CHAP, in.] SIGHT. 1211 



brighter we do not recognize that it is brighter. Hence it is 

 much easier to distinguish 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 rush- 

 light and a wax candle ; but two suns, or even two bright lamps, 

 one of which compared with the other gave out just that addi- 

 tional amount of light, just that additional quantity of luminous 

 energy, which a wax candle gives out in addition to that given 

 out 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, however, 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 because the whole surface has become so bright. 



On the other hand, when we carefully compare the visual 

 sensations excited by measurable differences of luminosity, we 

 come upon the following remarkable result. If we place two 

 candles so as to throw two shadows of some object on a white 

 surface, the shadow caused by each light will be illuminated 

 by the other light, and the rest of the surface will be illuminated 

 by both lights. If now we move one candle away we shall reach 

 a point at which the shadow caused by it ceases to be visible, 

 that is to say, we fail at this point to appreciate the difference 

 between the surface illuminated by the near light alone and that 

 illuminated by the near light and the far light together. If 

 now, having noted the distance to which the candle had to be 

 moved, we repeat the same experiment with two bright lamps, 

 moving one lamp away until the shadow it casts ceases to be 

 visible, we shall find that the lamp has to be moved just as far 

 as the candle ; that is to say, the least difference between the 

 illumination of the bright lamps which we can appreciate is the 

 same as in the case of the dimmer candles. Many similar 

 examples might be given shewing a similar result ; 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 y^th) of the total lumi- 

 nosity employed. As we shall see, the same relation holds good 

 with regard to the other senses as well. It may be put in a 

 general form, as a law of sensation, often called Weber's law, 

 somewhat as follows : The smallest change in the magnitude of a 

 stimulus which we can appreciate through a change in our 

 sensation always bears the same proportion to the whole magni- 

 tude of the stimulus. It should however be stated that this law 



