126 



SCIENCE 



[N. S. Vol. XLIII. No. 1100 



great results have been acliieved, our meth- 

 ods and mathematical tools are those of fifty 

 years ago. We stiU calculate lenses largely 

 by the cut and try method of triangulating 

 a bundle of rays through the lens and find- 

 ing whether they meet in the image plane. 

 It is possible that no other method of cal- 

 culating lenses will ever prove of practical 

 value, yet a number of our ablest math- 

 ematical physicists have attempted to applj' 

 the best modern mathematical methods to 

 lens design. Their results have been in- 

 teresting, but of practical value only in 

 limited fields. The consensus of opinion 

 to-day appears to be that if the seven lens 

 aberrations could but be expressed in a 

 suitable mathematical language, they would 

 assume comparatively simple forms readily 

 soluble. It is quite certain, however, that 

 such simplicity is impossible in any of the 

 mathematical systems yet tried, and that 

 the desired result will only be possible in 

 some system not yet invented. 



Our next greatest needs in lens design 

 are generalizations and publicity. In every 

 complete set of calculations for a given lens, 

 conclusions are arrived at relating changes 

 in radii, thicknesses, separations and glass 

 indices to variations in the degree of cor- 

 rection, in other words, a set of differentials 

 is obtained, by the laborious methods of ray 

 triangulation. Yet these very valuable re- 

 sults are regularly allowed to go either to 

 the waste basket or to the locked notebook. 

 The renowned Abbe set a worthy example 

 of world-wide usefulness by having pre- 

 pared and published tables for the selection 

 of companion glasses for telescope objec- 

 tives, thereby saving others hundreds of 

 hours of labor. If we followed his worthy 

 example, we should publish sets of differ- 

 entials applicable to each of the important 

 lens types as soon as obtained and thus ob- 

 viate a tremendous waste of time in dupli- 

 cating results. 



In particular, we need publication and 

 public discussion of such material as gen- 

 eral rules for the spectral correction of ob- 

 jectives for photographic and visual pur- 

 poses, general rules for reducing distortion, 

 for locating and displacing Gauss points, 

 limits of tolerance in definition and resolv- 

 ing power, the best methods of testing ob- 

 jectives and the like. 



In the design of optical instruments a 

 similar lack of coordination and generali- 

 zation is apparent. The instrument-using 

 public has been too often ignorant and al- 

 ways tolerant of defective design. The 

 average user accepts without question, as 

 he is without recourse, instruments hastily 

 conceived and imperfectly worked out in 

 design. Our largest makers employ spe- 

 cialists in the design of each class of instru- 

 ments. Lesser makers of the less used in- 

 struments, such as spectroscopes, photome- 

 ters and radiometers, seldom have the bene- 

 fit of the crystallized general opinion of 

 those users of his instruments who know 

 what the performance of a first-class in- 

 strument should be. We trust that every 

 class of both user and designer of optical 

 instruments will derive benefits from this 

 organization. 



No optical instrument can be of any serv- 

 ice without either an eye or a photographic 

 surface as an adjunct. The properties of 

 these should, therefore, be well known to 

 the designer of lenses and instruments as 

 well as to those more directly interested 

 in them. The material of these three chief 

 branches of applied optics (lens design, 

 vision and photography) is, however, widely 

 scattered and few who are well posted in 

 one branch are even well informed in the 

 other two. 



The fundamental problem of the photo- 

 graphic surface is the rendering of the light 

 impressed upon it. The quantitative rela- 

 tions between exposure, development and 



