No. XIX.] APPENDIX. 281 



alone. This amount may be called X, and the quantity denoted varies 

 directly as the base AB, and the line CD, and inversely as the line BO. 



By similar triangles AB:BC::X:DC; therefore X = AB X PG 



BC 



an equation which gives the value of X in every position. 



" In studying these principles nothing has more astonished me than 

 the fact of the colours which overlap to the two eyes not giving the com- 

 pound colour, which would result if they were mixed and seen by one eye. 

 In all those parts of a picture where colours overlap, much skill will have 

 to be exercised by the painter, as the appearance in nature is that of a 

 film or coloured gauze overlapping other colours, and the result is not the 

 ordinary compound colour. 



" One of the few artists who have seen Turner paint, stated to me that 

 in painting the near objects he lightly touched with his brush and then 

 placed his finger over it, whereby he produced a semi-transparent streak 

 instead of a line. This streak enabled the more distant objects to be seen 

 behind it, and thus the conditions of binocular perspective were in part 

 fulfilled. 



" Another curious phenomenon connected with binocular perspective 

 is observable in the case of a landscape viewed through a window, for in 

 that instance the vertical bars become either wholly or partially trans- 

 parent, and the objects behind them are seen with a shade over them. 

 The horizontal bars retain their solidity and obscure all the parts they 

 shade. This phenomenon occurs when the head remains in its ordinary 

 position ; but when the head is turned so that the eyes are one above the 

 other, the horizontal bars become transparent, and the vertical bars retain 

 their solidity. It is requisite for the observance of these effects that a 

 distant object should be the point of sight, and not the window bar. 



" According to the laws which have been detailed, we observe that 

 objects behind the point of sight are seen in two places, although indis- 

 tinctly, from being out of focus, and from being seen at the lateral part of 

 the retina. From these facts it is apparent that a painter should depict 

 the objects in the background of a neutral or tertiary tint and very indis- 

 tinct. In nature the object directly viewed is alone seen in perfection, 

 and he that would carefully study nature should contrive that his prin- 

 cipal subject should be the brightest in colour and most distinct in detail, 

 when it will stand forth in all its beauty. 



" The outline effects of binocular perspective may be readily obtained 

 by placing two candles at 2 2 inches apart, from flame to flame, and ex- 

 amining the shadows which are produced upon a white screen. It will 

 then be seen that objects near the screen will have a light shade at each 

 lateral border. Small objects will, at a greater distance, appear double ; 

 and the double images being superimposed, a body different from either 

 wHl be produced. A finger held horizontally across the flames will have 

 the end prolonged by its shadow, but it will be observed that no change 

 takes place at the upper and lower edges. By this experiment only the 

 outline effect is produced; but I cannot too highly recommend to the 

 painter to shut himself up with two candles and study these effects. 



" As a rule, the image of an object in two places is not appreciated 

 entirely, because one object falling upon the margin of the retina is 

 scarcely visible. These considerations curiously bring before our mind 



