On a Simple Property of a Refracted Ray. 223 



specimen could still vibrate slowly from side to side, but 

 came to rest in a position displaced on one side or the other 

 of the central position. The buckling load was taken as 

 that which would cause the beam to come to rest so that the 

 displacement from the central position was the smallest 

 appreciable. The results of all the experiments can be seen 

 at a glance from the accompanying table. 



It was found of importance that the sides of the strips 

 should be exactly vertical, for if they were very slightly 

 inclined , a displacement was noted at comparatively small 

 loads. A delicate adjustment was necessary, so that when 

 the buckling load was reached the strips would remain at 

 rest, very slightly displaced, on either one side or the other 

 of the central position. 



In every case the buckling loads were determined experi- 

 mentally before their values were calculated by equation (1) 

 in order that the determination of the experimental loads 

 should not be influenced by a knowledge of the calculated 

 values. This was necessary because it was difficult to decide, 

 within 2 or 3 per cent., at what load buckling began. 



XX. Sote on a Simple Property of a Refracted Ray. 

 By Alice Everett *. 



LET AP be a ray incident at a point P on any refracting 

 surface, BP the refracted ray, CPN the normal, C the 

 centre of curvature in the plane of incidence ; <£, <fi' the angles 

 of incidence and refraction, and -^r, i|r' the angles GAP, OBP 

 made by the rays with a transversal CAB through C cutting 

 them at A and B. Then + ^r' = ^>' + ^r = fy, say. The 

 angle 7 plays a leading part in some modern optical 

 generalized formulae (see Optical Society's Transactions,, 

 vol. xx. pp. 23-31, Nov. 1918, where it is pointed out that, 

 for a spherical refracting surface, 7 is also the angle made 

 with the axis by the line joining C to the points of inter- 

 section of the rays with the aplanatic surfaces), but objection 

 has been raised that this angle is not readily visualized. 

 The following simple property which, curiously enough, 

 seems hitherto to have escaped notice, may be of service 

 in this respect. 



* Communicated by the Author. From a communication to the 

 Transactions of the Optical Society for March 1919, p. 203. 



