words are printed in lines for reading material. It is generally agreed that very long lines of print tend to lessen legibility. After experimenting, Dearborn (8) came to the conclusion that a line from 75 to 85 mm long and with type 1.5 mm high gives a satisfactory and efficient reading line. Huey (18) thought that 90 mm should be the maximal line-length and 60 to 80 mm the optimal. Both Dearborn (8) and Huey (18) agree that regularity in length of line is an important factor in reading, because of the 'short-lived motor habits' set up by the eye in reading lines of uniform length. In an analytical study Judd (20) found that doubling the size of elevenpoint type, or reducing it to half-size made only a slight difference in efficiency for adult reading. In a more elaborate study Gilliland (15) recorded eye-movements, using two series of reading material which ranged in size of type from 6 to 54 points and from 3 to 90 points. He concluded that "the reading of the average adult is not greatly affected by changes. in the size of type between the limits of 36-point and 6-point type." In going over the various investigations, Gray (16) reports that it is generally agreed that printed letters should be a deep black, and the paper pure white and without gloss. The influence of colored paper on ocular efficiency has not been thoroughly investigated and no definite conclusion can be made concerning it. In England, the Industrial Fatigue Research Board is carrying out an investigation (13) to determine the most effective contrast between colored papers and inks. Preliminary results suggest that color contrast is of comparatively small importance in hygienic printing. Starch (28) reports a study which agrees with this view. THE PLAN OF OUR INVESTIGATION WITH FORMULÆ In this investigation, which is the preliminary part of a larger study on the reading of formulæ, the attempt has been made to compare the legibility of certain parts of mathematical formulæ by comparing the reading-time of the digits 1 to 5, and the letters n, m, x, y, and t, when occurring in the body of the formulæ, to the reading-time when they occur as exponents or subscripts. This comparison is designed to throw some light on the relative legibility of the parts considered when the reading is done under approximately normal reading conditions. Most of the previous experiments which have investigated the legibility of isolated letters, words, or like material, have used some form of short-exposure apparatus. While this kind of experiment has achieved noteworthy results, it is desirable here to provide a closer approximation to the normal reading situation. In his outstanding study of visual fixation Dodge (10) gave some consideration to this and later when investigating the psychological effects of alcohol (11) he devised a technique and apparatus for the determination of the reading-time of four-letter English words. In this latter publication he states the following important conditions. The stimulus should appear suddenly, all at once, in the field of clear vision, in order to increase to a maximum the visual controls which ordinarily complete the process which is begun in the prefixational perception of the reading material. There should be provision for satisfactory adaptation to distance and to illumination. The stimulus should remain in view until the act of perception has been completed and the response made. Continuation of the exposure after perception has taken place may be used as a check on misperception. The fulfilment of these conditions seemed to us to offer the best possibilities in our experiment. ment. Three faculty members and four students in the Department of Psychology at Stanford were subjects in this experiFive of these had the equivalent of about two courses in high school mathematics, and the other two had completed calculus. This arrangement gave us a mediocre and a skilled group so far as mathematical training goes. All were tested with the Snellen chart for visual acuity. Those who wore glasses were allowed to keep them on in the visual test since. they wore them while observing in the experiment. They all tested 20/20, or above, on the chart. In order that the material to be read might approach as closely as possible the real conditions encountered by the student, mathematical formulæ were cut from 4 standard algebra texts (12, 23, 24, 30) and pasted on small cards about 7 cm by 3 cm in size. These formulæ were of various sorts and lengths. About -inch below the left end of each formula a large black dot was placed for pre-exposure fixation. The distance from the left end of the formulæ to the parts to be read could not be exactly controlled. On the average, the exponents and subscripts were 0.5 of a letter-space nearer the left end than the digits, and 0.3 of a letter-space nearer the left end than the letters, in the body of the formulæ. Therefore any advantage derived from being nearer the left end of the formula would go to the exponents and subscripts. Apparatus for Reading Reaction? The apparatus used for exposing the formulæ and recording responses was the same general scheme as described by Dodge (11), but with the modifications introduced by Miles (2, 22) for freeing the experimental procedure from several distracting factors. Its main parts are: the exposure apparatus, a voice key, two electromagnetic markers, a large time-clock, and a Baltzar kymograph. The exposure apparatus was on a wooden screen large enough to hide from the observer the kymograph and markers, as well as the manipulations of the experimenter. In this screen, at a level with the observer's eyes, was a small window about 2 cm by 7 cm in extent. Behind this window was a light horizontal arm with one end attached to the screen and the other free to move past the window. The free end carried a pack of from 12 to 15 stimulus cards. The card-holding device was improved by Miles to hold several cards (he used packs of 25) instead of one as used by Dodge. With this arrangement the experimenter was able to slip out one of these cards after each exposure without any interruption of the kymographic record. Only the black dot on the stimulus card was visible to the subject during the pre-exposure interval, as the card-carrying arm was held up by an electro-magnet. This magnet was in circuit with the voice key, a marker and a switch on the kymograph. At 2 This equipment was largely made possible by the Thomas Welton Stanford Fund for Psychological Research. The apparatus, as shown in Fig. I, is mounted on a small table and is to be used as a permanent reading-reaction unit. It is economical in space occupied and can be easily moved as a unit from room to room. FIG. 1. Apparatus and conditions for reading reactions. K, voice key; L, screen with window; M, mag- each half revolution of the kymograph drum, an automatic circuit breaker attached to the shaft of the kymograph momentarily broke this circuit, releasing the free end of the arm carrying the cards, and at the same instant it caused the marker to record on the smoked kymographic paper. The arm quickly dropped far enough to bring the formula to the middle of the window at the spot where the fixation dot had been exposed. This arm was activated by a stout rubber band and was stopped suddenly and held firmly in the center of the window with very little noise and no vibration, by means of what Dodge calls the 'pendulum stop.' The main feature of this stop consists of two bars, one short and one long, riveted together in a movable joint. The long end of the lever thus made was attached to the movable end of the exposure-arm. The short end was attached to the screen directly below the attachment to the arm. When the exposure-arm was up the short part of the lever was horizontal, and when down, vertical, and thus parallel to the long bar of the lever. In this position, the arm holding the stimulus could move neither up nor down until the experimenter pushed the joint of the lever to one side. The stimulus card remained exposed until the experimenter reset the apparatus for the next exposure. With this type of exposure, the suddenly dropping card came to a rest without any rebound or secondary vibration so that the clearing up of the visual field was wholly physiological. Thus one obtained an exposure that has a minimum of interference with 'the normal and adequate perception' of the stimulus. The subject reacted by speaking into the voice key. This broke the circuit again and thus the marker recorded a second time on the same line as contained the exposure mark. A time-line giving the time in seconds ran parallel to the reaction-line. This made it easy to read the time interval between the beginning of the exposure and the beginning of the response. The subject sat with his eyes at a level with the exposure-window and at a comfortable reading distance from the stimulus card. With the exception For Dodge's description see Dodge and Benedict, Psychological effect of alcohol, Carnegie Instit. Washington, 1915, no. 232, p. 94, fig. 13. |