May 27, 1922] 



NATURE 



679 



a short distance from the flange, and could be 

 ilhiminated by sunlight or other means. A small 

 hole in the disc allowed the eye to look in the direction 

 of the axis of the tube, and when the piston was 



_^ 



Hush with the. flange the view obtained was of a 

 uniformly white surface ht by the light scattered 

 from D. 



The experiment consisted in withdrawing the piston 

 until it became invisible, the relative intensities of 

 the illumination of the flange or piston face then 

 being DC'/DA^. For sunlight the ratio was about 

 220 to 230 and for candle-light about 170, thus 

 indicating a definition 0-45 and 0-5 in each case. 



Analogous experiments were tried on sound by the 

 use of two lever clocks placed at some distance 

 apart. The distance was then noted at which the 

 ear had to be placed from each in order that one set 

 of " ticks " might be drowned by the other. Musical 

 sounds of the same pitch and loudness were tried 

 in the same way. It is always difficult to make in- 

 door experiments on sound on account of the echoes 

 from walls and furniture, but on the whole it appears 

 that the definition for the intensity of sound was not 

 so good, though of the same order, as for light: 



As regards the definition for wave-length, that is, 

 the recognition of colour and pitch, the range for 

 visible light waves is much narrower than that for 

 sound. The lengths of all the visible rays lie within 

 the ratio of two to one, while in sound a compass of 

 more than ten octaves is audible. Few people when 

 viewing the whole spectrum at once will distinguish 

 more than seven or perhaps eight colours, but when 

 only a small portion covers the visible field, the varia- 

 tions of tint are much more marked. I have been 

 told by one well-known observer that he could dis- 

 tinguish between the yellows a very short distance 

 on either side of the D lines. This would correspond 

 to a difference of wave-length of five or six parts in 

 a thousand, but since wave-lengths at the orange and 

 green end of the yellow do not differ by more than a 

 hundred parts in a thousand, the definition implied 

 is not better than five per cent. 



Few ears are so unmusical as not to be able to 

 distinguish intervals of a semitone (wave-length ratio 

 about ten per cent.), but fewer still can at once dis- 

 tinguish between a major and minor semitone (about 

 one per cent.), and even fewer between the true 

 semitones and their equal temperament substitute. 



The sensibiUty of the ear to change of pitch varies 

 largely in different parts of the audible range, and is 

 at its best in the two octaves above and the octave 

 below the middle C. 



In both light and sound the judgment is improved 

 if there is a fixed standard for reference. No standard 

 would be required by the normal eye to determine 

 whether an object was red, yellow, or blue, but doubt 

 might easily be felt as to the exact shade of the colour 

 if the objects were seen separately at considerable 

 intervals of time, and the longer the interval the less 

 as a rule is the judgment to be trusted. 



The relation of musical notes sounded in succession 

 in the same way is less correctly estimated when the 

 time intervals between them are long than when they 

 are short, except for those who have the sense of 

 absolute pitch. I have no good data as to the range 

 over which this rather rare sense extends, but have 

 reason to believe that in some cases and in the vocal 

 compass it is accurate to within one per cent. 



NO. 2743, VOL. 109] 



The same sort of memory which enables a definite 

 colour or pitch to be recognised without any external 

 standard of comparison is requisite also for the 

 mental division of intervals of space or time. I have 

 known people who could mark off inches and count 

 seconds by memory with errors of not much more 

 than one per cent., but they could not deal with feet 

 or minutes with anything like the same accuracy. 



In estimating fractions of a second a good transit 

 observer will approach a two per cent, standard, but 

 whether the second is the best time interval for mental 

 division may be questioned. 



As regards the division of space by estimation I 

 may mention the following simple experiment which 

 I have often repeated at intervals of years and always 

 -with the same result. 



On a sheet of ruled foolscap draw two straight lines 

 intersecting near one end of the sheet, and about 

 .six inches apart at the other (Fig. 2). Mark the inter 



sections of these lines with the ruling by well-defined 

 circular black spots, and from another sheet cut out 

 a slot about six and a half inches long and half an 

 inch wide. This when superposed on the first will 

 allow one pair of spots to be visible at the same time. 

 Now, always keeping the eye at the same distance 

 from the paper, mark in succession the point esti- 

 mated to be midway between each pair. These 

 marks should all lie on the bisector of the angle 

 between the first drawn divergent lines. 



In all my trials I found that so long as the subtense 

 of the pair of spots was small enough to allow of both 

 being seen clearly at the same time, the angular error 

 in the estimation of the bisection was more or less 

 constant and ranged from 1/500 to i/iooo [i.e. from ^ 

 to x\-is inch at ten inches, the distance of the eye from 

 the paper). The error, however, increased rapidly 

 when the spots were so far apart that they had to be 

 viewed in succession. This occurred when their sub- 

 tense was about 20°, and the best bisections were 

 made with a subtense of 15° to 12°. 



For smaller angles the definition was not so good, 

 for though the linear error on the paper did not change 

 much, it had to be compared with the smaller distance 

 between the spots. In my own case, for angles greater 

 than 20° the error in the bisection was always to 

 the left, but this probably is a personal matter. 



As for space, so for time, there must be some par- 

 ticular interval which is best suited for division of 

 estimation, and my impression is that this is some- 

 what, but not much, longer than a second. As an 

 example of the importance of the correct estimation 



