Studies in Visual Sensation. 



463 



the mid-grey should fall is apt to be placed too far from the centre. 

 The position of the mid-grey is also apt to be misjudged according as 

 we are shading from inner white to outer black or vice versa. In practice 

 I endeavour to avoid these disturbing effects, first by constructing discs 

 to shade both ways and taking the mean results, and, secondly, by 

 dealing with a reflected image of a portion of the disc, from centre 

 to circumference, in a slip mirror, 140 mm. long by 25 mm. wide, the 

 edges of which may be graduated. It is easier to judge of the accu- 

 racy of shading in such a band than in a complete disc. Making all 

 allowances, however, for misjudgment of position in the mid-point, 

 the smoothed curve drawn through the points experimentally deter- 

 mined by the method of graded rings does not shade satisfactorily. 



Before attempting to indicate the probable cause of this discrepancy, 

 it will be convenient to draw attention to the further experimental 

 work which it suggests. If the smoothed curve we have so far 

 obtained does not afford to the eye satisfactory shading, it obviously 

 remains to determine what curve does give results in sensation which 

 appeal to the judgment as approximately accurate. The shading of 

 the disc which expresses the curve passing through 20 per cent, of 

 white stimulus as the mid-point is so far satisfactory as to suggest 

 that the curve is right in principle but faulty in its application. And 

 a great number of experiments, which need not here be described, 

 convinced me that the introduction of + and - variations at different 

 parts of such a curve, so as to alter its character, only serve to make 

 matters worse and not better. It seems, therefore, that what requires 

 alteration is the position of the mid-point of the curve, or in other 

 words the value of the first of the series of smoothed steps, and that 

 of the factor required to give a geometrical progression of stimulus 

 increments. 



It is easy to construct a curve on the same principle which shall 

 pass through any desired mid-point, and to translate it into the 

 answering curve on a disc. It being obvious that the required mid- 

 point is less than 20 per cent., a series of discs were constructed in 

 which the value of the mid-point ranged from 20 per cent, down to 

 10 per cent. By using these, I found that the mid-point for con- 

 tinuous shading of white into black lies between 10 per cent, and 

 15 per cent. ; and by further experimental work, I found that 12 per 

 cent, gives the best result for my eye under the conditions of daylight 

 illumination which I employ. The accompanying figure shows the 

 curve representing the relation of stimulus to sensation which is 

 deduced from it. The firm line shows the curve passing through 

 12 per cent, as mid-point, the dotted line that passing through the 

 points determined by means of the graded disc with grey rings. 



It here naturally suggests itself that the data obtained for the 

 graded ring disc were erroneous, and that the discrepancy is due to 



