Interval.     I    II    III   IV     V
B.               83.3  76.9  69.2  (100)  Irrespective
A.         85.7  91.6  91.6  84.6  (100)   of extent. 
B.               73.3  71.9  53.8   (60)    Estimated
A.         85.7  91.6  91.6  84.6  (100)  quantitatively.

Next, the relation of the amount of increase in intensity introduced at a single position in such a series to the amount of error thereby occasioned in the apprehension of the adjacent intervals was taken up.  Two sets of experiments were carried out, in each of which five of the sounds were of equal intensity, while one, occurring in the midst of the series, was louder; but in one of the sets this louder sound was occasioned by a fall of the hammer through a distance of 0.875 inch, while in the other the distance traversed was 2.00 inches.  In both cases the extent of fall in the remaining hammers was uniformly 0.25 inch.  The results are given in the following table: 

TABLE XXXI.

                     Interval B.¹ Interval A.
  Ratio of Interval 0.875 in. 2.00 in. 0.875 in. 2.00 in. 
  B to Interval A. + = — + = — + = — + = —
  1.000 :  1.000 0 6 0 0 4 2 0 5 1 0 0 6
  0.909 :  1.000 2 4 0 0 4 2 0 2 4 2 2 2
  0.833 :  1.000 0 6 0 0 4 2 4 0 2 1 3 2
  0.770 :  1.000 0 6 0 2 2 2 2 4 0 4 0 2
  0.714 :  1.000 0 6 0 1 5 0 6 0 0 2 2 2
  Totals, 2 28 3 19 8 12 11 7 9 7 14
  T.E., T.J., 2 30 11 30 13 30 21 30
  and per cent., 6.6% 36.6% 60.0% 70.0%

   ¹Interval B in these experiments is of the same duration as all
   others but that following the louder sound; hence, judgments in
   the second column are correct.

Again the markedly greater influence of increased intensity on the interval following than on that preceding it appears, the percentage of errors being, for B (both intensities), 21.6 per cent.; for A, 56.6 per cent.  Also, in these latter experiments the direction of error is more definite in the case of interval A than in that of interval B.

The influence of changes in intensity on the amount of error produced is striking.  Two intensities only were used for comparison, but the results of subsequent work in various other aspects of the general investigation show that this correlation holds for all ranges of intensities tested, and that the amount of underestimation of the interval following a louder sound introduced into an otherwise uniform series is a function of the excess of the former over the latter.  The law holds, but not with equal rigor, of the interval preceding the louder sound.  So far as these records go, the influence of such an increase of intensity is more marked in the case of interval B than in that of interval A. It is to be noted, however, that the absolute percentage of errors