October sth, 1 8g'j?[ PROCEEDINGS. 



Ill 



In Fig, 2, let a ray of light AB be incident upon the surface 

 of C, as before, but at one extremity of the^ diameter of the semi- 

 cylindrical vessel, instead of at the centre, and let BD be the 



Fig. 2. 

 refracted ray. Describe a semi-circle BAF having its diameter 

 BF - BE = I and cutting the ray AB in A. Join AF and DE 

 and produce AB to G, joining EG. Now as AF and DE are 

 normal to AB and BD respectively and EB = BF ; AB and BD 

 are the sines of the angles a and /3' respectively. But a is 

 equal to the angle of incidence a and /3' to /3, therefore AB ( = BG) 

 and BD are also the sines of the angles of incidence and refraction. 



Although incidentally interesting it will be readily seen from 

 the figure that the refractive index of a medium is simply the 

 time that light takes to travel a distance in the medium which it 

 travels in unit time in air, or more correctly in a vacuum. 



It will now be quite evident that if an instrument be 

 constructed with BG and BD constant and their intersection 

 with their normals through E kept all in the semi-circle, the 

 phenomenon of refraction will be exhibited mechanically. 



Some time ago I designed such an instrument which 

 fulfilled to some extent these conditions. The principle is 

 shown in Fig. j, in which AB is made equal to the refractive 



Fifj. 3, 



