Deceptive Figures. 



23 



DECEPTIVE FIGUBES; 



WITH EEMAEKS ON SATUEN'S « SQUAEE-SHOULDEEED " PHASE. 

 BY E. A. PBOCTOE, B.A., E.E.A.S. 



In the April number of the Intellectual Observes, p. 224, 

 instances have been given of an optical illusion affecting our 

 estimate of the relative size of figures placed in particular 

 positions with respect to each other. In the figure accompa- 

 nying this article a somewhat similar illusion affecting shape is 

 illustrated ; the lines A B and B C, which appear to have a 

 decided curvature, being in reality straight lines. 



In figures constructed on a larger scale, and with concentric 

 circles closer together (in proportion), the deception is still 

 greater ; and it is remarkable that the illusion is increased by 

 drawing equidistant lines radiating from the centre of the 

 concentric circles. I notice, also, that a want of symmetry in 

 the drawing seems to destroy the illusion. 



The deception struck me as remarkably perfect in the case 

 in which I first observed it. I had drawn the meridians and 

 parallels for a polar star-map on the equidistant projection, to 

 the scale of an 18-inch globe — the parallels to every degree, 

 and the meridians, from the 20th parallel of N. P. D. to the 

 bounding parallel (N. P. D. 37° 23') of the map, also to every 

 degree. Thus the map formed a circle llf inches in radius, 

 with 37 concentric circles crossed by 360 radiating lines, 

 drawn with as much uniformity as possible. Now before 

 marking in stars, I wished, as a matter of curiosity, to deter- 

 mine the exact figure on the equidistant projection of the 

 spherical pentagon, which in my gnomonic maps appears as a 

 true pentagon. I accordingly drew in, in pencil, first the 

 inscribed pentagon, and then (through points determined by 

 their known R. A.'s and N. P. D/s) the five curved sides of 

 the figure I required. Thus the sides of the true pentagon 

 formed chords of the five sides of a curvilinear pentagon 



