Ij Couh St, /v//.s- — Phijx'ohxj'H-al Optics: 



revolved each on a vertical axis through the angle 



to the eyes whose nodal points are o and o', the 



appear by reflection at AB and A'B', the visual 



measured by the diffei 

 , nd &'. 

 i of th 



/? and p. The values ot a and a' can be expres 



abled to find for what value of <p the 

 difference, a—a\ becomes a maximum. For the values just 

 to Ac and oc, this condition is attained when ^=52° 

 25'. By ordinary methods in trigonometry two sides and the 

 included angle of each triangle being known, a and a! are then 

 determined, and their difference found, which in the present 

 case becomes 1° 25' 37". Assuming an average value, 1575 mm. 

 for the list;i if ■ from m d d point, o, to retina, E, the linear hor- 

 izontal displacement on the retina corresponding to 1° 25' 37" 

 is a trifle over -39 mm., or more than 80 times the diameter 

 corresponding to what has been estimated to be the minimum 

 visibile. For angles even smaller than 52° 25' both Mr. Share 

 and myself found it possible to detect double images at the 

 margin's of the binocular picture; this, however, did not pre- 

 vent the perception of tin; particular kind of relief, whether 

 concavity or convexity, which the arrangement necessitated. 

 In trying the experiment by continuous light many persons 

 have at first been contused, but a few moments of play of the 

 eyes were enough to produce clear perceptions, and the form of 

 the binocular image thenceforth remained distinct even when 

 the gaze was kept as nearly rigid as possible. Unless there 

 has been special training in binocular vision the duplication of 

 these marginal images is rarely perceived at all. 



On the other hand, to find the smallest retinal displacement 

 through which change of form in the binocular image can be 

 perceived in this manner, I have substituted series of circles in 

 which the ma was only 4 cm., keeping the dis- 



tance unchanged. Tip image became noticea- 



bly concave for a rotation of each through only 1°. By caleu- 

 lation the angular retinal displacement is here found to be only 

 47", an amount so small that under the most favorable circum- 

 stances no double image could be perceived with the acutest 

 vision thus far tested. These experiments therefore tend to 

 confirm the conclusion reached by Helmholtz,* in opposition 

 to many otl that neither play of the eyes nor 



tin: perception of double images is indispensable to the attain- 

 ment of Inn' < ilar relief, h< e\ mn i taut these elements may 

 sometimes lie in continuing our visual judgments, whether con- 



