To find the mean error of the series a slightly different method is necessary.
Place the tracing-point of the planimeter at c and read vernier, giving 1916; follow the dotted path from c to h, the straight line from h to i, the dotted path from i to k, the straight line from k to l, the dotted path from l to m, the straight lines from m to n and n to g, the dotted path from g to m, the straight line from m to l, the dotted path from l to k, the straight line from k to i, the dotted path from i to n, and the straight line from h to c, when a second reading is taken, which was in this case, 1806. Divide the difference of these two readings, 1100 mm., by the length of cd, 119 mm., and the result is 9.1 mm., or the mean error (mean variation).
It will be noted that this method gives the sum of the errors from the mean line cd; that is, the same result would be obtained if the tracing-point were (1) carried from c around all the area below cd, and this area were calculated as before; (2) carried from c around all the area above cd and the area measured as in other cases; and (3) these two results added and averaged.
To apply the method for ab, or constant error computation, to cd should give equal readings at c or a 0 mean error, a result evidently incorrect in the record selected.
After averaging results by the planimeter, the collection of data has been arranged by months; the record for one month only can be presented here, but the method of tabulation is the same throughout.
Each figure given for N, M, c and v, in the accompanying typical table for the month of May, 1904 (pages 495-499), is the average from 20 or 50 lines, ruled as already shown, Fig. D.
RESULTS
It is necessary to observe that the limits of space imposed on the writer preclude all but the barest outline of the deductions to be drawn from the investigation, and to this fact is due whatever of dogmatism is inherent in the argument; for it is manifestly impossible to present all the material, and the writer asks, then, the indulgence of the reader when he claims to have impartially examined and presented the evidence.
HAND MOVEMENTS
Simple movements
Lines 14 cm. long.