1893.] on The Just-Perceptible Difference. 19 



portions of these papers, however valuable they may be in themselves, 

 do not interest me, in which case it has been a never-flagging source 

 of diversion to compare my capabilities of following the reader when 

 I am using my eyes, and when I am not. The result depends some- 

 what on the quality of the voice ; if it be a familiar tone I can 

 imagine what is coming much more accurately than otherwise. It 

 depends much on the phraseology, familiar words being vividly re- 

 presented. Something also depends on the mood at the time, for 

 imagination is powerfully affected by all forms of emotion. The 

 result is that I frequently find myself in a position in which I hear 

 every word distinctly so long as they accord with those I am 

 perusing, but whenever a word is changed, although the change is 

 perceived, the new word is not recognised. Then, should I raise my 

 eyes from the copy, nothing whatever of the reading can be under- 

 stood, the overtones by which words are distinguished being too faint 

 to be heard. As a rule, I estimate that I have to approach the 

 reader by about a quarter of the previous distance, before I can 

 distinguish his words by the ear alone. Accepting this rough 

 estimate for the purposes of present calculation, it follows that the 

 potency of my hearing alone is to that of my hearing plus imagina- 

 tion as the loudness of the same overtones heard at 3 and at 4 units 

 of distance respectively ; that is as about 3 2 to 4 2 , or as 9 to 16. 

 Consequently the potency of my auditory imagination is to that of a 

 just-perceptible sound as 16 — 9 to 16, or as 7 units to 16. So the effect 

 of the imagination in this case reaches nearly half-way to the level of 

 consciousness. If it were a little more than twice as strong it would 

 be able by itself to produce an effect indistinguishable from a real 

 sound. 



Two copies of the same newspaper afford easily accessible 

 materials for making this experiment, a few words having been 

 altered here and there in the coj>y to be read from. 



I will conclude this portion of my remarks by suggesting that 

 some of my audience should repeat these experiments on themselves. 

 If they do so, I should be grateful if they would communicate to me 

 their results. 



Optical Continuity. — Keenness of sight is measured by the angular 

 distance apart of two dots when they can only just be distinguished 

 as two, and do not become confused together. It is usually reckoned 

 that the normal eye is just able or just unable to distinguish points 

 that lie one minute of a degree asunder. Now, one minute of a 

 degree is the angle subtended by two points, separated by the 300th 

 part of an inch, when they are viewed at the ordinary reading distance 

 of one foot from the eye. If, then, a row of fine dots touching one 

 another, each as small as a bead of one 300th part of an inch in 

 diameter, be arranged on the page of a book, they would appear, to 

 the ordinary reader to be an almost invisibly fine and continuous line. 

 If the dots be replaced by short cross strokes, the line would look 

 broader, but its apparent continuity would not be affected. It is im- 



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