CHAP, ii.] SIGHT. 521 



The intensity of the sensation varies with the luminous inten- 

 sity of the object ; a wax candle appears brighter than a rushlight. 

 The ratio, however, of the sensation to the stimulus is not a simple 

 one. If the luminosity of an object be gradually increased from a 

 very feeble stage to a very bright one, it will be found that though 

 the corresponding sensations likewise gradually increase, the incre- 

 ments of the sensations due to increments of the luminosity 

 gradually diminish ; and at last an increase of the luminosity 

 produces no appreciable increase of sensation; a light, when it 

 reaches a certain brightness, appears so bright that we cannot tell 

 when it becomes any brighter. Hence it is much easier to distin- 

 guish a slight difference of brightness between two feeble lights 

 than the same difference between two bright lights; we can easily 

 tell the difference between a rushlight and a wax candle ; but two 

 suns, or even two bright lamps one of which differed from the 

 other merely by just the number of luminous rays which a wax 

 candle emits in addition to those sent forth by a rushlight, would 

 appear to us to have exactly the same brightness. In a darkened 

 room an object placed before a candle will throw what we consider 

 a deep shadow on a sheet of paper, or any white surface. If, 

 how r ever, sunlight be allowed to fall on the paper at the same 

 time from the opposite side, the shadow is no longer visible. The 

 difference between the total light reflected from that part of the 

 paper where the shadow was, and which is illuminated by the sun 

 alone, and that reflected from the rest of the paper which is 

 illuminated by the candle as well as by the sun, remains the same; 

 yet we can no longer appreciate that difference. 



On the other hand, if using two rushlights we throw two 

 rhadows on a white surface and move one rushlight away until the 

 shadow caused by it ceases to be visible ; and, having noted the 

 distance to which it had to be moved, repeat the same experiment 

 with two wax candles; we shall find that the wax candle has to 

 be moved just as far as the rushlight. In fact, it is found by 

 careful observation, that within tolerably wide limits, the smallest 

 difference of light which we can appreciate by visual sensations 

 is a constant fraction (about T Joth) of the total luminosity employed. 

 The same law holds good with regard to the other senses as well. 

 The smallest difference in length we can detect between two lines, 

 one an inch long and the other a little less than an inch, is the 

 p.ame fraction of an inch, that the smallest difference in length 

 we can detect between a line a foot long and one a little less than 

 a foot, is of a foot. Put in a more general form then, the law, 

 which is often called Weber's law *, is as follows : When a stimulus 

 is continually increased, the increase of stimulus necessary to call 

 forth the smallest appreciable increase of sensation always bears 

 the same proportion to the whole stimulus. 



1 From which Fechner, by an assumption, obtained a mathematical expression 

 cr formula, which is sometimes incorrectly spoken of as Fechner's law. 



