334 



SUMMARY OF CURRENT RESEARCHES RELATING TO 



therefore about one-seventli of the maximum value, but as it is in this 

 last seventh that the difficulties of correction increase most rapidly, 

 it is hardly to be expected that the aperture can be much enlarged : 

 it remains, therefore, to diminish A by using an immersion liquid of 

 high refractive index, and to find a form of objective which will enable 

 the corrections to be made with the least difficulty. 



If a glass hemisphere be placed with its plane surface on a printed 

 page it will be found that the letters are magnified exactly in the 

 ratio of the indices of glass and air. The rays which pass through 

 the centre of the sphere suffer no aberration, so that in this case it is 

 possible to magnify an object without spherical or chromatic 

 aberration. 



On the same principle, it will be found that using homogeneous 

 immersion and a liquid of high index the absolute efficiency corre- 

 sponding to that index can by the alteration of a single surface be 

 augmented without involving any essential change in the correction. 



Let B E C D, fig. 69, be the section of a hemspherical front lens, 

 A the point of the object which lies in the axis ; let a spherical 

 surface B F of radius A B be hollowed out, and the space between 



A and B F C filled with a liquid of high refractive index, then the 

 efficiency of the objective is increased in the ratio of the indices of 

 the crown-glass and the liquid ; and if the surface B F C is accurately 

 formed and the objective previously corrected for homogeneous 

 immersion, the rays from A suffer no aberration ; secondary aberrations 

 only appear at some distance from A, and may be corrected by a 

 slight alteration of the back lenses. 



To strengthen the lens it is better to give it the form of fig. 70, 

 the radius of the spherical cavity B" F' C" being immaterial so long as 

 its centre is at A. Here B' E C' is more than a hemisphere. 



Using oil-immersion lenses of the above form. Dr. Altmann finds 

 that without further correction the desired result is in fact attained, 

 at least so far that with the same diameter the objective has its focal 

 length diminished, and consequently the efficiency increased, in 

 proportion to the index of refraction. At the same time he points 

 out that three difficulties will be encountered in carrying out the 

 conditions required. These are, firstly, the construction of the 



