_Series No. V._--The fifth series, which was suggested by the second, presents the problem of the lines in greater simplicity than the second; and, unlike the earlier series, it shows in all the individual averages the same sort of preponderance as is shown in the general average (straight line, 31; broken line, 38). The footings of the columns, moreover, show an aggregate in favor of the broken line in the case of every pair of lines that were exposed together. The results in this case may therefore be regarded as cleaner and more satisfactory than those reached before, and come nearer, one may say, to the expression of a general law. The theoretical interpretation, however, would be in both cases the same. [Illustration: FIG. 5.] TABLE V. 1 2 3 4 5 6 L A L A L A L A L A L A I. 28 26.5 24.5 29.5 25 28 26 28.5 26 29.5 25.5 29.5 II. 35 41.5 42 34.5 31.5 47.5 53 50.5 52 52 48 48 III. 16.5 19.5 24 29 41 29.5 35.5 29 21 40 39 40 IV. 40 41.5 37 45 32.5 45.5 36.5 43.5 33.5 38 36.5 43.5 V. 49 53 45 47 45.5 36.5 32.5 51 37 46 40 51 VI. 18 31.5 16 45 22.5 30.5 25 25 24.5 37 25 22 VII. 43 39.5 52 54.5 52.5 53.5 51 54.5 40.5 55 48 48.5 VIII. 23 23 27 29.5 38 40 34.5 32 23 37 42 38.5 IX. 23 48 48 47.5 35 46.5 48 35 28.5 48 46.5 34.5 X. 18 33 19.5 31.5 20.5 30 22 29.5 16.5 35.5 19.5 33 XI. 22.5 33.5 18 41 26 23 19 35.5 5 38 7 50.5 316 390.5 353 434 370 410.5 383 414 307.5 456 377 439 Averages. L A I. 25.83 28.58 II. 43.58 45.66 III. 29.50 31.16 IV. 36.00 42.83 V. 41.50 47.41 VI. 21.83 31.83 VII. 47.83 50.91 VIII. 31.25 33.33 IX. 38.16 43.25 X. 19.33 32.08 XI. 16.25 36.91 31.91 38.54 _L_: Line (straight line). _A_: Angle (broken line). General average: _L_, 31.91 sec.; _A_, 38.54 sec. TABLE VI.