Note Footnote 1: — Chapter VI

Until a concomitant variation has been fully explained, it is merely an empirical law, and any inference that it extends at the same rate beyond the limits of observation must be made with due caution. "Parallel variation," says Professor Bain, "is sometimes interrupted by critical points, as in the expansion of bodies by heat, which suffers a reverse near the point of cooling. Again, the energy of a solution does not always follow the strength; very dilute solutions occasionally exercise a specific power not possessed in any degree by stronger. So, in the animal body, food and stimulants operate proportionally up to a certain point, at which their further operation is checked by the peculiarities in the structure of the living organs.... We cannot always reason from a few steps in a series to the whole series, partly because of the occurrence of critical points, and partly from the development at the extremes of new and unsuspected powers. Sir John Herschel remarks that until very recently 'the formulæ empirically deduced for the elasticity of steam, those for the resistance of fluids, and on other similar subjects, have almost invariably failed to support the theoretical structures that have been erected upon them'."1