While general averages could not _prove_ the contention of a constant ratio between reserves and deposits for individual banks, general averages can _disprove_ the contention. A constant general average would be consistent with wide variation in individual practices, on the principle of the "inertia of large numbers." But if the general average is _inconstant_, it is impossible that the individual factors making it up should be constant. This disproof is readily at hand, both for the ratio of deposits to reserves in the United States, and for the ratio of demand obligations to reserves among European banks (most of which do not make large use of the check and deposit system).
For the United States, from 1890 to 1911, taking yearly averages, we have a variation in the ratio of reserves to deposits of over 73% of the minimum ratio. The ratio was 26% in 1894, and 15% in 1906. "The juxtaposition of these extreme variations shows how inaccurate is the assumption that the deposit currency may be treated as a substantially constant multiple of the quantity of money in banks."[167] For New York City, the annual average percentage of reserves of Clearing House banks to net deposits varies from 24.89% in 1907 to 37.59% in 1894.[168] The extreme variations[169] in weekly averages are (for the sixteen years, 1885-1900) 20.6% in August, 1893 and 45.2% in February, 1894. These figures are extreme, since the number of occurrences is small for them, but there are numerous occurrences of deviations from the mean as wide apart as 24% and 42%.[170] The yearly fluctuation in all these ratios is very great.
The ratio of money held by the banks and money held by the people also shows wide variation, and considerable yearly fluctuation. There is a further complication, for the United States, of varying proportions of the total monetary stock held by the Federal Treasury. As between the banks and the public, the banks held about a third in 1893 (average for the year), and nearly half in 1911.[171] Whatever may be the relations between money in the hands of the people, money in banks, and volume of deposits, in "the static state," there is no statistical evidence whatever to justify the notion of fixed relations among them in real life.[172] We shall later show that there can be no static laws whatever governing the relations of credit and reserves.[173]