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Mr. C. Lloyd Morgan. 



them in the terms afforded by the arbitrary scales. The percentages 

 are as follows : — 



Sensation 25 50 75 100 



Stimulus.... 6-5 20 47 100 



Stated in this form, while the sensations are in arithmetical progres- 

 sion there is at first sight no very definite series in the stimuli. But if 

 we express the results in a somewhat different form the stimuli fall 

 into an orderly sequence. The following figures give the increments of 

 sensation and of stimulus : — 



Sensation + 25 + 25 + 25 + 25 = 100 



Stimulus +6-5 + 13-5 + 27 + 53 = 100 



It is clear that the stimulus increments are here nearly in geo- 

 metrical progression. And if we may base a purely provisional and 

 empirical generalisation on so slender an experimental foundation, we 

 may say that equal increments of sensation require increments of 

 stimulus in geometrical progression. 



Such being the preliminary results obtained from a series of approxi- 

 mately equal sensation steps, we may now, on the basis of our pro- 

 visional generalisation, interpolate other points between those obtained 

 by observation, and through them sweep a smoothed curve. And 

 having clone so, we can translate the curve on to a disc which shall 

 give a continuous geometrical increase of stimulus from our zero black 

 to our 100 per cent, of white. And this on rapid rotation should 

 afford a smooth passage from black to white in sensation. There 

 ought to be a perfectly even and uniform ascending slope of sensation 

 from our zero black through progressively lightening shades of grey 

 to our limit of 100 per cent, of white. Our mid-grey should lie just 

 in the middle between the extremes. When the disc so prepared is set 

 in rapid rotation, however, though there is a gentle shading from 

 white into black, this shading is not uniform. There is a lack of 

 balance. The mid-grey does not appear to be just half-way between 

 black on the one hand and white on the other hand. It lies too near 

 the black, and the shading is therefore too rapid from this mid-grey 

 into black, not rapid enough in the opposite direction towards white. 

 The appearance is not that of a uniform slope of sensation, but rather 

 that of a gentle convex curve, the surface appearing slightly spherical. 



It may here be noted in passing that we have to be on our guard 

 against the misleading effects of a so-called optical illusion. In our 

 rotating disc we have to judge the position of the mid-grey, which 

 should lie equidistant from the black and the white. But in a disc or 

 a sector thereof there is a tendency to misjudge the distance, from the 

 centre, of a circle which bisects the radii. The inequality of the areas 

 tends to confuse the judgment as to distance, and the position where 



