4 ART. 3. — AICHI AND TANAKADATE : THEORY OF 



2. Airy's theory. 



It will be necessary, in the first place, to state Airy's theory 

 in a form convenient for use in subsequent investigations. First, 

 let us nesjlect the visual angle of the drop, i.e. the radius of 

 the drop compared with the distance of the observer from the 

 drop (in the case of table experiment, we have to consider the 

 observer's distance as infinity, the telescope being so focussed). 

 Describe a unit sphere having the centre c coinciding with that 

 of the drop, and let the points o and 8 on the sphere be the 

 directions of observer and point-source of light respectively, seen 

 from c, and oti be the direction of the ray of minimum devia- 

 tion in the plane sco. The position of the observer with 

 respect to the sun is specified by the angle 6-co, or by the 

 angle mco. 



Put 



d = jmco = D — l.çco (1) 



where \) = r: — angle of minimum deviation, 

 r = radius of the drop, 

 n = index of refraction, 

 P — Ï = number of internal reflections, 





Then the emergent wave-surface, being the surface of rotation 

 with the axis sc, is specified by the curve of the intersection 

 with the plane sco. Taking the coordinate origin at c, y — axis 

 in cm and ;c— axis perpendicular to it, we have the equation 

 of the curve 



y = - -^^ , (2) 



