38 



its impression at once, nor can any part of it be affected 

 apparently, without its neighbourhood being affected also, 

 any brilliant object dazzles the eye, and in this way objects 

 will appear slightly longer than they really are. Both the 

 correct limb of the sun, and Venus appear a little larger from 

 irradiation than the real size, of either the sun or planet, by 

 the breadth of the irradiated circle ; hence from irradiation 

 between the two lights is produced the so-called black drop 

 or ligament. The effect of these irradiations is at times so 

 great, that it becomes quite impossible to execute correct 

 measurements of them. This troublesome illusion, for such it 

 is, has been investigated with great acuteness by M. Plateu, 

 who has thrown much light on the subject. For the sake of 

 distinctness, and because of their practical value, they are 

 here given in the form of separate and substantive proposi- 

 tions. Irradiation is a fact completely established, and 

 readily confirmed, very variable, but capable of being measured 

 with precision. It occurs whatever the distance of the object 

 at which we look, its amount, or the visual-angle which it 

 subtends is independent of that distance, and therefore the 

 absolute breadth to be attributed to it is, all else being 

 equal, proportional to the distance which seems to exist 

 between the object and the eye. It increases with the 

 brightness of the object, but not proportionally, "if its 

 increase is represented by a curve, whose abscissae represent 

 increasing brightness, beginning at darkness or zero, and 

 having for its ordinates the corresponding amount of irradia- 

 tion, this curve would pass through the origin of the co- 

 ordinates, with its concavity towards the axis of the abscissae, 

 and finally pass into an asymptote parallel to that axis. For 

 a brightness equivalent to that of a star in a clear sky, the 

 curve will be found very close to its asymptotes." When 

 the space surrounding the object looked at is not wholly dark, 

 the irradiation belonging to the object is diminished, and 

 when the illumination of the field of view approaches equality 

 with the brightness of the object, the illusion attributable 

 to irradiation altogether vanishes. Here, then, are two im- 

 portant practical consequences, when two objects of equal 

 brightness touch, irradiation is at zero at their point of contact, 

 and any two irradiations occurring in the same neighbourhood 

 diminish each other, the diminution being the greater in pro- 

 portion as the edges of the luminous spaces are nearer to each 

 other. 



Irradiation depends very much on the state of the eye, or 

 impressibility of the retina, it varies considerably in the same 

 individual, or by personal equation ; it is greatly modified 

 when a lens is placed before the eye, it is diminished by 



