570 BELL SYSTEM TECHNICAL JOURNAL 



ment would, of course, be classed as wrong. All reported "no choice" 

 judgments have been distributed equally between the "right" and 

 "wrong" classes. It will be noticed that there was some discrimina- 

 tion at even the smallest change made, that is 0.045 milliradian, and 

 that there was lack of complete discrimination at the largest change, 

 that is 0.27 milliradian. The "no choice" judgments comprised 15 per 

 cent of the total at the smallest change and only 2 per cent at the 

 largest. 



It is interesting to note that for the null changes the "no choice" judg- 

 ments comprised only 17 per cent of the total, indicating either that 

 the observers were reluctant to admit that they were guessing or that 

 they were judging coincidental small changes in the film due to its 

 bending in the gate or to its photographic processing. (We did ob- 

 serve, in establishing the lens position for sharpest focus, that film at 

 the start of a reel required a slightly difTerent lens setting from that at 

 the end of the reel, and we ascribed it to the varying tension during 

 projection, or to the varying degrees of curvature in storage on 

 the reel.) 



The four sets of points in Fig. 2 exhibit rather striking similarities. 

 Each set may be fairly represented by a normal error curve (straight 

 line on this arithmetic probability paper). We have drawn in four 

 such normal curves, passing each one through the 50 per cent point at 

 the null change and giving each a common slope. The appropriate 

 value of slope was determined by inspection of an auxiliary plot in 

 which the four reference values were superimposed and the four sets 

 of points were plotted to a common ordinate scale of differences. These 

 normal curves are considered to represent the data as well as any more 

 elaborate relations that might have been used. 



We varied the resolution only in the direction of decreasing it with 

 respect to the reference values. We presume that had the variation 

 been in the opposite direction the data would have been represented 

 equally well by the same normal curves, which are accordingly extended 

 in dotted lines. 



In Fig. 2 we have indicated the magnitude of a difference of one limen 

 by means of supplementary scales of ordinates. Since the four normal 

 curves have a common slope, the difference limen turns out to have a 

 constant value, 0.090 milliradian (0.3 minute of arc), independent of 

 the size of the figure of confusion in the range from 0.71 to 2.8 milli- 

 radians. Why this should be so is a problem of physiological optics 

 which is rather beyond the scope of this paper. The supplementary 

 scales also serve to illustrate the meaning of differences two and three 

 times as large as the difference limen. That is, a change in the side of 



