APPENDIX A 247 



percentage by which the actual clearings depart from it. Thus the 

 bank clearings in 1873 were approximately 30 per cent above normal, 

 while those of 1906 were about 35 per cent above the normal for that 

 year. In other words, when the secular trend is eliminated we find 

 that a departure of about eight million dollars from the normal in 1873 

 was only a little less important than one of twenty-seven million in 

 1906. When the percentages for each year have thus been computed, 

 a curve can be drawn showing the cyclical variations without the secu- 

 lar trend. This is what has been done in this book. 



The normal curves showing the secular trend may be convex, straight 

 or concave. In Figure 27 the line for bank clearings is decidedly con- 

 cave, and that for pig iron is nearly straight, but both rise rapidly on 

 the right, since business in the United States increases at a constantly 

 accelerating pace. The curve for prices, on the other hand, is quite 

 different from* the others. On the left it descends rapidly, for from 

 1870 to 1890 prices fell because of improvements in manufacturing 

 processes, transportation facilities, etc. In the nineties, however, the 

 excessive production of gold began to lead to inflation of prices, so 

 that the later part of the curve rises. 



In plotting the normal curves mathematical accuracy is not possible. 

 Sudden changes in the direction of the smoothed lines must be avoided, 

 and too much weight must not be given to temporary fluctuations. 

 Thus personal judgment must play some part. When the work is 

 checked by averages, however, this is reduced to small proportions. 

 Moreover, a considerable deviation from the absolute position of the 

 true normal does not affect our conclusions. Suppose that the position 

 of the normal is too low by 5 per cent, which would be a large error. 

 Three successive years which actually departed from the normal by 

 30 per cent, 10 per cent, and — 10 per cent would appear to depart 

 by 36.8 per cent, 15.8 per cent, and —5.3 per cent. The difference 

 between the two extremes, however, that is, the intensity of this par- 

 ticular fluctuation, would be nearly the same, namely 40 per cent in 

 the first case, and 42.1 per cent in the second. On the other hand, 

 suppose that the secular trend were not eliminated, and that two 

 exactly similar series of years occurred thirty years apart so that the 

 normal in the second case was twice as great as in the first. The 



