DISTRIBUTION OF COLLEGE CREDITS 397 



mate answer to this question will be the discovery of units of measure- 

 ment in every school subject, and the construction, by scientific 

 methods, of scales that can be applied as the foot-rule is now applied, 

 regardless of time, or place or persons. The best possible ratings of 

 individuals by relative position are only temporary eipedients that must 

 some day give way to ratings by means of standard scales. The nearest 

 approach to such a scale, and a perfect illustration of the method, is E. 

 L. Thorndike's " Handwriting," Teachers College Record, March, 1910. 

 The Courtis Standard Tests in Arithmetic also furnish a means of 

 comparing the achievement of one school with that of another, and the 

 work of one year with that of another. We are not likely to continue 

 to spend bQlions of dollars on education and be satisfied with guessing 

 at results. Measurements of results with quantitative precision will be 

 made as soon as people know enough to demand such measurements. 



Lacking the necessary units and scales, we may even now ask 

 whether the differences among individuals in mental capacities are 

 explainable by any simple causes and amenable to any single type of 

 description. They are not, if we are to accept the tables and figures 

 just presented as correct records of the abilities of college students. 

 But fortunately we are not dependent on such unscientific data. Psy- 

 chologists have recently given us many rigorously scientific studies of 

 the distribution of mental traits. 



These studies have shown that in any group of individuals repre- 

 senting a single species, the distribution of any trait not greatly influ- 

 enced by natural selection appears to be that of a chance event. The 

 surface of frequency for that trait approaches that of the probability 

 integral. It is like the cross-section of a pile of sand dumped from a 

 cart. The most convenient way to represent tables of frequencies is by 

 means of diagrams in which distances along a base line represent the 

 different quantities, or units of measurement, and the heights of col- 

 umns erected upon it represent the frequencies of the several quantities. 

 Fig. 9 presents several illustrations, D representing the results of a 

 memory test. By such graphic representations rather that algebraic 

 formulae, the answer to our question and the evidence for it can be made 

 clear even to one unfamiliar with the mathematical properties of the 

 surface of frequency of a chance event. 



Fig. 9, A, gives the distribution, or surface of frequency, of the type 

 to which we assume that all distributions of mental traits conform. 

 Fig. B is the same type of distribution with a coarser separation into 

 grades. This type is called the normal surface of frequency. It de- 

 scribes, for example, the distribution of accidental errors in scientific 

 observation. Thorndike's numerous measurements show a remarkable 

 uniformity in the distribution of mental traits among individuals. Fig. 

 9, D, showing the memory span for digits in 123 American women stu- 



