TJie President's Address. Bij E. M. Nelson. 167 



only half the battle, the other half being to find the moat suitable 

 form for the lenses. The mathematical analysis of this part of the 

 subject was investigated by Sir George Airy, and his results are given 

 both by Coddington and Potter ; it is rather long, and unfortunately, 

 when done, will not serve our purpose, for the following reasons : — 

 (a) One may calculate a form that will give the best field, but any 

 one with a trained eye using such an eye-piece becomes painfully 

 conscious of the great falling off in the definition of details. (/3) If 

 the calculation is made with a view to secure the best definition, 

 then the outer portions of the field become so woolly that they have 

 to be cut out by a diaphragm, and the remaining central part becomes 

 too small for practical purposes. In brief, the conditions are antago- 

 nistic ; therefore one must be content with a compromise. This has 

 often been stated before ; and as you are all perfectly familiar with 

 this phenomenon it will be needless to enlarge further upon it. The 

 analysis shows that for field the lenses should be menisci, and for 

 definition biconvexes ; the plano-convex, which is a mean between 

 these forms and also the cheapest lens, is the ODe generally used. 

 It will be understood that for rigid accuracy a different form of lens 

 must, be employed for different values of p ; if therefore a plano- 

 convex is a mean form for a telescope, where p is large, it will no 

 longer be so with a Microscope, where p is small. 



I had the curiosity some time ago to calculate and try various 

 forms for a Microscope eye-piece, but nothing particularly new be- 

 yond the conclusions stated above was discovered ; but it seemed that 

 something better than the plano-convex form might be coostructed. 

 It will be generally conceded that sharp definition is of primal im- 

 portance in critical work both with the Microscope and telescope, 

 and that this quality is to be preferred to a large field ; and further, 

 we have seen that it is possible to attain this advantage by reducing 

 the size of the field. The best English Microscopes have what is 

 called a ten-inch field, by which expression is meant, that the 

 apparent diameter of the field is 10 in. at a distance of 10 in. In 

 Continental Microscopes, however, the field is restricted to about 

 5 or 6 in. ; so then by reducing the size of the English field to 

 that of the Continental we shall have it in our power to improve 

 the central definition. After several experiments the form which 

 appeared to yield the best results was a field-lens giving minimum 

 aberration for the direct pencil, combined with an eye-lens with a 

 ratio of radii of 3:1, having its flatter curve next the eye, the glass 

 of which the lenses were composed being of low dispersive crown. 

 In conclusion, the formulae necessary for computing the radii of 

 the lenses will now be given. 



Field-lens. — Let 



— 1 =2 t* , and v -r-n — = e ; 



P H- + Z 



