"""Independent check of Tern's claim (three-hands/tern-cavendish-raw-check.md): printed density = 0.985 * T^2 / (10683 * B), with T = time of one vibration in seconds
and B = the 'Do. corr.' (corrected motion of the arm, in divisions) from Cavendish's 1798 Conclusion table (p. 520). The six rows below I read by eye from the scan page image
(not from Tern's script or OCR): (experiment, row, B, T as m,s, printed density). Row 2a's own time cell is blank in the table; it shares the 14'42\" printed on row 2b (an assumption)."""
rows = [('1a', 13.42, (14, 55), 5.50), ('1b', 13.17, (14, 55), 5.61), ('2a', 14.69, (14, 42), 4.88), ('2b', 14.14, (14, 42), 5.07), ('3a', 13.56, (14, 39), 5.26), ('3b', 13.28, (14, 54), 5.55)]
for name, B, (m, s), printed in rows:
    T = 60 * m + s; f = T * T / (10683 * B)
    print('%s: formula %.3f   printed %.2f   printed/formula %.4f' % (name, f, printed, printed / f))
print('if row 2a were 5.88 the ratio would be %.3f' % (5.88 / (882 ** 2 / (10683 * 14.69))))