses. 

 When the spherical aberration of the convex lenses, equals the aberra- 

 tion of the concave ones, with a given aperture, I have found from 

 experiment, that if the aperture be diminished, the aberration of the 

 convex will be too great for that of the concave ; and that if the ap- 

 erture be enlarged, the aberration of the convex will be too small to 

 counteract that of the concave lens or lenses. Were it not for this 

 property, which exists in all the achromatic combinations that I have 

 examined, so many lenses as we are now obhged to use for one ob- 

 ject-glass, (in order to have a good one,) would not be necessary. 

 The secondary aberration of figure is not a sensible defect in object- 

 glasses for long achromatic telescopes, though I am induced to be- 

 lieve that it will materially affect very short ones. This aberration 

 might be corrected by making all the surfaces spherical except one, 

 which should be formed by the revolution of an ellipse on its conju- 

 gate diameter, when the elliptic surface is convex. But as this is 

 impracticable, there is no way yet known of entirely destroying the 

 secondary aberration. It was, however, much reduced in the sex- 

 tuple lens above mentioned, by making one of the uncemented sur- 

 faces as nearly elliptic as was practicable. 



The achromatic microscope might be much improved, if some 

 new arrangement of lenses, with spherical surfaces, could be devised, 

 that would entirely destroy the secondary aberration of figure. Of 

 this defect the sextuple lens has less than any other combination con- 

 sisting of a smaller number of single lenses ; because the radii of the 

 flint lenses are greater, when the focal distance of the compound lens 

 is the same. 



I find by experiment that a more minute object can be seen in blue 

 or purple light than in any other, provided the microscope is suffi- 

 ciently powerful. This probably arises from the rays of light hav- 

 ing a greater magnitude, at the red, than at the purple or violet ex- 

 tremity of the spectrum.* 



* See " Library of Useful Knowledge," No. 12, p. 32; where the limit of mi- 

 croscopic vision, depending on the magnitude of the rays of light, is treated of 

 b}' Fraunhofer. 



