to show a definite, simple relationship between homogeneityheterogeneity and the magnitude of the work decrement. We felt, however, that there might be many sets of tasks in which the variation of homogeneity-heterogeneity would not be the dominating factor in determining decrement. If the more heterogeneous of such tasks were also the more delicately adjusted, these more heterogeneous tasks might be as susceptible to the decrement effect as more heterogeneous tasks of the same general sort. The part-activities in the former case might tend to compete with each other and to offer great possibilities of interference, so that the fact that smaller elements of frequency and recency of functioning were present might be more than compensated for by the increased possibilities of competition. We sought an experimental verification of this conception. We were successful in finding the verification in certain movements involving the use of one, of two, or of three fingers. In the case of these movements there was something like an equal decrement for the tasks of all three degrees of heterogeneity. We believe that the greater refractoriness set up in the more homogeneous activity by virtue of a greater factor of repetition was more than offset as the acts became more heterogeneous, because that very increase in heterogeneity of composition allowed in this case for an increase in the amount of possible competition between part-activities. We regard the experiments here reported as forming merely an entering wedge into the problem of the work decrement in psychological activities. The homogeneity-heterogeneity principle here demonstrated has, as we ourselves have shown, very definite limits. It may be obscured by a principle of competition. But we have here touched that principle only in the vaguest manner. One of us has pointed out 16 on general grounds the probable complexity of this principle and a thorough experimental study of it offers a real challenge. Other principles are also surely fundamental in the determination of the decrement and all of them offer rich territory for exploration. 16 Psychol. Rev., 1926, 33, 123–134. READING REACTIONS FOR MATHEMATICAL FORMULÆ1 BY MILES A. TINKER Psychological Laboratory, Stanford University REVIEW OF STUDIES ON LEGIBILITY The purpose of this study was to investigate the relative legibility of exponents and subscripts in mathematical formulæ as compared to the same symbols when used in the body of such formulæ. During the last twenty-five years, the experimental study of reading has been very prominent; and current methods of teaching the art of reading, as well as the efficient construction of books, are now making considerable use of the results of these investigations. Since an appreciable amount of the reading of students involves formula which are found in mathematical and scientific texts, it would be instructive to know more about the processes concerned in these ocular functions. Also it is important that such reading be made as rapid and as easy as possible. Sanford (26) very aptly says: "The problem is to get the greatest amount of matter with the greatest ease in reading on the least space; or, as it has been phrased, to get the greatest legibility to the square inch." Several investigations have concerned themselves with the legibility of the printed page. Some of the earliest of these experiments attempted to determine the legibility of the various letters of the alphabet and of various types of printing. As far back as 1881, Javal (19) came to the conclusion, after experimentation and observation, that the letters whose design was least desirable from the standpoint of legibility are: a cefgrst. Cattell (5, 6, 7) exposed both capital and small letters for very short intervals. In this way he determined the relative legibility of the isolated letters by taking the percentage of correct readings of the various letters 1 A summary of this paper was given at the meeting of the Western Psychological Association, Mills College, California, June 18, 1926. as: as exposed under these constant conditions. The order of capitals, from most to least legible, was found to be: W Z MDH KNXAYOGLQIS CTR PBVFUJE. For small letters the order was: dk mqhbpwuljtvzrof naxyeigcs. In a somewhat similar experiment with brief expositions, Sanford (26) used Snellen small letters. He found the order of the isolated letters, from most to least legible, to be: mwdqvyjp kfblighrxt ouanes cz. Using the distance from the eye at which they became legible, he again determined the order of legibility of the same letters wmqpvyjfhrdgkbxlnu atizocse. Showing a group of nine letters at each brief exposure, Finzi (14) used the percentage of misreadings to compute the relative legibility of the letters. The descending order for legibility he found to be: PUAQXTDSEWMVYZHCNFLR GBKOI. Finzi does not state what type or letter-form he used. Dockeray (9) obtained the legibility of isolated letters by determining the width of the field of distinct vision for each letter of the alphabet. The order of the letters from most to least legible for one of his three subjects was: m dk w p boqy jrx ag lvz istu hn c f e. The orders were similar, but not exactly the same, for the other two subjects. Shaw (27) summarized up to 1908 the results of the investigations on the legibility of small letters of the alphabet. The letters wmqpvjf he classed as most legible. Letters hrd g kb xl nu were classed as fair in legibility in comparison with the others; and the following letters were classed as poor: atizocse. TABLE I SUMMARY OF INVESTIGATIONS ON THE RELAtive Legibility Finzi (1900).. PUA QXTDS EWMVYZHCN FLRGBKOI Sanford (1888): The outcome of the studies on the relative legibility of the letters has been brought together in Table I to facilitate comparison. The most legible letters begin at the left of the table. From inspection it is seen that, with the exception of Finzi, there is considerable agreement in the results. In several instances a given letter occupies the identical rank in two or more investigations. In Sanford's two methods of procedure, e.g., v, y and j were found in the same rank. The letter m gained the same position by Sanford (distance) and Dockeray, and t and e the same by Sanford (short exposure) and Dockeray. Similar identical placements appear in comparing Cattell's results with those of the others. And where letters occupy different relative positions in the various studies, many of them are still in the same quartile. The amount of correspondence is best shown by correlating the different rankings with each other. This has been done by the rank-order nethod in Table II. Finzi's results do not TABLE II CORRESPONDENCE AMONG THE INVESTIGATIONS ON RELATIVE Legibility of LETTERS AS SHOWN BY RANK-ORDER CORRELATION correspond at all with Cattell's capitals. It is more than possible that he used a type or letter-form which prevents a reliable comparison with the other studies. The positions of Cattell's capitals show little correspondence with the positions of small letters in any of the experiments. The highest correlation coefficient here is only .38.12. This is to be expected because of the difference in form of capitals and small letters. The various placements of the small letters corresspond fairly well, the coefficients ranging from .57 .09 to .88.03. It is quite likely that these orders of legibility will not be materially altered by future investigations so long as the letter-forms remain about as at present. But there have also been studies so designed as to determine the relative legibility of the same letters or words when printed in different styles of type or when written by the hand. The effect of size, face, ornateness of type, as well as spacing, have been so studied. In an experiment to determine the influence of size and form on the legibility of letters, Griffing and Franz (17) found that it was always easier to read larger types than smaller; that, as the size of type decreased, the fatigue from reading rapidly increased; and that one could always read Gothic letters more easily than Roman. Roethlein (25) investigated the relative legibility of 26 different faces of printed types. The letters were presented singly and in groups. She came to the conclusion that legibility is a product of six factors; viz., the form and size of the letter, the heaviness of the letter-face (the thickness of the lines which constitute the letter), the width of the white margin which surrounds the letter, the position of the letter in the lettergroup, and the shape and size of adjacent letters. In working out a more legible form for a telephone directory, Baird (1) found that increasing the leading between lines by a small amount was was an important aid to legibility. Huey (18), Blackhurst (4), and Bentley (3) have also shown the importance of leading in the legibility of the printed page. After reviewing several studies, Gray (16) concludes: "(1) Legibility varies, to a greater or less extent, with style of type. The differences are much less when letters are presented in groups than when letters are presented in isolation. (2) Plain styles of type, such as Roman and Caslon, are much more legible than the more ornate styles of type, such as Old English and German type. (3) Handwritten and typewritten materials are less legible than material printed in plain type." Another factor in legibility enters when combinations of |