214 PROCEEDINGS OF THE AMERICAN ACADEMY 



beyond the plane of the diagram, or when it is convex to the line and 

 they are combined in front of the diagram, the binocular resultant is 

 always an arc of an ellipse turning its convexity obliquely away from 

 the observer. 



" Second. Of the binocular resultant of two ciradar arcs. 

 " In this, as in the preceding combinations, the optical centres are 

 to be regarded as immovable during the experiment. Each eye, while 

 viewing the successive points of the arc presented to it, revolves in 

 such manner as to carry the optical axis around in a conical surface. 

 Thus two conical surfaces are generated, having for their respective 

 apices the centres of the two eyes, and including all the directions 

 which the optical axes assume in combining the successive pairs of 

 corresponding points of the circular arcs. In general terms, therefore, 

 the binocular resultant in all such cases may he described as the curve 

 line in lohich the surfaces of the two visual cones Jinter sect one an- 

 other. 



" It is only, however, under special conditions that the resultant thus 

 formed is a plane curve. When the circular arcs presented to the two 

 eyes are of unequal curvature, the visual cones by their intersection 

 produce a curve which cannot be included in a plane, but lies in an in- 

 flected surface ; and this accordingly is the form which the resultant 

 takes whenever circular arcs of unlike curvature are combined either 

 with or without a stereoscope. 



" The several effects of the binocular union of circular arcs of 

 equal length and curvature may be thus summed up. 



" (a.) When the arcs are convex to one another, and are combined 

 behind the plane of the components, or when they are concave to one 

 another and combined in front of this plane, the resultant may be 

 either an hyperbola, a parabola, or an ellipse ; but in either case it 

 will be convex towards the observer and in a veitical plane. 



" (&.) When the arcs are concave to one another, and are combined 

 behind the plane of the components, or when they are convex to one 

 another and combined in front of this plane, the resultant is always 

 an arc of an ellipse concave towards the observer and in a vertical 

 plane. 



" Whenever, in any of the combinations referred to, the resultant 

 curve takes the position of the sub-contrary section of the cone, it of 

 course becomes an arc of a circle.'''' 



Professor C. C. Felton exhibited to the meeting a series of 



