The same is then done for each of the succeeding points of a letter. By means now of the vertical measurements, the points on the speed curve which correspond to the points on the letter may be found. By means of the horizontal readings the corrections for the movement of the pencil out of the vertical line may be determined. Thus, after the letter itself has been gone over, the plate is set at the first vertical reading and the point found on the speed curve which is on the same horizontal line with this. This, of course, is the beginning of the curve. The horizontal reading of this point is then taken. The plate is then set at the second vertical reading and the corresponding point found on the speed curve. The horizontal reading of this point is taken and so on for the rest of the curve. Each successive horizontal reading is subtracted from the one following it, and the differences corrected by the amount of horizontal displacement found in measuring the letter. The length of a unit of time line is then measured and the horizontal differences of the speed curve divided by this unit. The typical series of measurements is shown in Table I.

on

TABLE I

Illustration of the readings and operations involved in measuring the speed of the first two divisions of a letter

In order to present the results of these measurements graphically a curve is drawn, the base of which represents the successive millimeter distances of the letter and the altitude the

10

corresponding times in thousandths of a second. Such a curve (of the letter "o") is shown in Figure 3. The interpretation of this curve indicates that the reactor took considerable time (105) to get started and to traverse the first section of the letter. The pencil then moved at an average rate of 1 mm. in 17 σ

FIGURE 3-Speed curve of letter "O."

until it came to the curve at the base of the letter. The section at this point took 530-three times as long as the average millimeter on the down stroke. The up stroke was still faster than the down stroke. The turning point at the top of the stroke was slow however, occupying 124 σ. The last outward stroke was rapid. This was the typical record of the speed changes of the movement during the writing of a letter.

The pressure curve from the letter "o" by the same reactor is shown in Figure 8, in the appendix. The pressure curves are to be read from right to left. This curve can be correlated with the speed curve by reversing the process used in measuring a letter. In that case we found the time represented by a given distance on the strip by dividing this distance by the distance for one tenth of one second. Now in order to find the distance on the pressure record which corresponds to the time of

a given section of the letter, the distance for one tenth of one second on the pressure record is multiplied by the fraction of a second which represents this time. We may thus determine the points on the pressure curve which correspond to the successive points of the written letter. In this way, in the present instance, the position on the pressure curve of three points was determined. These are the end of the first millimeter distance, the bottom turn of a letter and the top of the upstroke, corresponding to divisions 1, 6 and II of the letter.

From an inspection of the pressure curve it will be seen that the pressure increased during the first millimeter to almost its maximum amount. Upon the down stroke the pressure decreased. It increased again at the beginning of the upstroke but fell to the minimum about the middle of this stroke. It then steadily increased while the readjustment at the top of the stroke and the final outward stroke were being made, reaching its maximum on the latter. The drop at the end is abrupt.

The methods here used for analyzing writing movements may be briefly compared with those which have been previously used. The only other methods known to the writer by which a speed analysis of the writing movement may be made are those of the Edison pen used by Binet and Courtier (4), the spark method described by McAllister (12), and writing over contact lines described by Diehl (5) and Meumann (15). The present method possesses the advantages in comparison with that of Binet and Courtier, first, that the conditions are more normal (since the Edison pen weighs a quarter of a pound and contains machinery in rapid vibration); second, that it permits the measurement of the duration of a pause; and third, that it permits a more exact measurement of the more rapid parts of a letter. The advantages over the spark method are similar to those over the Edison pen with perhaps even greater emphasis on the first point. The defect of the system of contact lines is that the units of distance which are measured by it are not uniform. This criticism was made above.

The only method of analyzing the pressure curve with which the present method may be compared is that of Diehl and of

Meumann. The other methods of recording pressure, for example those of Goldscheider (8) and Kraepelin, furnish no means of determining the correspondence between the pressure and the parts of the letter. The correlation between the pressure curve and the written letter is in any case only as exact as the speed analysis of the letter. Since the latter, in the method of Diehl (5) and Meumann (5 and 15), is inaccurate the correlation of the pressure curve with the written letter is correspondingly inaccurate.

The reactors in the experiment consisted of four adults and ten children. Of the adults, three were graduate students, T. T. G., R. D. W., and F. N. F., and the fourth a college senior, D. H. Of the children, five were boys and five girls. The ages ranged from 9 to 15. C. K., 14 years, was in the second year in high school. H. H., 13 years, was in the first year in high school. M. G., 13 years, and G. B. 15 years, were in the eighth grade. O. B., 14 years, and E. C., 12 years, were in the sixth grade. C. N., II years, and A. S., II years, were in the low sixth. E. H., 10 years, was in the fourth, and M. H., 9 years, in the third grade. C. K., H. H., O. D., C. N., and A. S. were boys and M. G., G. B., E. C., E. H., and M. H. were girls. For the oppor'tunity of working with the children the writer is indebted to Mr. Harry Houston, Supervisor of Penmanship in the New Haven Schools, who arranged to have the children come to the laboratory and was present himself at several of the experimental periods.

There were first measured two and in some cases three specimens of each letter of the alphabet of the writing of a single reactor, F. N. F. This was done in order to determine the differences and relationships between the different letters of the alphabet and thus to avoid generalizations which might rest on a study of part of the letters. Means was thus furnished also of choosing letters for use with the other subjects which might represent different typical facts in regard to their writing. From each of the remaining subjects then, records of the writing of three or four letters were obtained. In the case of adults there was some variation in the particular letters used, but with the