In the interval, ¼ P.E. to ½ P.E., there occurs a slight piling up of values which is compensated for by a greater lack in the succeeding interval, ½ P.E. to P.E. Apart from this, the correspondence between the calculated and the actual results is satisfactory. The symmetry of the distribution leaves something to be desired. The values below the average preponderate a little in number, those above preponderate a little in amount of deviation: only two of the largest eight deviations are below the mean value. The influence of attention referred to above, the fluctuations of which in the separate series show greater deviations toward the upper limit than toward the lower, has not, therefore, been quite compensated by the combination of several series.
The correctness of the observations and the correspondence of their distributions with the one theoretically demanded are greatly improved in the second large series of tests. The latter comprises the results of 84 series of tests taken during the years 1883-84. Each test consisted in memorising six series of 16 syllables each, carried on in each case to the first errorless reproduction. The whole time necessary for this amounted to 1,261 seconds with the probable error of observation of ± 48.4—i.e., half of all the 84 numbers fell within the limits 1,213-1,309. The exactness of the observations thus had greatly increased as compared with the former series of tests:[1]
The interval included by the probable error amounts to only 7½ per cent of the mean values as against 14 per cent in the earlier tests. In detail the numbers are distributed as follows:
- ↑ Of course, the exactness obtained here cannot stand comparison with physical measurements, but it can very well be compared with physiological ones, which would naturally be the first to be thought of in this connection. To the most exact of physiological measurements belong the last determinations of the speed of nervous transmission made by Helmholtz and Baxt. One record of these researches published as an illustration of their accuracy (Mon. Ber. d. Berl. Akad. 1870, S. 191) after proper calculation gives a mean value of 4.268 with the probable error of observation, 0.101. The interval it includes amounts, therefore, to 5 per cent of the mean value. All former determinations are much more inaccurate. In the case of the most accurate test-series of the first measurements made by Helmholtz, that interval amounts to about 50 per cent of the mean value (Arch. f. Anat. u. Physiol. 1850, S. 340). Even Physics, in the case of its pioneer investigations, has often been obliged to put up with a less degree of accuracy in its numerical results. In the case of his first determinations of the mechanical equivalent of heat Joule found the number 838, with a probable error of observation of 97. (Phil. Mag., 1843, p. 435 ff.)
