OF ARTS AND SCIENCES. 213 



in the atmosphere, and explained their use and the great 

 importance of the observations based upon them. 



Professor Rogers also exhibited a series of diagrams ex- 

 planatory of certain conditions of binocular combination not 

 hitherto described, and intended especially to demonstrate 

 the form of the curve which results froyn the binocular union 

 of a straight line ivith a circular arCy or of two equal circu- 

 lar arcs with one another. 



" First. Of the binocular resultant of a straight line and a cir- 

 cular arc. 



" Assuming the optical centres of the two eyes as fixed during the act 

 of combination, the centre of the eye directed to the circular arc may 

 be regarded as the vertex of a cone whose surface includes all the 

 positions of the optical axis of that eye as successively directed to the 

 different points of the arc. This cone will of course be right or ob- 

 lique, according to the direction in relation to the plane of the paper of 

 the line joining the optical centre with the centre of the circle of which 

 the arc is a part. The axis of the other eye, in ranging from end to 

 end of the vertical line, vibrates in a plane which during the binocular 

 combination intersects the conical surface in an attitude depending on 

 the distance between the optical centres, the place of the diagrams, and 

 the relative position of the component lines. 



" The two optical axes, directed each moment to corresponding 

 points of the vertical line and arc, meet in the conical surface, forming 

 optically a series of resultant points which together compose the binoc- 

 ular resultant curve. This curve must, therefore^ he a conic section^ 

 the nature of which will depend on the direction of the cutting plane 

 in reference to the conical surface. 



" Considering the several cases in which the arc is convex towards 

 the right line or concave towards it, and in which the combination is 

 effected before or behind the plane of the diagram, all the results may 

 be thus summed up. 



" («.) When the arc is convex to the right line and they are united 

 beyond the plane of the diagram, or when the arc is concave to the 

 line and they are combined in front of it, the binocular resultant may 

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

 will turn its convexity obliquely towards the observer. 



" {I.) When the arc is concave to the right line and they are united 



