OPTICAL INSTRUMENTS. 



13 



different magnifying powers, aberra- 

 tions, and separatio?i of colour, or 

 chromatic dispersion, (this latter error 

 is explained in 23 :) their respective va- 

 lues are shown in the following Table : 



Piano convex lenses 

 with convex side ex- 

 posed to parallel rays. 



Glass 



Sapphire 



Diamond 



Magnifying Longitudinal 

 .power*. aberration. 



150 

 250 

 400 



1.167 

 1.005 

 0.950 



Chromatio 

 dispersion . 



48 

 26 

 38* 



But this difference in the longitudinal 

 aberration would be much greater if the 

 lenses were so formed as to give the 

 same magnifying powers ; for this error 

 always decreases as the squares of their 

 respective radii, while the lateral aber- 

 ration or area of the circle of confusion 

 will be as their cubes. 



Hence, in sapphire and diamond lenses 

 of high magnifying powers, the indis- 

 tinctness arising from their figure would 

 barely be discernible in practice, thus 

 producing a kind of natural aplanatic 

 magnifier. 



The valuable properties possessed by 

 these stones were ' known to Sir Isaac 

 Newton, and Martin, and have been 

 more particularly pointed out by Dr. 

 Brewster, in his Treatise on New Optical 

 Instruments. But their hardness and 

 crystalline form probably occasioning 

 difficulties in the formation of spherical 

 polished surfaces almost insurmount- 

 able, has retarded their adoption as 

 lenses : however, we have lately learned 

 that Mr. Pritchard has succeeded in 

 forming these substances into lenses, 

 and their \ application to the microscope 

 is so favourable, that, if any new disco- 

 veries are to be made in the minutife of 

 nature, they seem most likely to develope 

 them. 



The process by which these lenses 

 are worked, and their application to the 

 microscope, are detailed in the Journal 

 of Science of the Royal Institution, 

 vol. ii. page 15 (New Series). This 

 paper was communicated by Dr. Go- 

 ring, who suggested to Mr. Pritchard 

 the advantages which diamond lenses 

 would most probably possess. 



The adaptation of these lenses to 

 telescopes in place of the ordinary eye- 

 glasses would, in all probability, be at- 

 tended with equal success, where every 

 circumstance calculated to produce a 

 perfect representation of the object is of 

 the utmost importance. 



* When it is considered, that the refraction of 

 diamond is nearly three times that of glass, it 

 follows, that in equal refractions its dispersion will 

 be only one-third of the latter. See Optks, p. 24. 



21. The great advantage of duly con- 

 sidering the aberration of lenses will be 

 evident, if we combine two lenses, of 

 twice the focal distance, instead of one, 

 to produce any given power, as the 

 aberration will, be decreased to one 

 quarter of that of a single lens of equi- 

 valent power, and, therefore, the aper- 

 ture of the compound lens may be in- 

 creased, while the error will be less than 

 in a single lens. In the common tele- 

 scopes (figs. 15 and 16), if two lenses 

 were used, instead of the single object 

 and eye-glass, as there shown, the aper- 

 tures of each might be increased, and, 

 consequently, the instruments would be 

 improved in light and field. 



(22.) M. Huygens has demonstrated, 

 that when the greatest possible distinct- 

 ness is required for the eye-piece of a te- 

 lescope, it may be obtained by two plano- 

 convex lenses, placed as in/g-. 19, with 



Fig. 19. 



their plane sides outward, and the focus 

 of the eye-lens E must be of that of 

 the field-lens F, with a distance between 

 them equal to the difference of their 

 focal lengths. This combination, from 

 the purpose it has been adapted to, is 

 called the astronomical positive eye- 

 piece ; and the telescope, by this addi- 

 tion, will have four times the distinct- 

 ness of a single lens D, of equivalent 

 power, while the distortion of the object 

 will only be \ of that produced by a sin- 

 gle lens ; for the refraction of the object- 

 lens brings the image of the marginal 

 rays nearer to itself than the central, 

 therefore the image will be formed 

 convex next the lens F, as shown by 

 the aiTOw; and as the radius of 

 curvature of the lens F is twice 

 that of the single lens D, the distor- 

 tion will be decreased in the square 

 of this ratio, or 4 times. On this ac- 

 count, a similar combination is used for 

 the eye-pieces of telescopes for astrono- 

 mical quadrants, and other graduated 

 instruments, when the convex side of 

 the field-lens is turned towards the eye- 

 glass E, because equal divisions on a 

 micrometer correspond with equal an- 

 gles, subtended by objects measured by 

 this instrument, This combination, which 



