236 



Prof. Silvanus P. Thompson on 



a lens prints a curvature of one dioptrie upon a plane wave 

 which is incident upon it. For the present proposal to 

 extend the use of the term from focal powers (i. e. imprinted 

 wave-curvatures) to the curvatures of curved surfaces in 

 general, the writer is responsible. 



4. Notation. 



In adopting a notation which embodies the new method it 

 is obviously advisable to choose one which lends itself most 

 readily to the existing and accepted notations. In the great 

 majority of books on optics, the recognized symbol for focal 

 length is /; that for radius of curvature r. And in the 

 Cambridge text-books for many years the distances from lens 

 or mirror of the point-object and the point-image have 

 respectively been designated by the letters u and v. 

 Now it is the reciprocals of these which occur in the expres- 

 sions for the curvatures of surfaces or of waves. The symbols 

 adopted respectively for the four reciprocals are accordingly 

 $j 31; tfl. and ty. The accepted symbol for the index of 

 refraction is the Greek letter /x; for the velocity-constant, 

 which is its reciprocal, we take the letter h. The following 

 is a tabular statement of the symbols and their meanings. — 



Symbol. 



1) 

 h 



Meaning. 



Focal curvature, or Focal power of lens or 

 mirror ( = dioptries, if metre is taken as unit 

 of length) 



Curvature of Surface 



Curvature of Incident wave ; i. e. curvature 

 which it has acquired by having travelled 

 from point of origin (" incident focus ") to 

 incidence 



Curvature of Kesultant wave ; i. e. curvature 

 with which wave emerges from the lens 



Velocity-Constant of medium ; i. e. velocity of 

 light in that medium compared with velocity 

 in air taken as unity 



Equivalent in 

 Current 



Notation. 



Expansion of Curvatures. — If the curvature @l of a wave 

 at any point is known it is easy to calculate the curvature at 



