108 



points less separated will appear nearer, and the more separated will 

 appear further. 



Suppose the two correspondent vertical lines of the openings or 

 frames of the pictures be more distant than the two correspondent 

 points of the furthest plane of the pictures themselves, then the open- 

 ings or frames will appear behind the pictures ; and suppose the cor- 

 respondent vertical lines of the openings be less distant than the two 

 correspondent points of the nearest plane of the pictures themselves, 

 then the openings or frames will appear before the picture. 



Therefore, when we wish to have the picture appearing behind the 

 openings or their mountings, we have only to take care that the cor- 

 respondent vertical lines of the mountings should be laterally less 

 distant than the two correspondent points of the first plane of the 

 picture. This can be easily done by taking the measure of the two 

 correspondent points of the first plane by means of a pair of com- 

 passes, and tracing the two pairs of correspondent vertical lines 

 bounding the openings, after having slightly reduced the angle of 

 the compasses. 



A very simple experiment may show the cause of the illusion of 

 concavity of flat surfaces when examined through semi-lenses, and 

 further prove that semi-lenses may give alternately the illusion of 

 concavity and convexity according to the position of their thin edges ; 

 of concavity when their edges are towards each other, and of con- 

 vexity when they are placed contrariwise. For this experiment we 

 have only to employ a pair of those spectacles mounted with a spring 

 whereby they are held on the nose. 



When we read, holding such spectacles with both hands, we may 

 by the elasticity of the spring adjust the two lenses so that the pupils 

 of the eyes can coincide, first, with the two nearest edges, secondly, 

 with the two centres, and thirdly, with the two furthest edges of 

 the lenses. 



In the first case, the page of the book will appear concave, because 

 the pupils will look through the thin edges of the lenses which bend 

 the vertical lines with their concave sides turned towards each other ; 

 in the second, the page will appear flat, because the pupils will look 

 through the centres of the lenses which show the vertical lines per- 

 fectly straight ; and in the third case, the page of the book will ap- 

 pear convex, because the pupils will look throiigh the thin edges of 



