1893.] on The Just-Perceptible Difference. 21 



embroidery and tapestry, and coarser still by those obsolete school 

 samplers which our ancestresses worked in their girlhood, with an 

 average of about sixteen stitched dots to each letter. Perhaps the 

 coarsest lettering, or rather figuring, that is ever practically em- 

 ployed is used in perforating the books of railway coupons so familiar 

 to travellers. Ten or eleven holes are used for each figure. 



A good test of the degree of approximation with which a cyclostyle 

 making 140 perforations to the inch is able to simulate continuous 

 lines, is to use it for drawing outline portraits. I asked the clerk 

 who wrote the circular just exhibited to draw me a few profiles of 

 different sizes, ranging from the smallest scale on which the cyclostyle 

 could produce recognisable features, up to the scale at which it acted 

 fairly well. I submit some specimens of the result. The largest is 

 a portrait of ltj inches in height, by which facial characteristics are 

 fairly well conveyed ; somewhat better than by the rude prints that 

 appear occasionally in the daily papers. It is formed by 366 dots. 

 A medium size is £ inch high and contains 177 dots, and would be 

 tolerable if it were not for the jagged strokes already spoken of. The 

 smallest sizes are ^ inch high and contain about 90 dots ; they are 

 barely passable, on account of the jagged flaws, even for the rudest 

 portraiture. 



I made experiments under fairer conditions than those of the 

 cyclostyle, to learn how many dots, discs, or rings per inch were 

 really needed to produce a satisfactory drawing, and also to discover 

 how far the centres of the dots or discs might deviate from a strictly 

 smooth curve without ceasing to produce the effect of a flowing line. 

 It must be recollected that the eye can perceive nothing finer than 

 a minute blur of one 300th part of an inch in angular diameter. If we 

 represent a succession of such blurs by a chain of larger discs, it will be 

 easily recognised that a small want of exactitude in the alignments of 

 the successive discs must be unimportant. If one of them is pushed 

 upwards a trifle and another downwards, so large a part of their 

 respective areas still remains in line, that when the several discs 

 become of only just perceptible magnitude, the projecting portion 

 will be wholly invisible. When the discs are so large as to be plainly 

 perceptible, the alignment has to be proportionately more exact. 

 After a few trials it seemed that if the bearing of the centre of each 

 disc from that of its predecessor which touched it, was correctlv given 

 to the nearest of the 16 principal points of the compass, N., NNE., 

 NE., &c, it was fairly sufficient. Consequently a simple record of 

 the successive bearings of each of a series of small equidistant steps 

 is enough to define a curve. 



The briefest way of writing down these bearings is to assign a 

 separate letter of the alphabet to each of them, a for north (the top 

 of the paper counting as north), 6 for north-north-east, c for north- 

 east, and so on in order up to p. This makes e represent east, i south, 

 and m west. 



To test the efficiency of the plan, I enlarged one of the cylostyle 



