488 



Mr. B. T. LoTOe on some 



[Jan. 11, 



being so arranged that each illuminates the shadow cast by the other. 

 I, however, added a woodcut, in which I had preyiously determined the 

 ratio of white and black in the shades by examining it with a microscope 

 and low-power objective. This woodcut was so placed that it was illu- 

 minated by the light from both candles ; by varying the distances of the 

 candles I produced shadows of the same intensity as the shades in the 

 print, determining the intensity of the shadow by making it fall close to 

 the corresponding shade in the print Tvithout overlapping it. When the 

 two appeared continuous, -Niewed at such a distance that the ruled sur- 

 face was still a ruled surface to the eye if attentively observed, I found 

 the proportion of the reserved white in the ruled surface varied as the 

 square root of the intensity to which the illumination of a wholly white 

 surface had to be reduced to match the other. 



I found, for instance, in my first experiment, that when the candles 

 were placed at the distances of two and four feet respectively, the 

 faintest shadow was somewhat brighter than that portion of the wood- 

 cut in which |- was black and -J white, and the darker was somewhat 

 darker than a half-black surface. 



Considering the light thrown on the screen by the nearer candle to 

 have the value of 100 units, that of the more removed gives 25 units. 

 The total illumination of the screen was, then, 125 units — that of the 

 darker shadow 25 units, and that of the brighter 100. The portions of 

 the screen, therefore, have the following ratios of illumination : — 



100 : 80 : 20. 



Eut the sensations produced are nearly equal to those of a shaded 



„ , . 10 9 4-2* 



surtace having To 10 10 white, 



or as 



10 : 9 : 4-2, 



the square roots of the lumiQous intensities nearly. 



In every case I found the apparent illumination, measured by a re- 

 ference to a ruled surface, varied inversely as the distance of the source 

 of light. 



There is no difhculty in obtaining a very close approximation, as the 

 eye easily detects a shadow dilfering by ^ of the whole hght, as has 

 been shown by Lambert, Arago, Helmholtz, and others. 



The experiments made by the method iQdicated are vitiated to a 

 certain extent by the difficulty of guarding against diffused light ; but 

 when moderate precautions are taken a black surface differs in no per- 

 ceptible degree from the shadow cast by making the two shadows over- 

 lap, so that the diffused light may, I think, be neglected. 



tin order to test further the degree of accuracy of which the ex- 



* Tlie decimal is only estimated, not measured. 



t The account of these experiments was received December 11. 



