June 22, 1888.] 



SCIENCE 



297 



■should improve the designs of machines now being built. The 

 best dimensions to give the different parts of any dynamo is a per- 

 fectly definite problem, involving, besides questions of electrical 

 efficiency, questions of the cost of the iron and wire and labor. How- 

 ever, the problem can be solved, and each maker of dynamos 

 should have it solved. In a recent paper. Professors Ayrton and 

 Perry have considered the magnetic circuit of dynamo machines, 

 and have arrived at some important conclusions. Considering the 

 resistance of the magnetic circuit, they find, that, when a machine 

 is working at its best permanent output, its iron magnetic resist- 

 ance plus the air magnetic resistance of the clearance is equal to 

 the air magnetic resistance of the space on the outside of the arma- 

 ture occupied by the winding. The paper of Professors Ayrton 

 and Perry, with those above mentioned, will greatly aid in the 

 improvement of dynamo-electric machinery. 



MENTAL SCIENCE. 



The Relative Legibility of the Small Letters. 



Reading is one of the most widespread of modern activities, and 

 the endless multiplication of books and cheap editions makes a 

 study of the factors of this process of great importance. In the 

 end the process reduces to the differentiation of black or colored 

 marks on a white or colored surface. ' Black on white ' is current 

 as an expression for clearness, leaving the question of the shapes of 

 the letters as the important one. Inasmuch as the Roman alpha- 

 bet is in use for the chief languages of civilization, and a large ma- 

 jority of the characters are formed by the small letters, the investi- 

 gation of the forms of these letters is naturally the point of prime 

 value. If by any means we can make the reading of these letters 

 an easier task, the improvement, however minute, when multiplied 

 by the number of times the letter is read, will be very great. This 

 is, however, not the only consideration. Tint and quality of paper, 

 length of lines and spaces between them, the size of the letters and 

 their distances from one another, — all affect the legibility. The 

 end to be aimed at is to attain " the greatest legibility to the 

 square inch," with due regard to taste and economy. The solution 

 of this problem has been experimentally attempted by Dr. Javal 

 and by Dr. Cattell, and has recently been again studied with im- 

 proved apparatus by Mr. E. C. Sanford {American Journal of Psy- 

 chology', May, 1 888). 



The first method of obtaining an order of legibility of the letters 

 •consisted in measuring the distances at which they could just be 

 read. The letters were fastened to the edge of a rotating disk, and 

 were viewed through a square hole of 2 centimetres, in a black 

 screen placed in front of the disk. Test-type letters of a clear 

 bold pattern were used, the short letters being about 1.8 and the 

 long letters about 2.2 millimetres high. The whole apparatus was 

 mounted on runners sloping upwards from the floor at an angle of 

 about fourteen degrees, and could be moved to any distance from 

 the eye by pulling an endless cord. 



The first method of these distance-tests consisted in showing the 

 letters at a fixed distance for the whole alphabet, and noting the 

 number of times each letter was rightly and wrongly named, as 

 well as the letters with which it was liable to be confused. An- 

 other fixed distance is then chosen, and the test repeated. The 

 result, with five subjects and the letters at distances varying by 10 

 centimetres from about 1.5 to 3.2 metres, was as follows, the num- 

 bers expressing the percentage of cases in which the letters were 

 correctly read : — 



m, 90.9 



V, 71.0 



X, 63.0 



n, 46.2 



■zv, 88.1 



k, 70.9 



a, 60.8 



e, 46.2 



/. 84.4 



b. 704 



z, 60.6 



f, 45-1 



P, 84.3 



y. 70.4 



/, 58.6 



0, 44-9 



g, 80.9 



h, 69.9 



11, 55.2 



2, 34.1 



r, 78.7 



d, 68.3 



s, 53-0 





J. 77-6 



.,-, 68.2 



i. 46.5 





These percentages are based on about three hundred answers for 

 each letter, the preferred letter being counted as the only answer in 

 cases of doubt between two or more letters. 



From the same record we can obtain an order of the liability of 

 the letters to confusion and the chief causes of confusion. This 



order is substantially the same as the former, and would be still 

 more closely like it were it founded on precisely the same data. The 

 order, with the letters most likely to be confused with them, as well 

 as the percentages of cases in which the confusion occurred, are 

 given below : — 



m with 



•w, 52. 







h with b, i,\. 







7U " 



V, 53- 







X 



' n, 19 



2, 15- 





P " 



r,^^. 







a 



• u, 16 ; 



n, 14 ; s. 



13 



f " 



r, 37- 







s 



' n, 14 ; 



cr, 12. 





r " 



V, 22. 







I 



' i< 39 



y. 36. 





g •' 



g, 30. 







u 



' «. 18; 



s, 12. 





J " 



/,25 



/. 



21. 



I 



' /, 58. 







V " 



'-. 33- 







t 



' i, 40. 







y " 



p, 61. 







n 



■ a, 41. 







d " 



ag, 11. 







e 



' c, 40. 







g " 



r, 12 



t. 



10. 



z 



' e, 19 ; 



s, 17; a, 



16 



b " 



h, 45. 







c 



' ^. 34 ; 



0, 23. 





k " 



-1^, 34- 











' ^, 34 ; 



e, 23. 





Mr. Sanford also tested the letters by setting them so far away 

 that they could not be read, and then having the subject slowly 

 draw them near until he could read them ; in general, recording 

 both the distance at which the subject would first hazard a guess, 

 and the distance at which he felt confident that he had correctly 

 read the letter. Here differences in eyesight of the subjects tested 

 make average results meaningless, but the order for any one sub- 

 ject agrees fairly well with that obtained by the other test. If the 

 letters be divided into three groups of eight, ten, and eight, — calling 

 those in the first group good, those in the second fair, and in the 

 third poor, — all the orders agree in making ?f , m, g, good ; b and 

 X, fair ; and z, 0, c, s, e, poor : and the balance of the evidence 

 goes to make the good letters, w, m, g, p, v,y,j; the ten fair ones, 

 k, r, d,g, k, b, X, I, n, u ; and the eight poor ones, a, t, i, z, 0, c, s, 

 and e. 



By an ingenious apparatus a dark box in which one of the letters 

 was set could be illuminated for a very minute yet accurately 

 measurable time, and the proportion of cases in which each letter 

 could be correctly named when seen for a definite fraction of a sec- 

 ond would again measure its relative legibility. The letters were 

 exposed for times varying from .0013 to .004 of a second, and each 

 letter was shown about two hundred times. A table comparable 

 with that for distance is given below : — 



m, 82. 



p, 61. 



A, A7- 



n, 34- 



w, 73. 



A, 61. 



r, 43- 



^. 33- 



d,67. 



/.58. 



X, 42. 



s, 27. 



g,66. 



/', 52. 



A39- 



c, 26. 



V, 63. 



/, 49- 



0, 39- 



z, 23. 



J'. 62. 



2, 48. 



u, 38. 





y,6i. 



g,A7- 



'^.35- 





The order of legibility by the two methods agrees very well, and 

 yields the important conclusion that the letters read at the greatest 

 distance are also the letters most rapidly recognized at an ordinary 

 distance. The order for the two methods, as well as that found 

 by Dr. Cattell by a different mode of time-measurements, are : — 

 Order for time, inwdgvyjp kfblighrxt ouanescz 



Order for distance, wiiigpvyjf Jtrdgkbxlnu atzzocse 



Order for time (Cattell), dkmghbpw idjtvzrofn axyeigcs 



It so happens, that, of the eight letters most fully represented in 

 a full font of type, three («?, a, s) are the very letters that all the 

 tests agree in regarding as the worst, and six (e, a, s, 0, z, f) are 

 among those regarded as poor by two of the results. 



Among the deductions formed from this study are, that the con- 

 centration of differentia is an important aid to clearness, while the 

 lack of it leads to confusion. Thus, b, d, p, g, are all made of a 

 straight stem and a loop, and yet are easily distinguished (except 

 that b is confused with h) ; while g and a, though having few 

 points in common with other letters, are confused with several. 

 The group of confusables {e, 0, c) should be differentiated, the c 

 being left wide open, and some other form, such as the Greek e, or 

 an E with square corners, substituted for e : u, n, a, should be sim- 

 ilarly treated ; u, a, n, having their openings kept well open, and a 

 changed perhaps to an inverted v ; s, too, needs reform, and a shape 



