Curvature Method of Teaching Optics. 469 



attacking lens problems, of which one only, and that probably 

 the Least suitable, has been given a fair trial in this country. 

 They may perhaps be enumerated as follows : — 



(a) The method of reckoning in conjugate distances — 



Geometrical or Gauss method. 

 (6) The physical or curvature method. 

 ((•) The method of deviations — Yon Seidel. Finster- 



walter, 

 (d) The use of the characteristic function, or principle 



of least time — Hamilton. Thiesen, and Chalmers. 

 v f Thermodynamic method — Clausius. 

 ^ I Employment of the " eikonal " — Brims. 

 ( t ) Vector or Quaternion treatment. 



Of these methods (e), (c), and (d) are the ones which the 

 writer believes will be found most suitable, and it will be 

 shown, as is almost self-evident, that they are essentially 

 similar. Of the eikonal treatment he has no experience, but 

 is inclined to think that its nse is confined to problems of an 

 advanced nature, and that it is unsuitable for a general ele- 

 mentary treatment. As to (/) it seems curious that no one 

 ha- proposed the application of the modern vector calculus 

 of Prof. Henrici. Mr. Oliver Heaviside, and Prof. Gibbs, to 

 geometrical optica, as it should be capable of effecting con- 

 siderable simplifications. For example, if a is a unit vector 

 representing the direction of an incident ray, b the corre- 

 sponding refracted ray, and n the vector normal to the 

 surface, both of the ordinary laws of refraction are summed 

 up in the simple vector relation 



/*i [a n] = fi 2 U> n ], 

 or in Heavisidc's notation 



/\ A. A, y\ 



fjbi Ya a = a? V6 n. 



The writer has deduced a few interesting consequences of 

 this fundamental expre->ion, but has not yet had an oppor- 

 tunity of following it up completely ; moreover, as the method 

 is a purely geometrical one. ii could only have advantages 

 in a possible simplification of ordinary procedure, and would 

 not have any other physical signification. 



Practical <Ji>tic<tl Units, — The simple device of opticians 



spectacle-lens notation was to adopt two units which are 



now fairly generally known. The first of these may be u>e.l 



to express either the curvature of a surface or the power of 



