948 SUMMARY OF CURRENT RESEARCHES RELATING TO 



Hence it is that all the celebrated opticians have had recourse to 

 trigonometry for calculating the direction of the refracted rays, and 

 I have done the same myself. But I have been able to formulate the 

 results thus obtained, on account of the small difference in refraction 

 which is found in the different kinds of glass, crown and flint, and 

 have constructed tables which give in algebraical form the relation 

 between the radii of curvature and the indices of refraction of the two 

 media which enter into the construction of the objective, whether 

 microscopic or telescopic. 



The formula only contains the indices of refraction of the two 



media n and n', their relative dispersion ^-,, and some constants the 



an 



value of which depends solely on the index of refraction of the least 



refractive medium. But what is more important is the fact that by 



the help of this formula the problem can be reversed, and we can find 



the indices of refraction and the dispersion necessary to render the 



double lens aplanatic and achromatic. 



With the help of the tables I have constructed and the formula 



referred to, I have found that the best results are obtained when the 



following conditions are fulfilled. 



Q.71 



1st. The dispersion should be such that -r-7 = 0-5, and this 



relation should be the same for all the partial dispersions from red 

 to violet. Then the achromatism is perfect. 



This condition can be realized by a mixture of aromatic substances, 

 of which some react more on the red whilst the others, on the contrary, 

 enlarge the violet part of the spectrum. By mixing two or three 

 substances we can obtain the refraction and dispersion given by the 

 formula for making the objective aplanatic and achromatic. 



2nd. The index of refraction of the mixture should be n' = 1 • 63242, 

 for example, when the crown-glass used in the construction has an 

 index n = 1-5296. The formula gives the change in n' for any 

 other value of n. 



3rd. All the radii are then identical. Hence I call the objective 

 symmetrical, for the last radius r^ = 00, that is to say the last surface 

 becomes a plane surface. 



Any one can make his own telescope or Microscope without any 

 calculation by taking a lens of quartz or crown-glass of any descrip- 

 tion and the mixture of aromatic bodies which gives to it a dispersion 

 twice as great, or equal for all the rays of the spectrum. 



We obtain the lens of the Microscope by reversing this lens, that 

 is to say, the plane surface is placed on the side of the object. 



The lens being corrected, it is combined with one or two other 

 symmetrical lenses in the well-known mode, by which doublets and 

 triplets are obtained perfectly aplanatic and achromatic ; then, on 

 going beyond the focus either way, no trace is found of the secondary 

 spectrum. 



The test objects which I have used are globules of mercury on a 

 black ground, with sunlight, and the plate of M. Abbe of Jena, viz. 

 a plate of silvered glass ruled with cross-lines in different directions. 



