Various kinds of evidence converge toward this conclusion. Thus, the evidence of clearings, total items presented by banks to the clearing houses of the country. New York clearings are usually nearly twice as great as total clearings for the rest of the country. New York clearings fluctuate in general harmony with transactions on the New York Stock Exchange. This has been commented on many times. The extent to which it holds has recently been carefully measured by Mr. N. J. Silberling, whose results appear in the _Annalist_ for August 14, 1916, under the title, "The Mystery of Clearings." Mr. Silberling applies the "coefficient of correlation" to the problem, getting in one significant figure a measure of the extent to which two variables, as share sales on the New York Stock Exchange and New York clearings, vary together. This coefficient has been used enough by economists not to require detailed explanation here. It is a figure always between +1 and -1. +1 indicates that the two variables in question are perfectly correlated, whereas 0 indicates no correlation whatever. -1 indicates an inverse correlation, such that two variables vary exactly and inversely with reference to one another.[257] Mr. Silberling's studies show the following correlations: New York share sales (numbers of shares, not values) to New York clearings, using weekly figures, for the years 1909-10, r = .628. This is a high correlation. Limiting the observations to the middle weeks of the month for the same period, he gets r = .731(46). The reason for taking only middle weeks in the month is that thereby the disturbing factor of monthly settlements is avoided. The monthly settlements may be for stock transactions, or may be for other things, but as they are not dependent on the stock transactions _of the week_ in which they occur, their effect is to lessen the evident degree of connection between stock sales and clearings. Thus the middle weeks show a closer correlation between the two variables than do all the weeks taken as they come. If figures for the month were taken, this complication would be smoothed out, and a fairer result might be expected to appear. The middle weeks, eliminating monthly settlements, probably eliminate more other things than they do share sales (which are in large degree paid for in 24 hours[258]), and so exaggerate somewhat the relation between shares and clearings. Monthly figures avoid both complications, though they lose something of the concrete causation. An intermediate figure might be expected for the monthly correlation, and this we find: r = .718(23).