128 



NATURE 



■— 1890 

 -h- 32CX) 



-T- 1640 



diffuse daylight. Each result stated below is the mean of from 

 ten to fifty readings under fairly favourable circumstances, d is 

 used for the whole division or space on which the position of the 

 index was estimated ; and i is the inch, which is the unit used 

 throughout. 



(1) The first question is the average amount of error made by 

 different persons with regard to the fraction of division ; in fact, 

 the personal variation of average error. This on a lo-inch space 

 was — 



By A mean error </ -=- 1 12 

 „ B „ oT -4- 60 



.» C „ </-T- SO 



„ D „ ^-T- 36 



,, E „ </-T- 21 



(2) The average amount of error with regard to the fractions 

 of an inch (the divisions being too small to see the above frac- 

 tions of them) were — 



By A on space oi i ~- 41 mean error 

 » A „ i-^ 139 „ 



>i C ,, » -f- 41 ,, 



Under the best circumstances and reading with the right eye, 

 A's mean error is only » -f- 5000 on the space of i'-r- 139 ; and 

 as the distance was about six inches, this is 3 ^ q j of the dis- 

 tance ; agreeing with the size of the smallest line visible, which 

 is about TTwir to -ririTnr of the distance according to circum- 

 stances, but without any shadow to the wire examined. As to 

 the observers, A has had practice lately in measuring ; B had 

 much practice some years ago ; C and E are ladies of artistic 

 tastes but unmetrical ; D is moderately accustomed to measuring, 

 but has a difference between the focus of his eyes. It would bs 

 highly interesting to have a good collection of statistics on this 

 question, from among surveyors, mechanics, and the unmetrical 

 classes. I proceed to readings for other points, made by A. 



(3) The mean errors on spaces of various lengths stand 

 thus : — 



10 i space, mean error d ~ 112 

 li „ „ d-^ 89 



(1-^-41 ,, ,, d -^ 'JO read by right eye only) 



» -T- 41 ,, ,, :.d ~ 106 if read by both eyes. 



Thus the size of the division does not seem to much affect the 

 estimation, the extreme difference being 4:5. If the angular 

 width of a space exceed 5° it is not so easily grasped by the eye, 

 though the error is not perceptibly increased till it exceeds 20°. 

 The J -T- 41 space was read with a magnifier, ( x 3), so it was 

 equivalent to ?' -i- 14. 



(4) The relative error of the first guess (or the numerical idea 

 produced instantaneously at the first glance) and the most care- 

 fully considered readings stand thus : — 



Carefully 

 considered 

 d~ 114 



^-^ 78 



d-~ 13 



apparently indicating that the first gwess is worst where the 

 space is rather too wide angularly to be grasped by the eye at 

 once ; and therefore that the want of grasp is the defect corrected 

 by consideration. 



(5) The effect of looking at the space askew was tried by 

 viewing it at 30° to either side ; shifting sides ten times so as to 

 avoid any gradual change in the quality of the reading, and so 

 as to call up the contrast more strongly. The results of careful 

 readings were : — 



In sum of errors, 

 per cent. 

 + 



10 J space to right hand 31 69 



10 «■ „ left „ 45 55 



and it was noticeable that the fraction nearest to the reader was 

 invariably guessed smaller at first sight, than it appeared on 

 careful examination, showing that the tendency to diminish the 

 nearest side which is noticeable in the above percentage of the 

 space to right hand, was still stronger at first, and was corrected 

 by consideration. 



So far the results have been independent of differences between 

 the eyes, but it would seem that these are considerable from the 

 following : — 



(6) Comparison of the percentage of -1- and — errors of the 

 two eyes separately ; the sum of the amounts of errors being 

 taken, and not the number of errors. 



First sight. 

 10 i space, ^ ^ 55 

 li „ </ -f- 54 



Ratio. 



2'i : I 

 14: I 



Distanse of 

 observer. 

 1 10 i or I id 

 18 i „ 18^ 

 6/ ,, 840^? 



I / space 

 li „ 

 t-^139 » 



Right eye. 



-f- 



55 45 

 75 25 

 92 8 



[pec. 16, 1875 



Left eye. 

 + 



58 42 white light 

 34 66 coloured light 

 28 72 on silver 



Mean ... 73 27 39 61 



The elements of this mean, and all others after, are weighted by 

 the number of observations. As in all these readings the zero 

 was to left hand, it would seem that each eye imagines the frac- 

 tion on its own side smaller than it really is, this being in exact 

 accordance with the effect produced by both eyes viewing the 

 object from one side. See (5). 



(7) When both eyes are used together the readings appear to 

 be well balanced on an average : — 



per cent. 

 + - 



lojspace 42 58 



I' ,. 59 41 



Mean 53 47 



The variations, however, of different series of readings are as 

 wide as + 80, — 20 ; and + 20, - 80 ; this may be partly due 

 to temporary rest of one eye, involuntarily ; and lo a slightly 

 skew view of the space. 



(8) The comparative amount of error of the two eyes stands 

 thus : — 



Right : Left I : 



II space 100 : 109 white light 



I i ,, 100 : 120 coloured lights 



«-f-l39 ,, 100 : 150 on silver 



Mean 100 : 121 



So 5 : 6 is the relative error of the right and left eyes. 



(9) The relative errors of each eye separately and of both 

 together are : — 



Right eye. Left eye. ^^-^^ ^ogused 



I /space ... I "52 ... 1*64 ... 1-59 ... 100 

 So that the advantage of two eyes over one is more than ^2 : i, 

 which it would be, if regarded as the mean of two readings ; the 

 excess of 1*59 over ^/z may be due to the restraint of keeping 

 one eye shut. The accuracy seems to be about Y^~the number 

 of eyes. 



(10) A most important practical question is that of the influ- 

 ence of colour on the error of estimation. On trying this with 

 coloured glasses the results were most unexpected. 



Relative amount of error. 



1 1 space . . . 

 ii 



Mean 



No glass. Blue. 



.. i-o -81 



I'o 1*17 



Green. 

 I -06 



Red. 

 170 

 1-23 



I'O 



•99 '97 I -46 



The two series (each of ten readings with each colour) are given 

 to show how far uniform the results are ; they were read on 

 different days, completely reversing the order of the four columns • 

 and they were equally divided between the eyes, five by right 

 and five by left. 



I had expected that red would hold about the above relation 

 to white ; but that green, and especially blue, would have been 

 worse ; the colours were spectrally tolerably pure, except the 

 blue, which contained some yellow. The badness of blue on 

 the second trial in diffuse daylight is accounted for by a want of 

 sufficient light ; blue containing such a small proportion of lif^ht- 

 rays. 



So far I have remarked on those points which are perhaps, or 

 probably, not due to idiosyncrasies ; the question of partiality for 

 certain digits is clearly a personal error, as has been demonstrated 

 in Nature ; so it is not worth noting further, as its interest ia 

 individual cases is confined to the observer, who should try 

 (being "forewarned") to be "forearmed," and so allow for it 

 in reading ; of course a series of statistics on it would have much 

 interest. 



(11) One point, however, which is probably alike in all is th< 

 relative amount of error in different parts of a scale ; the mean 

 find to be thus : — 



o to 1 I to 2 2 to 3 3 to 4 4 to s 5 to 6 6 to 7 7 to 8 8 to g 9 to la* 



•65 I '53 I '36 I '52 1-47 154 22 1-30 1-09 I -14 



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